Efficient Exploration

Traditionally, decision support studies how humans use machine learning models to make better decisions. In modern agentic systems, this division of roles is increasingly reversed: AI agents act on behalf of users, while humans and tools becomes support mechanisms around them. This role reversal brings reliability concerns to the forefront, since agentic errors can be consequential and agent behavior must remain aligned with human goals and constraints. Departing from the classical view of decision support, we revisit its two basic principles, the cost--value tradeoff of seeking support and the role of uncertainty quantification, in a setting where AI agents are the central actors. We propose a framework for strategic decision support for AI agents through an optimization problem that minimizes support usage subject to controlling a counterfactual missed-support error: the probability that the agent acts alone on instances where support would have materially improved its output. At the population level, we show that the optimal policy is a threshold rule on the value of support. Building on this structure, we develop an online algorithm that adaptively thresholds such a score and uses randomized exploration to control missed-support error without distributional assumptions. We further introduce a calibration-on-the-fly method that reduces unnecessary support calls online. We instantiate this framework across diverse scenarios, including information gathering, human--AI collaboration, and tool use, showing how each can be modeled through the same strategic decision-support lens. Experiments across these settings show that our method reliably controls the target error while substantially reducing support usage in practice.

Reactive motion generation in unstructured environments remains an open challenge in robotics. Due to the computational complexity of collision-free motion generation, existing methods either generate global trajectories for static scenarios, or employ models that make conservative assumptions about the environment. This paper identifies the primary bottleneck as the runtime performance demand of planning on high-fidelity environments, and the temporal integration between the perception and planning modules. Therefore, we propose a framework that does not compromise on runtime performance and world representations for perception and planning by accelerating world modeling and vector-field based planning using the GPU. This allows us to achieve faster parallel state exploration for quasi-global trajectory planning, and tighter coupling of the perception-action loop in real-time for dynamic cluttered environments with off-the-shelf depth sensors. We quantitatively evaluate the computation-time and success rate differences for the CPU and GPU versions of our planner, and perform qualitative evaluations of our coupled framework using real-world experiments on a 7-DoF Franka Emika robot. Experimental results demonstrate that our GPU-based framework achieves up to a 5x speedup over the CPU version and successfully avoids collisions across both trivial and challenging physical world scenarios.

Planning under uncertainty requires agents to balance goal achievement with information gathering. Active inference addresses this through the Expected Free Energy (EFE), a cost function that unifies instrumental and epistemic objectives. However, existing EFE-based methods typically employ specialized optimization procedures that are difficult to extend or analyze. In this paper, we show that EFE-based planning can be formulated as Variational Free Energy minimization on a generative model augmented with epistemic priors. Our main result demonstrates that minimizing a Variational Free Energy functional with appropriately chosen priors yields a decomposition into expected plan costs (the EFE) plus a complexity term. This formulation reinforces theoretical consistency with the Free Energy Principle by casting planning as the same inferential process that governs perception and learning. We validate our approach on three environments of increasing complexity: a deterministic T-maze, a stochastic Reactivity Maze, and a partially observable MiniGrid DoorKey-8x8 environment. The experiments demonstrate that the epistemic priors induce information-seeking behavior, that the variational formulation yields policy-based inference outperforming plan-based methods under stochastic transitions, and that temporal factorization enables scalability to environments where existing tabular active inference methods cannot operate.

Classical theories of cognition describe problem solving as exploratory search through structured problem spaces in which repeated interaction gradually compresses search into efficient representational structures. Predictive artificial intelligence systems introduce a distinct regime in which stabilization may occur before exploratory diversification unfolds, supplying solutions and decision trajectories prior to internally generated search. This paper develops a geometric dynamical framework in which attention evolves over a landscape of strategies shaped by stabilizing drift, endogenous exploratory perturbation, and responsiveness-gated learning. Predictive assistance is modeled as a process of exogenous exploratory compression that stabilizes trajectories before self-generated exploration broadens the accessible regions of strategy space. The framework yields three main results. First, sustained predictive stabilization reduces exploratory responsiveness by attenuating the effective influence of intrinsic perturbations even when exploratory variability remains present. Second, curvature accumulates and relaxes asymmetrically, producing hysteresis and delayed recovery of exploratory mobility after assistance withdrawal. Third, developmental outcomes depend critically on the timing of stabilization, with early intervention narrowing future exploratory traversal before broad representational diversification has occurred. The framework generates empirically testable predictions concerning exploratory entropy, premature convergence, and delayed recovery following predictive stabilization. More broadly, the results suggest that predictive systems may reshape the geometry of exploratory cognition itself.

Contextual queueing bandits provide a framework for learning to schedule heterogeneous jobs under unknown context-dependent service rates. Under stochastic contexts, existing algorithms achieve $\widetilde{\mathcal{O}}(T^{-1/4})$ queue length regret, defined as the expected difference between the learner's and oracle's queue lengths at horizon $T$. In this paper, we improve this rate to $\widetilde{\mathcal{O}}(T^{-1/2})$. The key observation is that random exploration is needed only up to a carefully chosen cutoff round, rather than throughout the entire horizon. We propose CQB-$η$-2, a three-phase algorithm: (i) pure random exploration to construct an initial estimator, (ii) $η$-random exploration combined with a UCB rule to continue learning while maintaining negative drift, and (iii) pure UCB after the exploration cutoff. Our proof decomposes the queue length regret at the cutoff round. Before the cutoff, negative drift suppresses queue length differences caused by suboptimal choices. After the cutoff, the first two phases provide sufficient random exploration samples, ensuring that UCB decisions incur small departure-rate gaps. Combining these two bounds yields queue length regret of order $\widetilde{\mathcal{O}}(T^{-1/2})$. We further prove a minimax lower bound of order $Ω(T^{-1/2})$. The proof constructs two hard instances that are statistically indistinguishable up to the final service decision, and uses a queue-specific coupling argument to convert the resulting testing error into queue length regret. Together, our upper and lower bounds characterize the minimax dependence on the horizon $T$ up to logarithmic factors.

Retry-based objectives such as pass@K and max@K optimize the best return obtained from multiple sampled trajectories, and recent work has shown that they can promote exploration without explicit exploration bonuses. In discrete action spaces, ReMax was shown to do so by adapting to return uncertainty. In this work, we introduce pathwise derivative estimators for retry objectives and use them to extend ReMax to continuous action spaces. We study the resulting learning dynamics and show that, even with deterministic rewards, ReMax can encourage stochastic exploration by reshaping the policy-gradient landscape. In particular, it alters gradients both in direction, biasing updates toward higher policy entropy, and in magnitude, damping gradients and slowing convergence. We further show that Adam's adaptive normalization can mitigate this damping, depending on its numerical stabilization parameter. Empirically, we instantiate this objective as ReMax Actor-Critic (ReMAC), an off-policy actor--critic algorithm that optimizes the ReMax objective using a pathwise derivative estimator. Our experiments show that ReMAC can promote higher policy entropy without entropy regularization and achieves performance comparable to SAC.

Active inference casts decision-making as inference, with the Expected Free Energy (EFE) unifying goal-directed and information-seeking behavior. Recent work showed that EFE minimization can be written as Variational Free Energy (VFE) minimization on a generative model augmented with epistemic priors. We prove that the VFE of the augmented model can be rewritten as the VFE of the predictive model plus explicit entropy-correction terms, making the EFE contribution transparent. We then show that proper EFE-based planning requires combining these epistemic corrections with a planning correction that turns marginal inference into policy optimization, yielding a full variational characterization of EFE-based planning. This clarifies which corrections are needed for cross-entropy planning and for full EFE-based planning. The same entropy-corrected formulation leads to a detailed message-passing scheme for EFE-based planning together with simpler ablations. Experiments on three grid-world environments show that full EFE-based planning outperforms ablations that omit either the planning correction or the epistemic corrections.

As neural networks are increasingly deployed in safety-critical domains, testing is essential to evaluate and improve their reliability. Existing testing methods, whether black-box or white-box, primarily use global mutation or coverage-guided strategies, both of which struggle to efficiently uncover diverse model failures while remaining proximate to the original data distribution and semantics. We propose BayesWarp, a testing framework that addresses this limitation by mutating decision-critical input regions identified via interpretable saliency techniques and adaptively guiding the testing process using an uncertainty-aware Bayesian Optimization strategy, enabling the discovery of diverse failures while preserving distributional and semantic proximity to the original data. Evaluation on MNIST, CIFAR-10, and ImageNet across six neural network models shows that BayesWarp improves failure discovery, failure diversity, test case quality, and critical neuron coverage under a fixed mutation budget. These results demonstrate that BayesWarp improves testing effectiveness. Moreover, fine-tuning with the generated failure cases leads to improvements in model performance.

Physical systems do not merely add noise to search processes; they impose constraints that generate structured correlations. We propose a principle of constraint-enhanced physical search in which temporal correlations in exploration are matched to constraint-induced spatial correlations in the update dynamics. Using a minimal tug-of-war bandit model (TOW), we show that a conservation law converts local observations into differential evidence across alternatives, while a temporally correlated drive controls the order of exploration. Search efficiency is improved not by stronger randomness or by maximal anti-correlation, but by matching the temporal correlation to the physical update scale that converts feedback into evidence. A scaling estimate identifies the update-noise-to-contrast ratio as the leading parameter that limits how strongly temporal anti-correlation can be used. The results suggest a general organizing principle for physical search: constraints and fluctuations can generate structured spatiotemporal correlations, and efficient exploration emerges when these correlations are matched to the update dynamics.

Large Reasoning Models (LRMs) have achieved remarkable progress thanks to Reinforcement Learning with Verifiable Rewards (RLVR) on Chain-of-Thoughts (CoTs). However, since long CoTs naturally contain trial and errors and mainstream RLVR approaches choose outcome-correct CoT trajectories for memorization, the redundant explorations in long CoTs are inevitably reinforced, which results in the over-thinking issues of LRMs. Previous attempts to resolve this issue mainly give more advantage to shorter trajectories, yet their learning signals are still outcome-based and cannot reduce the memorization of redundant explorations in long CoTs. Therefore, we propose ThoughtFold, a framework that leverages fine-grained preference learning to mitigate redundant explorations for efficient reasoning. ThoughtFold employs an introspective strategy to identify redundancy within each correct trajectory, which yields a spectrum of candidate sub-trajectories. Leveraging this spectrum, we introduce a masked preference optimization objective that explicitly penalizes redundant explorations and encourages the model to directly bridge essential reasoning segments, effectively folding its reasoning chains into a more concise path. Extensive experiments show that ThoughtFold significantly enhances efficiency. It reduces the token usage of DeepSeek-R1-Distill-Qwen-7B by approximately 56% while maintaining state-of-the-art accuracy.

Instance Goal Navigation (IGN) requires an embodied agent to find a specific object instance among distractors from an under-specified natural-language description. Such ambiguity often cannot be resolved from perception and language alone, making interaction with an oracle a natural mechanism for disambiguation. Prior interactive methods allow oracle queries but treat lightweight clarification and route-level guidance alike, letting agents boost success rate through repeated high-information questions rather than by resolving the underlying ambiguity efficiently. We recast interactive IGN as a cost-sensitive uncertainty-reduction problem, where the agent should ask the question whose answer provides the largest reduction in navigation uncertainty relative to its penalty. To this end, we apply an information-gain analysis on existing navigation corpora to identify which cues reduce navigation uncertainty, yielding a compact set of question types and data-derived weights. However, existing interactive navigation benchmarks do not model the cost of different question types or evaluate how efficiently agents use interaction, making them unsuitable for studying cost-sensitive interaction. Based on this taxonomy, we construct a benchmark for diagnosing interaction behavior and efficiency, together with a Weighted Success Rate metric that penalizes each query by its derived cost. We further propose a zero-shot MLLM navigator that selectively queries at each decision step only when the expected uncertainty reduction justifies the interaction cost.

As reinforcement learning (RL) increasingly applies to sensitive domains, such as health care and recommendation systems, privacy-preserving techniques have become essential to protect users' sensitive information. We investigate privacy-preserving RL under an episodic setting, focusing on algorithms based on randomized exploration, such as Randomized Least Squares Value Iteration (RLSVI). The overall goal is to study how randomized exploration interacts with the injected noise required by privacy mechanisms. In this work, we show a new privacy analysis that characterizes how the noise in RLSVI set for exploration simultaneously provides privacy protection. Specifically, we prove that RLSVI is $(\varepsilon(δ),δ)$-joint differentially private in tabular MDP as is with $\varepsilon(δ) = \frac{2AK}{H^2\log(2HSA)} + 2\sqrt{\frac{2AK\log(1/δ)}{H^2\log(2HSA)}}$, where $S$ and $A$ are the number of states and actions respectively, $H$ is the length of an episode and $K$ is the number of episodes.

In open-ended environments, exploration is fundamental for autonomous agents, yet current language model agents struggle with this. Effective exploration requires memory, but retaining raw interaction histories is computationally expensive over long trajectories. While latent memory offers a solution to compress interaction histories, its training lacks reliable supervisory signals. We introduce \textbf{J}oint \textbf{A}gent \textbf{M}emory and \textbf{E}xploration \textbf{L}earning (\textbf{JAMEL}), a framework that trains agentic memory and exploration policy together through novelty-driven interaction. We observe that memory and exploration form a mutually dependent loop: sustained exploration requires memory to distinguish exhausted behaviors from unseen ones, while novelty-seeking interaction provides the supervision needed to make memory useful for future exploration. By utilizing deterministic and persistent novelty signals such as code coverage in the GUI domain, we provide natural, annotation-free supervision for the memory module. Empirical evaluations demonstrate that \ours successfully generalizes to unseen environments. Its exploration capability outperforms open-weight baselines and rivals the exploration depth of a closed-source model while reducing token consumption. Our code and model are open-sourced at https://github.com/MobileLLM/JAMEL.

Preference alignment is central to improving large language models, but standard reward-based formulations can be restrictive when human preferences are cyclic, non-transitive, or otherwise not representable by a scalar reward. Nash Learning from Human Feedback (NLHF) addresses this limitation by modeling alignment as a preference game and targeting a Nash equilibrium rather than a reward maximizer. However, the learning-theoretic foundations of scalable NLHF remain limited. Existing regret guarantees rely on oracle-based methods that estimate a general preference model and solve KL-regularized minimax problems, while iterative NLHF methods directly optimize policy-level preference losses and are easier to implement but lack regret guarantees. We study online iterative NLHF under general preference models and identify exploration as the key obstacle. First, we show that standard iterative NLHF can suffer an exponential dependence on the KL-regularization parameter, revealing that implicit exploration through policy updates is insufficient for controlling regret. Second, we propose an explicitly exploratory iterative NLHF algorithm that combines SFT-based regularization with adversarial policy exploration. The resulting method retains the direct policy optimization structure of iterative NLHF, avoids explicit preference model estimation, and achieves an $O(\sqrt{T})$ regret bound without an exponential dependence on the KL-regularization parameter. We show that the regret can be improved to $O(\log(T))$ with access to a minimax oracle, clarifying the computational-statistical tradeoff in learning general preference games. Finally, we instantiate our method for LLM fine-tuning and evaluate it on \texttt{Llama-3-8B-Instruct} across multiple benchmarks, where explicit exploration yields consistent improvements over existing NLHF baselines.

Multi-arm bandit algorithms are increasingly used in online platforms, clinical trials, and social science experiments, but valid statistical inference on their performance remains an open challenge. After deploying bandits, a natural question is whether one can construct a confidence interval for its mean reward and assess whether it reliably outperforms a baseline policy. The total reward achieved in any single bandit deployment is random, and deploying a bandit twice on the same population typically yields different reward trajectories due to stochastic rewards. Standard statistical inference methods cannot be used because bandit algorithms introduce complex dependencies in the collected data, which violate the i.i.d. assumption underlying many classical approaches. Moreover, existing inference methods for adaptively collected data only apply to estimands that do not depend on the data-collection algorithm (such as the mean reward under a fixed action). We propose Bandit Simulation for Inference (BSI), a framework that fits a simulator of the bandit environment from observed data--either on-policy or off-policy--and uses it to estimate the mean reward under any evaluation policy, including adaptive blackbox algorithms. BSI formally propagates uncertainty in the estimated simulator parameters into the confidence interval construction. Furthermore, for BSI to be valid, it requires only weak exploration assumptions on the behavior policy and avoids importance weighting. We prove that BSI yields asymptotically valid confidence intervals, and demonstrate empirically that it maintains nominal coverage in settings where standard off-policy evaluation methods fail.

Recent advances in Multimodal Large Language Models (MLLMs) have led to promising progress in web agents. However, existing web agents often rely on handcrafted execution pipelines or expensive expert trajectories, limiting their adaptability to complex, dynamic environments. To address these challenges, we propose SCALE (Self-Cognitive-Aware Learning and Exploration), which leverages three adversarial roles, Selector, Predictor, and Judger to autonomously discover the agent's limitations and expand its cognitive boundaries through environmental exploration. Moreover, we propose SCALE-Hop, a graph exploration strategy that facilitates global planning and helps agents avoid local exploration traps. To further support learning, we construct SCALE-20k, a large-scale dataset collected from 19 real-world websites, containing diverse task types and structured demonstrations generated from SCALE's exploration traces. Experimental results show that our approach significantly improves the performance and generalization of multiple MLLMs in various web environments. Our framework offers a scalable and generalizable solution for building truly autonomous and adaptive web agents.

In reinforcement learning (RL), agents benefit from exploration only because they repeatedly encounter similar states: trying different actions can improve performance or reduce uncertainty; without such retries, a greedy policy is optimal. We formalize this intuition with ReMax, an objective that evaluates a policy by the expected maximum return over $M$ samples, where $M$ is a positive integer, while accounting for return uncertainty. Optimizing this objective induces stochastic exploration as an emergent property, without explicit bonus terms. For efficient policy optimization, we derive a new policy-gradient formulation for ReMax and introduce ReMax PPO (RePPO), a PPO variant that optimizes ReMax while generalizing the discrete retry count $M$ to a continuous parameter $m > 0$, enabling fine-grained control of exploration. Empirically, RePPO promotes exploration, without any explicit exploration bonuses, on the MinAtar and Craftax benchmarks.

Exploration in reinforcement learning for autonomous driving is inherently unsafe: agents must experience novel behaviors to learn, yet exploration can lead to collisions or off-road driving. We propose an uncertainty-aware framework that leverages expert advice to guide exploration while avoiding long-term dependence. Advice is triggered when epistemic or aleatoric uncertainty exceeds adaptive thresholds derived from rolling buffers, ensuring advice evolves with the agent's confidence. A commitment-cooldown strategy with a stochastic early-stop heuristic regulates the duration and frequency of guidance, exposing the agent to coherent maneuvers without exhausting the advice budget. Expert and agent experiences are combined in a shared replay buffer within an off-policy implicit quantile network (IQN) backbone, enabling efficient reuse of expert trajectories. Experiments in CARLA show that our method outperforms the IQN baseline, improving success by 5-7% and reducing failures, demonstrating that risk-sensitive uncertainty coupled with regulated expert integration enables safer and more efficient exploration for sensor-based RL policy learning in unsignalized intersection navigation.

Recent advances in mobile GUI agents have shown strong potential for automating mobile tasks, but most effective systems still depend on large vision-language models for screenshot understanding and long-horizon planning. Small GUI agents that can be deployed directly on mobile devices are more attractive for practical use, offering lower inference cost and better protection of sensitive on-device information. However, due to limited model capacity, such lightweight agents remain unreliable when planning and executing GUI tasks end-to-end from screenshots alone. We propose Knowledge-Oriented Behavior Exploration (\textbf{UI-KOBE}), a framework that improves lightweight mobile GUI agents with reusable app-specific graph knowledge. UI-KOBE first autonomously explores a mobile application and constructs an app knowledge graph, where nodes represent distinct UI states and edges represent executable transitions. At runtime, a lightweight GUI agent uses the graph as external guidance: given a user task and the current screenshot, it identifies the current graph node and selects among self-loop actions, neighboring transitions, task completion, or fallback free actions associated with that node. By supporting runtime decisions with app-specific graph guidance, UI-KOBE reduces the burden of end-to-end GUI planning and helps lightweight models perform mobile GUI tasks more effectively, offering a practical step toward efficient, interpretable, and privacy-conscious on-device GUI agents.

Multi-agent systems (MAS) have substantially advanced autonomous software engineering (SWE), but their growing inference energy demands raise sustainability concerns. In this paper, we demonstrate that this cost is concentrated in an overlooked source: redundant output tokens generated across agents. Two empirical findings ground this claim. First, our per-token energy attribution for MAS reveals a sharp asymmetry: an output token consumes 30 to 1,000 times more energy than an input or cached token. Second, MAS inflate per-episode output because agents repeatedly re-explore overlapping repository regions. To address this inefficiency, we propose Librarian, a persistent search sub-agent that tracks repository-search history and suppresses redundant exploration actions across agents. By returning short references to file regions instead of full file excerpts, Librarian further reduces output-token volume. On SWE-Bench Verified and SWE-Bench-Live, Librarian reduces per-episode GPU energy consumption of existing multi-agent SWE systems by 11 to 30% while preserving task performance. Our code is available at https://github.com/ml-postech/Librarian.

We systematically investigate all 25 public ARC-AGI-3 games and find that every one is reachable through non-intelligent strategies: 10 in a single blind step, 5 after one probing action, 1 via repeated ACTION1 presses, 1 via diverse exploration, and 8 via single repeated actions with sufficient budget (50-200 steps). A library-level null-coordinate vulnerability additionally bypasses 18 games in 1 step. This benchmark critique implies the public evaluation set cannot discriminate intelligent exploration from trivial heuristics - the private 55-game evaluation is the only genuine intelligence test. Against this backdrop, we present AERA (Adaptive Epistemic Reasoning Agent), a three-phase (EXPLORE / VERIFY / PLAN) agent achieving RHAE=0.2116 (4/25 solved) on these 25 games with Qwen2.5-0.5B, while random and no-explore baselines score 0.0000. We formalise AERA through a Speed--Depth trade-off framework: under a convexity assumption (proved for a class of environments in the Appendix), RHAE's quadratic form emerges as a second-order penalty for deviating from the Pareto frontier between action efficiency and information gain. Contributions: (i) a benchmark validity analysis showing that current interactive reasoning benchmarks fail to measure the exploration they claim to require, and (ii) the EXPLORE-before-PLAN framework and model-capability x exploration interaction. The linked code track entry achieves RHAE=0.30 on the full 55-game private evaluation. Code: CC0.

We study a stochastic multi-armed bandit problem where an agent is granted a free exploration budget before regret accumulates, a setting not captured by the classic regret minimization or pure exploration paradigms. The goal is to design an adaptive policy that strategically explores the bandit instance in the initial free exploration phase and minimizes the cumulative regret in the subsequent phase. We formalize this regret minimization with free exploration problem and identify an interesting regime where the free exploration budget scales logarithmically with the time horizon. To quantify the amount of regret saved with high probability as a result of the availability of the free exploration phase, we introduce a novel set of policies known as $(α,β)$-probably saving policies. We propose a two-phase, probably saving algorithm, UFE-KLUCB-H, which consists of a principled free exploration policy, UFE, and a history-aware regret minimization policy KLUCB-H. Instance-dependent upper bounds on UFE-KLUCB-H are derived, showing that UFE-KLUCB-H accumulates strictly less regret than policies that do not have access to a free exploration phase. Complementarily, we derive instance-dependent lower bounds based on novel multi-instance perturbation arguments tailored to the free-exploration setting, demonstrating the near-optimality of UFE-KLUCB-H for two-valued bandits. Our upper and lower bounds reveal sharp phase transitions in the accumulated regret depending on the amount of available free exploration. Simulations are conducted to demonstrate that forced exploration and adaptivity in the algorithm lead to greater regret savings.

Robotic systems with redundant degrees of freedom can achieve the same task outcome using multiple configurations, resulting in solution sets that form manifolds in the configuration space. Existing approaches typically exploit such redundancy locally through Jacobian-based techniques to compute individual solutions or trajectories. While effective for solution computation, these methods do not retain a representation of the geometry of the solution set itself. In this work, we adopt a representation-centric approach to estimate the geometric structure of the solution space. We consider solution manifolds induced by general task-defining maps and construct an implicit scalar field over the configuration space, whose zero-level set corresponds to the solution manifold. To this end, we generate samples in the neighborhood of the solution manifold using a Jacobian-guided exploration strategy, which efficiently captures its local and global structure. The resulting implicit representation is defined over the configuration space and naturally induces a continuous, distance field that encodes proximity to the solution manifold. Experiments on a planar three-link robot and a seven-degree-of-freedom Franka manipulator demonstrate the effectiveness of the proposed representation. Furthermore, the framework enables consistent modeling of solution spaces across families of tasks with continuous variation.

Recent work on recursive architectures has shown that tiny neural networks can be surprisingly powerful on structured reasoning tasks. The trick is to model reasoning trajectories with a latent dynamical system. We argue that the inference-time behaviour of these architectures is best understood as approximate inference over latent reasoning trajectories, with deterministic recursion as the one-particle, zero-noise limit. We make this view operational through guided stochastic exploration: stochastic perturbations of the reasoning dynamics propose neighbouring trajectories, and the model's existing early-stopping head reweights them online. The framework yields three label-free diagnostics: local stability, guide alignment, and cloud-token entropy. These predict, from inference traces alone, whether the procedure will help and which of its outputs to trust. On Sudoku-Extreme it lifts exact-solve accuracy from $85.9\%$ to $98.0\%$ without retraining; on Maze-Hard the diagnostics flag a misaligned guide, as validation performance later confirms. The same machinery thus characterises both when recursive reasoning has room to improve at the trajectory level and when the model's internal guide can recover it.

Scaling test-time compute has proven highly effective for language models, yet this opportunity remains largely unexplored for industrial Click-Through Rate (CTR) prediction. CTR models suffer from a fundamental asymmetry: feature combinations well-represented in training yield confident predictions, while sparsely observed ones produce unreliable outputs. Existing training-phase solutions such as adaptive gating learn a fixed selection function subject to the same sparsity, offering no per-instance recourse at deployment.We propose UTTSI (Uncertainty-Triggered Test-Time Selective Inference), a training-free model-agnostic framework that scales inference depth proportionally to per-instance uncertainty. A dual-signal estimator combining model logit confidence with a data-level frequency prior distinguishes epistemic uncertainty from aleatoric ambiguity. Every instance undergoes adaptive feature filtering to remove unreliable embeddings; uncertain instances additionally receive stochastic feature-path explorations whose predictions are aggregated via consistency-weighted ensembling. Confident instances bypass exploration entirely, keeping average overhead at approximately $2.8\times$ base model cost with worst-case latency unchanged.Experiments on four datasets with three backbone architectures demonstrate consistent, statistically significant gains over all training-phase baselines. A seven-day online A/B test further confirms a 5.3% relative CTR gain ($p < 0.01$), establishing selective test-time compute allocation as a practical complement to training-phase advances for CTR prediction.

With the continuous advancement of Large Language Models (LLMs), intelligent agents are becoming increasingly vital. However, these agents often fail in environments governed by implicit rules--hidden constraints that cannot be observed directly and must be inferred through interaction. This causes agents to fall into repetitive trial-and-error loops, ultimately leading to task failure. To address this challenge, we propose Test-Time Exploration (TTExplore), a framework where a thinker component analyzes interaction history to infer these implicit rules and guide an actor. Effective exploration in this setting critically depends on the reasoning ability of the thinker. However, evaluating deep reasoning trajectories is inherently unstable and difficult, which poses a major obstacle to effective training. To overcome this issue, we introduce a novel and stable reinforcement learning pipeline. The core idea is to use accurate task-level scores as indirect rewards to bypass the difficulty of evaluating intermediate reasoning, and to retain only a single thinking node per trajectory to alleviate reward sparsity. Using this pipeline, we train a specialized 7B model, Exp-Thinker. Experiments on five text-based embodied tasks show that TTExplore equipped with Exp-Thinker improves baseline agent performance by an average of $14$-$19$ points, demonstrating the effectiveness of explicitly reasoning about implicit rules.

We present Semantic-Aware Guided Exploration, SAGE, a system for open-vocabulary exploration in unknown 3D indoor environments that preserves coverage-oriented behavior while allowing semantic cues to reprioritize frontier selection. Building on the FALCON volumetric explorer, SAGE integrates Contrastive Language-Image Pre-training (CLIP) via four key components: object-centric embedding storage, a temporal cache that projects recent observations onto the free-unknown boundary, object frontiers for high-similarity detections, and a unified semantic-geometric planning cost. This cost function bounds semantic reweighting influence, ensuring frontiers are prioritized without sacrificing total coverage. In Matterport3D-based simulations, SAGE outperforms FALCON and a semantic-only ablation in object discovery across map-query pairs. Compared to Finding Things in the Unknown (FTU), SAGE completes exploration 9.0 to 25.9 times faster across the nine shared map-query pairs, achieving a mean speedup of 13.7. Furthermore, SAGE achieves substantially higher volumetric throughput than FTU. Finally, we deploy SAGE in five real-world flights in two environments on a Modal AI Starling 2 quadrotor with onboard sensing and planning, and offboard CLIP inference. Comparing SAGE and FALCON, we find that while FALCON results in faster exploration and shorter mapping trajectories, SAGE outperforms FALCON in terms of object discovery.

The complete collection of sparse resources in large, unknown environments remains a challenging problem for autonomous robot swarms. Previous studies have shown that a substantial portion of total mission time is consumed during the final stage of collection, where only a small fraction of randomly scattered resources remain. Consequently, many existing swarm foraging algorithms (search and collection) focus on collecting most resources within a limited time window, rather than improving end-stage efficiency for collecting all resources. We propose a grid-based stochastic foraging strategy that explicitly reduces redundant visits and accelerates late-stage collection. The unknown search area is partitioned into a grid map, which is maintained by a lightweight central server. To maintain scalability, both robots and the server operate within limited memory and computational constraints. The server updates the grid-level visitation counts based on robot-reported locations, producing a global estimate of the exploration density. For each new foraging trip, a robot selects its next search area from a local 3 X 3 neighborhood of grids probabilistically with the lowest visitation count, thus biasing exploration toward under-visited regions while maintaining stochasticity. Extensive simulation experiments demonstrate that the proposed strategy consistently outperforms the canonical centrally placed baseline foraging algorithm (CPFA). Compared to CPFA, the proposed method reduces the total collection time by up to 33% and improves collection efficiency by more than 48% during the final stage of the mission. These results indicate that the proposed strategy is robust, flexible, and scalable for near-complete and complete resource collection in robot swarms and can serve as a general enhancement for stochastic swarm foraging methods under limited onboard resources.

In this work, we address the problem of multi-robot adaptive coverage, where teams of robots perform dynamic sampling by continuously adjusting their positions to collect data in an environment. This task can be challenging, particularly when robots must be efficiently allocated to new sampling locations over time. Ergodic search methods optimize robot trajectories by ensuring that the robots' time-averaged spatial distribution aligns with the spatial distribution of environmental information. While these methods promote effective exploration provided a target distribution, they often fail to account for unknown prior distributions of the environment. To overcome this limitation, we propose an adaptive coverage strategy that utilizes real-time feedback from an environmental model to adjust robot sampling behavior in response to unknown conditions. Our approach enhances traditional ergodic trajectory optimization by constructing a target spatial information distribution based on parametric models of the environment, which are updated online. This strategy assumes that the environment is either static or changes slowly compared to the robot's motion. Our framework allows robots to dynamically prioritize regions of high interest, improving coverage efficiency, synthesizing effective control policies for individual agents, and optimizing resource use in settings with unknown prior distributions. We validate our approach through simulations, demonstrating its effectiveness in enhancing coverage and resource allocation.

Safe exploration remains a fundamental challenge in reinforcement learning (RL), limiting the deployment of RL agents in the real world. We propose Sampling-Based Safe Reinforcement Learning (SBSRL), a model-based RL algorithm that maintains safety throughout the learning process by enforcing constraints jointly across a finite set of dynamics samples. This formulation approximates an intractable worst-case optimization over uncertain dynamics and enables practical safety guarantees in continuous domains. We further introduce an exploration strategy based on constraining epistemic uncertainty, eliminating the need for explicit exploration bonuses. Under regularity conditions, we derive high-probability guarantees of safety throughout learning and a finite-time sample complexity bound for recovering a near-optimal policy. Empirically, SBSRL achieves safe and efficient exploration both in simulation and in real robotic hardware, and readily extends to practical deep-ensemble implementations that scale to high-dimensional continuous control problems.

Muon is a matrix-aware optimizer that leverages Newton-Schulz (NS) iterations to enforce spectral gradient orthogonalization by driving all singular values of the momentum matrix toward 1. While this uniform spectral whitening enhances exploration and outperforms AdamW in LLM pretraining, we show it could lead to fundamental limitations beyond pretraining in two regimes: (i) cross-modality vision-language-action (VLA) training, where inherently low-rank action-module gradients cause amplification of noisy tail directions, and (ii) reinforcement learning with verifiable rewards (RLVR), where low-SNR gradients and the need to preserve per-head specialization from prior training make whitening unstable. To address these challenges, we propose Pion, a drop-in replacement for Muon that preserves its computational efficiency while replacing uniform spectral whitening with a two-stage Promotion+Suppression mechanism, which we call the high-pass NS iteration. This design induces a sharp spectral high-pass effect, anchoring dominant singular values at 1 while suppressing noisy tail components toward 0, with controllable filter strength. To preserve pretrained per-head heterogeneity, Pion also supports a per-head mode that applies updates independently across attention heads via a simple reshape, at no extra cost. In VLA training on LIBERO and LIBERO-Plus, Pion consistently outperforms both baselines across l_1-regression (VLA-Adapter) and flow-matching (VLANeXt) architectures, e.g., reaching 100% success rate on LIBERO Object after 1,500 training steps with VLA-Adapter, vs. 97.0% for Muon and only 32.2% for AdamW. The advantage of Pion further extends to a real Franka Research 3 robot with a pi_0.5 backbone under the DROID setup on three grasp-and-place tasks. In RLVR post-training on Qwen3-1.7B/4B with GRPO and GMPO, Pion also outperforms AdamW on MATH and GSM8K while Muon collapses to zero.

Adaptive decision-making in biological and artificial intelligence requires balancing the exploitation of known outcomes with the exploration of uncertain alternatives. Although prior work suggests that uncertainty generally promotes exploration, it has typically treated distinct sources of environmental uncertainty as equivalent. We consider environments with latent reward states that drift over time (volatility) and are observed through noisy outcomes (stochasticity). Both increase posterior uncertainty, yet we show they drive optimal exploration in opposite directions: volatility enhances it, stochasticity suppresses it. We establish this asymmetry formally by extending the Gittins index framework to Gaussian state-space bandits with latent dynamics. We further derive Cause-Aware Uncertainty-Sensitive Exploration (CAUSE), a closed-form exploration bonus obtained via control-as-inference that inherits the same monotonicities. CAUSE outperforms standard exploration strategies in environments with heterogeneous noise structure, and also improves on a Gittins-per-arm policy whose rested-bandit optimality does not transfer to restless settings. Learning and exploration are governed by the same noise-inference asymmetry, and the framework predicts that pathological noise inference produces \emph{reversed} rather than merely impaired exploration, with implications for computational accounts of psychiatric conditions.

Reinforcement learning has become a cornerstone for aligning and unlocking the reasoning capabilities of large-scale models. At its core, the training loop of GRPO and its variants alternates between rollout sampling and policy update: the policy first samples rollouts from its action space, and then updates its parameters according to the advantages computed over them. Unlike supervised learning, where each gradient step is anchored to an explicit ground-truth target, the optimal gradient direction for updating model parameters in this setting is not known a priori; the high-quality rollouts drawn during the sampling stage therefore act as the implicit "teacher" that guides every parameter update. However, mainstream RL algorithms such as GRPO adopt a simple sampling scheme that conditions all rollouts on the same original prompt. When a task lies beyond the policy model's current capability, this sampling scheme rarely yields a high-quality rollout, leaving the policy model without a meaningful gradient direction when updating its parameters, which causes training to stall. To address this issue, we propose FBOS-RL. Specifically, we let the model perform Feedback-Guided Exploration Enhancement based on the feedback provided by the environment, and on top of this we design two mutually reinforcing training objectives: EPA and ECC. Extensive experiments demonstrate that EPA and ECC can mutually reinforce each other, forming a positive flywheel effect that significantly improves both the training efficiency and the final performance ceiling of reinforcement learning. Specifically, under both an identical number of rollouts and the same number of training steps, FBOS-RL learns substantially faster than GRPO and feedback-based baselines and ultimately attains a higher performance ceiling, while exhibiting higher policy entropy and lower gradient norms throughout training.

Executable world models can be read, edited, executed, and reused for planning, but only if the program captures the environment's transition law rather than semantic shortcuts in its surface vocabulary. We study online executable world-model learning under prior misalignment, where an agent must induce state-dependent dynamics from interaction evidence alone, without rule descriptions, reward signals, or trustworthy lexical priors. We introduce Alice, a closed-loop system that treats failed candidate updates as structural signal: when a candidate explains a new transition but loses previously explained ones, the preservation conflict reveals dynamics that the current program had conflated. Alice refines these conflicts into hypothesis classes that both provide compact, class-stratified preservation counterexamples for update and guide frontier exploration toward transitions that are novel and underrepresented with respect to the current program. We evaluate Alice on Baba in Wonderland, a prior-misaligned variant of Baba Is You that preserves simulator dynamics while replacing semantically meaningful rule-property labels with unrelated words. Experiments show that Alice substantially improves executable world-model learning under prior misalignment, and ablations show that both class refinement and class-aware exploration contribute.

Large language model based agents often fail in unfamiliar environments due to premature exploitation: a tendency to act on prior knowledge before acquiring sufficient environment-specific information. We identify autonomous exploration as a critical yet underexplored capability for building adaptive agents. To formalize and quantify this capability, we introduce Exploration Checkpoint Coverage, a verifiable metric that measures how broadly an agent discovers key states, objects, and affordances. Our systematic evaluation reveals that agents trained with standard task-oriented reinforcement learning consistently exhibit narrow and repetitive behaviors that impede downstream performance. To address this limitation, we develop a training strategy that interleaves task-execution rollouts and exploration rollouts, with each type of rollout optimized by its corresponding verifiable reward. Building on this training strategy, we propose the Explore-then-Act paradigm, which decouples information-gathering from task execution: agents first utilize an interaction budget to acquire grounded environmental knowledge, then leverage it for task resolution. Our results demonstrate that learning to systematically explore is imperative for building generalizable and real-world-ready agents.

Most exploration algorithms search broadly until uncertainty is resolved. When the action space is too large to resolve within budget, practitioners default to $\varepsilon$-greedy, which bounds disruption but spends its override blindly. We introduce \textit{Delight-gated exploration} (DE), a host--override rule that spends exploratory actions only when their prospective delight (expected improvement times surprisal) exceeds a gate price. This practical heuristic recovers a classical result: Pandora's reservation-value rule for costly search, with surprisal setting the effective inspection cost. Resolved arms exit the gate, fresh arms shut off above a prior-determined threshold, and selected linear-bandit overrides consume finite information budget. Across Bernoulli bandits, linear bandits, and tabular MDPs, the same hyperparameters transfer without retuning, and DE shows much weaker regret growth than Thompson Sampling and $\varepsilon$-greedy in the tested unresolved regimes. Delight improves acting for the same reason it improves learning: it prices scarce resources by the product of upside and surprisal.

Can AI systems discover genuinely new knowledge through iterative self improvement, and if so, at what cost? We introduce the NOVA framework, which models the common ``generate, verify, accumulate, retrain'' loop as an adaptive sampling process over a knowledge space. We identify sufficient conditions under which accumulated genuine knowledge eventually covers a finite domain, and show how their violations produce distinct failure modes: contamination, forgetting, exploration failure, and acceptance failure. We then analyze imperfect verification and identify a contamination trap: as easy-to-find knowledge is exhausted, the model mass assigned to new valid artifacts shrinks, so even small false-positive rates can cause invalid artifacts to enter the knowledge base faster than genuine discoveries. We clarify that Good--Turing estimation is a local batch-diversity diagnostic, not an estimator of the historically undiscovered valid mass that governs long-term discovery. Under a separate tail-equivalence assumption relating the model's effective discovery distribution to a Zipf law with exponent $α>1$, we prove that the cumulative generation cost required to obtain $D$ distinct genuine discoveries satisfies $R_{\mathrm{cum}}(D)=Θ(c_{\mathrm{gen}}D^α)$, where $c_{\mathrm{gen}}$ is the per-candidate generation cost. This scaling law quantifies asymptotic diminishing returns as the discovery frontier advances. Finally, we formalize human amplification through guidance, generation, and verification, explaining why expert input is most valuable near autonomous exploration barriers.

Designing learnable information-theoretic objectives for robot exploration remains challenging. Such objectives aim to guide exploration toward data that reduces uncertainty in model parameters, yet it is often unclear what information the collected data can actually reveal. Although reinforcement learning (RL) can optimize a given objective, constructing objectives that reflect parametric learnability is difficult in high-dimensional robotic systems. Many parameter directions are weakly observable or unidentifiable, and even when identifiable directions are selected, omitted directions can still influence exploration and distort information measures. To address this challenge, we propose Quasi-Optimal Experimental Design (Q{\footnotesize OED}), an adaptive information objective grounded in optimal experimental design. Q{\footnotesize OED} (i) performs eigenspace analysis of the Fisher information matrix to identify an observable subspace and select identifiable parameter directions, and (ii) modifies the exploration objective to emphasize these directions while suppressing nuisance effects from non-critical parameters. Under bounded nuisance influence and limited coupling between critical and nuisance directions, Q{\footnotesize OED} provides a constant-factor approximation to the ideal information objective that explores all parameters. We evaluate Q{\footnotesize OED} on simulated and real-world navigation and manipulation tasks, where identifiable-direction selection and nuisance suppression yield performance improvements of \SI{35.23}{\percent} and \SI{21.98}{\percent}, respectively. When integrated as an exploration objective in model-based policy optimization, Q{\footnotesize OED} further improves policy performance over established RL baselines.

Classical coding-theoretic guarantees often rely on trust assumptions, such as requiring sufficiently many honest nodes compared with adversarial ones. These assumptions are difficult to enforce in open decentralized systems where participants are not centrally certified. At the same time, such environments often contain incentive mechanisms: participants may be rewarded only when their submitted data are accepted and the system remains functional. This changes the role of an adversary. Rather than acting as a pure saboteur, a strategic adversary may submit data that are consistent enough to be accepted while still degrading the quality of the final estimate. The game-of-coding framework models this strategic interaction between a data collector (DC) and an adversary. Existing works on the game of coding mostly consider the complete-information case, where the DC knows how the adversary trades off acceptance and estimation error. In this paper, we study an incomplete-information version of the game of coding in which the DC, acting as a Stackelberg leader, does not know the adversary's utility trade-off and must learn through repeated interaction. Prior work on the unknown-adversary setting considered an explore-then-commit objective, where only the final selected acceptance rule is evaluated. In contrast, we study the full learning trajectory: every acceptance rule used during the algorithm is executed and contributes to performance. We propose an algorithm that refines its search around promising acceptance rules, prove that it achieves sublinear cumulative regret, and evaluate its performance through numerical experiments.

Reinforcement learning with verifiable rewards (RLVR) recently thrives in large language model (LLM) reasoning tasks. However, the reward sparsity and the long reasoning horizon make effective exploration challenging. In practice, this challenge manifests as the \emph{entropy collapse} phenomenon, where RLVR improves single-rollout accuracy but fails to expand coverage on successful reasoning trajectories. Passive exploration techniques like entropy regularization tend to dismiss generation quality, resulting in noisy rollouts. In response to this issue, we propose an Information-Maximizing Augmented eXploration (IMAX) framework to train a pool of soft prefixes that reshapes the base model's prior over reasoning trajectories. Rather than relying on RL to incentivize exploration on top of the base model, each prefix acts as a trainable control knob that induces a distinct rollout distribution from the same backbone model. To encourage discovery of diverse and task-relevant reasoning behaviors, we derive an Information Maximization (InfoMax) reward to complement the verifiable rewards for RL training. IMAX is in general algorithm-agnostic and can be seamlessly integrated into existing RLVR pipelines. Experiment results have shown that across three backbone scales, IMAX consistently improves reasoning performance over standard RLVR, with gains up to 11.60% in Pass@4 and 10.57% in Avg@4.

In recent years, autonomous parking has made significant advances, yet parking tasks still face challenges in extreme scenarios such as mechanical and dead-end parking slots, often resulting in failures. This is mainly due to traditional parking methods adopting a multistage approach, lacking the ability to optimize the parking problem as a whole. End-to-end methods enable joint optimization across perception and planning modules to eliminate the accumulation of errors, enhancing algorithm performance in extreme scenarios. Although several end-to-end parking methods use imitation or reinforcement learning, the former is limited by data cost and distribution coverage, while the latter suffers from inefficient exploration. To address these challenges, we propose a Reinforcement learning End-to-end Autonomous Parking method (REAP). REAP employs Soft Actor-Critic (SAC) within an asymmetric reinforcement learning framework to improve training efficiency and inference performance. To accelerate model convergence, we distill the capabilities of a rule-based planner into the end-to-end network through behavior cloning. We further introduce a soft predictive collision penalty mechanism to reduce collision rates by penalizing obstacle-approaching actions. To ensure that the trained reinforcement learning network can directly transfer to real-world scenarios, we have established a Real2Sim2Real simulator. In the Real2Sim step, we use 3D Gaussian Splatting (3DGS) to transform real-world scenes into digital scenes. In the Sim2Real step, we deploy the end-to-end model onto the vehicle to bridge the Sim2Real gap. Trained in the 3DGS simulator and deployed on physical vehicles, REAP successfully parks in various types of parking spaces, especially demonstrating the feasibility of end-to-end RL parking in extremely narrow mechanical slots.

Differentiable planning enables gradient-based optimization of decision-making problems by leveraging differentiable models of system dynamics. However, in highly nonlinear and hybrid discrete-continuous domains, the resulting optimization landscapes are often ill-conditioned, with flat regions and sharp transitions that hinder effective optimization. We propose Model-Driven Policy Optimization (MDPO), a framework that introduces stochastic exploration into differentiable planning by injecting noise into the action space during optimization. Leveraging access to the model, MDPO further adapts the noise magnitude based on gradient-derived sensitivity of the trajectory objective, yielding a time-dependent exploration profile. This enables improved exploration of the objective landscape and helps escape poor local optima via dynamic allocation of exploration across timesteps and iterations. Experiments on benchmark domains demonstrate that MDPO consistently outperforms deterministic differentiable planning, including both the noise-free variant of our method and available state-of-the-art implementations, as well as model-free baselines such as PPO, significantly improving solution quality across challenging nonlinear and hybrid settings. We further analyze the evolution of the adaptive noise magnitude across both time steps and optimization iterations, providing insight into how exploration is allocated during learning.

Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token generation by propagating continuous states, yet replacing explicit derivations with latent computation can hurt tasks that require symbolic checking. We propose Latent-Then-Explicit Reasoning (LaTER), a two-stage paradigm that first performs bounded exploration in a continuous latent space and then switches to explicit CoT for verification and answer generation. In a training-free instantiation, LaTER projects final-layer hidden states back to the input embedding space, preserves the latent KV cache, and uses entropy and model-native stop-token probes to decide when to switch. We find that strong reasoning models already exhibit structured latent trajectories under this interface. On Qwen3-14B, training-free LaTER reduces total token usage by 16%-32% on several benchmarks while matching or improving accuracy on most of them; for example, it improves AIME 2025 from 70.0% to 73.3% while reducing tokens from 15,730 to 10,661. We further construct Latent-Switch-69K, a supervised corpus that pairs condensed solution intuitions with shortened explicit derivations. Fine-tuning with latent rollout and halting supervision yields additional gains: trained LaTER reaches 80.0% accuracy on AIME 2025, 10.0 points above the standard CoT baseline, while using 33% fewer tokens. Our code, data, and model are available at https://github.com/TioeAre/LaTER.

LLM-based multi-agent systems (LLM-MAS) have become a promising paradigm for solving complex tasks through role specialization, tool use, memory, and collaborative reasoning. However, these interactions create new security risks that malicious instructions injected through messages, tools, or memories can propagate across agents and rounds, causing system-level compromise. Existing defenses largely rely on local filtering or graph-based anomaly detection, but they often fail to trace fine-grained propagation paths or remediate contaminated states without disrupting benign collaboration. We propose PropGuard, a propagation-aware framework for safeguarding LLM-MAS. PropGuard constructs a dual-view spatio-temporal graph that combines response-centric risk estimation with full-state evidence preservation. Guided by these risk priors, a GE-GRPO trained inspector sequentially explores the full-state graph to recover compact suspicious propagation subgraphs. PropGuard then verifies harmful propagation through subgraph-aware diagnosis and applies source-guided remediation to correct upstream contamination and replay affected downstream interactions. Experiments across four communication architectures and five attack settings demonstrate that PropGuard consistently lowers attack success while maintaining high task-level defense success, achieving a favorable effectiveness--efficiency trade-off.

Recent progress in multi-turn reinforcement learning (RL) has significantly improved reasoning LLMs' performances on complex interactive tasks. Despite advances in stabilization techniques such as fine-grained credit assignment and trajectory filtering, instability remains pervasive and often leads to training collapse. We argue that this instability stems from inefficient exploration in multi-turn settings, where policies continue to generate low-information actions that neither reduce uncertainty nor advance task progress. To address this issue, we propose Token- and Turn-level Policy Optimization (T$^2$PO), an uncertainty-aware framework that explicitly controls exploration at fine-grained levels. At the token level, T$^2$PO monitors uncertainty dynamics and triggers a thinking intervention once the marginal uncertainty change falls below a threshold. At the turn level, T$^2$PO identifies interactions with negligible exploration progress and dynamically resamples such turns to avoid wasted rollouts. We evaluate T$^2$PO in diverse environments, including WebShop, ALFWorld, and Search QA, demonstrating substantial gains in training stability and performance improvements with better exploration efficiency. Code is available at: https://github.com/WillDreamer/T2PO.

Efficient exploration is a central problem in reinforcement learning and is often formalized as maximizing the entropy of the state-action occupancy measure. While unconstrained maximum-entropy exploration is relatively well understood, real-world exploration is often constrained by safety, resource, or imitation requirements. This constrained setting is particularly challenging because entropy maximization lacks additive structure, rendering Bellman-equation-based methods inapplicable. Moreover, scalable approaches require policy parameterization, inducing non-convexity in both the objective and the constraints. To our knowledge, the only prior model-free policy-gradient approach for this setting under general policy parameterization is due to Ying et al. (2025). Unfortunately, their guarantees are limited to weak regret and ergodic averages, which do not imply that the final output is a single deployable policy that is near-optimal and nearly feasible. In this work we take a different approach to this problem, and propose Policy Gradient Penalty (PGP) method, a single-loop policy-space method that enforces general convex occupancy-measure constraints via quadratic-penalty regularization. PGP constructs pseudo-rewards that yield gradient estimates of the penalized objective, subsequently exploiting the classical Policy Gradient Theorem. We further establish the regularity of the penalized objective, providing the smoothness properties needed to justify the convergence of PGP. Leveraging hidden convexity and strong duality, we then establish global last-iterate convergence guarantees, attaining an $ε$-optimal constrained entropy value with $ε$ bounded constraint violation despite policy-induced non-convexity. We validate PGP through ablations on a grid-world benchmark and further demonstrate scalability on two challenging continuous-control tasks.

Automatic feature engineering is an effective approach for improving predictive performance in tabular learning. However, expand-and-reduce methods, such as OpenFE, become increasingly computationally expensive as the input dimensionality grows. This limitation arises primarily from the combinatorial explosion of candidate features generated through operator-feature combinations. To address this issue, we propose SCOPE-FE, a structured search space control framework that improves efficiency by reducing the candidate space prior to feature generation. SCOPE-FE jointly regulates two major sources of combinatorial growth: the operator space and feature-pair space. First, OperatorProbing estimates the dataset-specific utility of candidate operators and eliminates low-contribution operators in advance. Second, FeatureClustering employs spectral embedding and fuzzy c-means clustering to group structurally related features, thereby restricting candidate generation to relevant within-cluster combinations. In addition, we introduce ReliabilityScoring, which incorporates variance across subsamples to stabilize pruning decisions. Experiments on ten benchmark datasets demonstrate that SCOPE-FE substantially reduces feature engineering time while maintaining competitive predictive performance relative to existing baselines. The efficiency gains are particularly pronounced for high-dimensional datasets. These results indicate that structured control of the search space is an effective strategy for scalable automatic feature engineering. The code will be made publicly available upon acceptance.

Deploying machine learning models under production constraints requires joint optimization over model family, quantization scheme, runtime backend, and serving configuration. This induces a hierarchical mixed-variable search space in which many configurations are invalid: evaluations may crash, exceed memory limits, or violate latency constraints. Standard black-box optimizers such as Tree-structured Parzen Estimators (TPE) and constrained Bayesian optimization are effective when valid configurations are common, but they can spend a large fraction of a small evaluation budget on invalid or uninformative trials in hostile deployment spaces. This paper studies that regime and asks whether optimization should be decomposed into an explicit exploration stage followed by model-guided exploitation. We propose Thermal Budget Annealing (TBA), a feasible-first exploration procedure that maps valid and feasible regions before warm-starting TPE. The method includes two robustness mechanisms for hostile hardware: trial timeouts that abort clearly infeasible evaluations early, and subspace blacklisting that temporarily suppresses categorical subspaces after repeated failures. We also introduce DeployBench, a benchmark suite for deployment optimization with hierarchical structure, hidden crash zones, hard constraints, and unequal evaluation costs. On synthetic benchmarks and real GPU deployment with five pre-trained vision models across five GPU targets (NVIDIA H100, A100, RTX 5080, L4, and T4), the proposed hybrid improves model-family discovery under tight constraints while reducing wasted budget relative to cold-start TPE.

Many sequential decision-making tasks involve optimizing multiple conflicting objectives, requiring policies that adapt to different user preferences. In multi-objective reinforcement learning (MORL), one widely studied approach} addresses this by training a single policy network conditioned on preference-weighted rewards. In this paper, we explore a novel algorithmic perspective: leveraging reward-free reinforcement learning (RFRL) for MORL. While RFRL has historically been studied independently of MORL, it learns optimal policies for any possible reward function, making it a natural fit for MORL's challenge of handling unknown user preferences. We propose using the RFRL's training objective as an auxiliary task to enhance MORL, enabling more effective knowledge sharing beyond the multi-objective reward function given at training time. To this end, we adapt a state-of-the-art RFRL algorithm to the MORL setting and introduce a preference-guided exploration strategy that focuses learning on relevant parts of the environment. Through extensive experiments and ablation studies, we demonstrate that our approach significantly outperforms the state-of-the-art MORL methods across diverse MO-Gymnasium tasks, achieving superior performance and data efficiency. This work provides the first systematic adaptation of RFRL to MORL, demonstrating its potential as a scalable and empirically effective solution to multi-objective policy learning.

Heterogeneous multi-robot systems feature significant adaptability for complex environments. However, effective collaboration that fully exploits the robots' potential remains a core challenge. This paper proposes a decentralized collaborative framework for heterogeneous multi-robot systems to autonomously explore indoor and outdoor 3D environments. First, a basic perception map that integrates terrain and observation metrics is designed. Improved supervoxel segmentation is developed to simplify the map structure and form a high-level representation that supports lightweight communication. Second, the traversal and observation capabilities of heterogeneous robots are modeled to evaluate the requirements of task views derived from incomplete supervoxels. These task views are grouped by requirements and clustered to streamline assignment. Subsequently, the view-cluster assignment is formulated as a heterogeneous multi-depot multi-traveling salesman problem (HMDMTSP) that incorporates constraints between view-cluster requirements and robot capabilities. An improved genetic algorithm is developed to efficiently solve this problem while ensuring global consistency. Based on the assignments, redundant views within clusters are eliminated to refine exploration routes. Finally, conflicts between robots' motion paths are resolved. Simulations and field experiments in cluttered indoor and outdoor environments demonstrate that our approach effectively coordinates exploration tasks among heterogeneous robots, achieving superior exploration efficiency and communication savings compared to state-of-the-art approaches.

Active perception is a fundamental problem in autonomous robotics in which the robot must decide where to move and what to sense in order to obtain the most informative observations for accomplishing its mission. Existing approaches either solve a computationally expensive traveling salesman problem over heuristically selected informative nodes, or adopt a more efficient but overly constrained shortest path tree formulation. To address these limitations, we explore beam search algorithms as scalable alternatives. While the standard beam search provides scalability by preserving the top-B paths at each depth level, it is prone to local optima and exhibits parameter sensitivity. Our first contribution is a node-wise beam search (NBS) algorithm, which maintains top-B candidates per node to enable more effective exploration of the solution space. Systematic benchmarking on graphs shows that NBS consistently outperforms other baselines and maintains strong performance even at low beam widths. As a second contribution, we integrate the concept of frontiers into the path selection criterion, introducing the expected gain metric, which better balances exploration and exploitation compared to existing alternatives. Our third contribution proposes the rapidly-exploring random annulus graph (RRAG), a novel graph construction method that preserves full orientation sampling and ensures connectivity in cluttered environments through a fallback local sampling-based planner. Extensive experiments demonstrate that NBS combined with RRAG achieves the highest performance across all three representative active perception tasks, outperforming state-of-the-art algorithms by at least 20% in one or more tasks. We further validate the approach on real robotic platforms in different scenarios.

Fair machine learning (ML) methods help identify and mitigate the risk that algorithms encode or automate social injustices. Algorithmic approaches alone cannot resolve structural inequalities, but they can support socio-technical decision systems by surfacing discriminatory biases, clarifying trade-offs, and enabling governance. Although fairness is well studied in supervised learning, many real ML applications are online and sequential, with prior decisions informing future ones. Each decision is taken under uncertainty due to unobserved counterfactuals and finite samples, with dire consequences for under-represented groups, systematically under-observed due to historical exclusion and selective feedback. A bank cannot know whether a denied loan would have been repaid, and may have less data on marginalized populations. This paper introduces a taxonomy of uncertainty in sequential decision-making -- model, feedback, and prediction uncertainty -- providing shared vocabulary for assessing systems where uncertainty is unevenly distributed across groups. We formalize model and feedback uncertainty via counterfactual logic and reinforcement learning, and illustrate harms to decision makers (unrealized gains/losses) and subjects (compounding exclusion, reduced access) of policies that ignore the unobserved space. Algorithmic examples show it is possible to reduce outcome variance for disadvantaged groups while preserving institutional objectives (e.g. expected utility). Experiments on data simulated with varying bias show how unequal uncertainty and selective feedback produce disparities, and how uncertainty-aware exploration alters fairness metrics. The framework equips practitioners to diagnose, audit, and govern fairness risks. Where uncertainty drives unfairness rather than incidental noise, accounting for it is essential to fair and effective decision-making.

Bridging the gap between embodied intelligence and embedded deployment remains a key challenge in intelligent robotic systems, where perception, reasoning, and planning must operate under strict constraints on computation, memory, energy, and real-time execution. In vision-and-language navigation (VLN), existing approaches often face a trade-off between reasoning capability and deployment efficiency on real-world platforms. In this paper, we present a deployable embodied VLN system that achieves both high efficiency and strong high-level reasoning on real-world robots. The system is decomposed into a fast perception-action layer and a deep reasoning layer running asynchronously at different time scales, with a shared memory layer enabling efficient interaction between them. To support long-horizon reasoning, we incrementally construct a compact memory graph and progressively feed decomposed subgraphs into a vision-language model (VLM). Furthermore, we formulate exploration as a Weighted Traveling Repairman Problem (WTRP) by jointly considering reasoning outcomes and the spatial distribution of candidate regions. Extensive experiments in simulation and real-world environments demonstrate improved navigation success and efficiency over existing VLN approaches while maintaining real-time performance on resource-constrained hardware. Code and additional real-world experiments are available at https://github.com/xukuanHIT/HiCo-Nav.

Self-consistency boosts inference-time performance by sampling multiple reasoning traces in parallel and voting. However, in constrained domains like math and code, this strategy is compute-inefficient because it samples with replacement, repeatedly revisiting the same high-probability prefixes and duplicate completions. We propose Distinct Leaf Enumeration (DLE), a deterministic decoding method that treats truncated sampling as traversal of a pruned decoding tree and systematically enumerates distinct leaves instead of sampling with replacement. This strategy improves inference efficiency in two ways. Algorithmically, it increases coverage of the truncated search space under a fixed budget by exploring previously unvisited high-probability branches. Systemically, it reuses shared prefixes and reduces redundant token generation. Empirically, DLE explores higher-quality reasoning traces than stochastic self-consistency, yielding better performance on math, coding, and general reasoning tasks.

Grounded Multimodal Named Entity Recognition (GMNER) aims to extract named entities and localize their visual regions within image-text pairs, serving as a pivotal capability for various downstream applications. In open-world social media platforms, GMNER remains challenging due to the prevalence of long-tailed, rapidly evolving, and unseen entities. To tackle this, existing approaches typically rely on either external knowledge exploration through heuristic retrieval or internal knowledge exploitation via iterative refinement in Multimodal Large Language Models (MLLMs). However, heuristic retrieval often introduces noisy or conflicting evidence that degrades precision on known entities, while solely internal exploitation is constrained by the knowledge boundaries of MLLMs and prone to hallucinations. To address this, we propose SAKE, an end-to-end agentic framework that harmonizes internal knowledge exploitation and external knowledge exploration via self-aware reasoning and adaptive search tool invocation. We implement this via a two-stage training paradigm. First, we propose Difficulty-aware Search Tag Generation, which quantifies the model's entity-level uncertainty through multiple forward samplings to produce explicit knowledge-gap signals. Based on these signals, we construct SAKE-SeCoT, a high-quality Chain-of-Thought dataset that equips the model with basic self-awareness and tool-use capabilities through supervised fine-tuning. Second, we employ agentic reinforcement learning with a hybrid reward function that penalizes unnecessary retrieval, enabling the model to evolve from rigid search imitation to genuine self-aware decision-making about when retrieval is truly necessary. Extensive experiments on two widely used social media benchmarks demonstrate SAKE's effectiveness.

Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure cases causes the advantage signal in group-relative algorithms (e.g., GRPO) to vanish, driving policies into mode collapse. To address this, we propose Constrained Uniform Top-K Sampling (CUTS), a parameter-free decoding strategy enforcing structure-preserving exploration. Unlike standard sampling that follows model biases, CUTS flattens the local optimization landscape by sampling uniformly from constrained high-confidence candidates. We integrate this into Mixed-CUTS, a training framework synergizing exploitative and exploratory rollouts to amplify intra-group advantage variance. Experiments on Qwen3 models demonstrate that our approach prevents policy degeneration and significantly boosts out-of-domain generalization. Notably, Mixed-CUTS improves Pass@1 accuracy on the challenging AIME25 benchmark by up to 15.1% over standard GRPO, validating that maintaining diversity within the semantic manifold is critical for rigorous reasoning.

Exploration is a cornerstone of learning from experience: it enables agents to find solutions to complex problems, generalize to novel ones, and scale performance with test-time compute. In this paper, we present a framework for post-training language models (LMs) that explicitly encourages optimistic exploration and promotes a synergy between exploration and exploitation. The central idea is to train the LM to generate sets of responses that are collectively accurate under the reward function and exploratory in their reasoning strategies. We first develop a general recipe for optimizing LMs with set reinforcement learning (set RL) under arbitrary objective functions, showing how standard RL algorithms can be adapted to this setting through a modification to the advantage computation. We then propose Polychromic Exploratory Policy Optimization (Poly-EPO), which instantiates this framework with an objective that explicitly synergizes exploration and exploitation. Across a range of reasoning benchmarks, we show that Poly-EPO improves generalization, as evidenced by higher pass@$k$ coverage, preserves greater diversity in model generations, and effectively scales with test-time compute.

Despite the rapid progress, LLMs for sequential decision-making (i.e., LLM agents) still struggle to produce diverse outputs. This leads to insufficient exploration, convergence to sub-optimal solutions, and becoming stuck in loops. Such limitations can be problematic in environments that require active exploration to gather information and make decisions. Sampling methods such as temperature scaling introduce token-level randomness but fail to produce enough diversity at the sequence level. We analyze LLM exploration in the classic Multi-Armed Bandit (MAB) setting and the Text Adventure Learning Environment Suite (TALES). We find that current decoding strategies and prompting methods like Chain-of-Thought and Tree-of-Thought are insufficient for robust exploration. To address this, we introduce DORA Explorer (Diversity-Oriented Ranking of Actions), a training-free framework for improving exploration in LLM agents. DORA generates diverse action candidates, scores them using token log-probabilities, and selects actions using a tunable exploration parameter. DORA achieves UCB-competitive performance on MAB and consistent gains across TALES, e.g., improving Qwen2.5-7B's performance from 29.2% to 45.5% in TextWorld. Our project is available at: https://dora-explore.github.io/.

Reinforcement learning (RL) has emerged as a promising paradigm for training reasoning-oriented models by leveraging rule-based reward signals. However, RL training typically tends to improve single-sample success rates (i.e., Pass@1) while offering limited exploration of diverse reasoning trajectories, which is crucial for multi-sample performance (i.e., Pass@k). Our preliminary analysis reveals that this limitation stems from a fundamental squeezing effect, whereby probability mass is excessively concentrated on a narrow subset of high-reward trajectories, restricting genuine exploration and constraining attainable performance under RL training. To address this issue, in this work, we propose Steering Probability Squeezing (SPS), a training paradigm that interleaves conventional RL with inverse reinforcement learning (IRL). SPS treats on-policy rollouts as demonstrations and employs IRL to explicitly reshape the induced trajectory distribution, thereby enhancing exploration without introducing external supervision. Experiments on five commonly used reasoning benchmarks demonstrate that SPS can enable better exploration and improve Pass@k. Beyond algorithmic contributions, we provide an analysis of RL learning dynamics and identify an empirical upper bound on Pass@k, shedding light on intrinsic exploration limits in RL-based reasoning models. Our findings suggest that alternating between RL and IRL offers an effective pathway toward extending the exploration capacity of reasoning-oriented large language models.

We present the Global Neural World Model (GNWM), a self-stabilizing framework that achieves topological quantization through balanced continuous entropy constraints. Operating as a continuous, action-conditioned Joint-Embedding Predictive Architecture (JEPA), the GNWM maps environments onto a discrete 2D grid, enforcing translational equivariance without pixel-level reconstruction. Our results show this architecture prevents manifold drift during autoregressive rollouts by using grid ``snapping'' as a native error-correction mechanism. Furthermore, by training via maximum entropy exploration (random walks), the model learns generalized transition dynamics rather than memorizing specific expert trajectories. We validate the GNWM across passive observation, active agent control, and abstract sequence regimes, demonstrating its capacity to act not just as a spatial physics simulator, but as a causal discovery model capable of organizing continuous, predictable concepts into structured topological maps.