Reinforcement Learning

Reinforcement learning (RL)-based post-training often improves the reasoning performance of large language models (LLMs) beyond the training domain, while supervised fine-tuning (SFT) frequently leads to general capabilities forgetting. However, the mechanisms underlying this contrast remain unclear. To bridge this gap, we present a feature-level mechanistic analysis methodology to probe RL generalization using a controlled experimental setup, where RL- and SFT-tuned models are trained from the same base model on identical data. Leveraging our interpretability framework, we align internal activations across models within a shared feature space and analyze how features evolve during post-training. We find that SFT rapidly introduces many highly specialized features that stabilize early in training, whereas RL induces more restrained and continually evolving feature changes that largely preserve base models' representations. Focusing on samples where RL succeeds but the base model fails, we identify a compact, task-agnostic set of features that directly mediate generalization across diverse tasks. Feature-level interventions confirm their causal role: disabling these features significantly degrades RL models' generalization performance, while amplifying them improves base models' performance. The code is available at https://github.com/danshi777/RL-generalization.

We introduce asRoBallet, to the best of our knowledge, the first end-to-end reinforcement learning (RL) locomotion policy deployed on a humanoid ballbot hardware platform. Historically, ballbots have served as a canonical benchmark for underactuated and nonholonomic control, which are characterized by a reality gap in complex friction models for wheel-ball-floor interactions. While current literature demonstrates successful handling of 3D balancing with LQR and MPC, transitioning to actual hardware for a humanoid ballbot using RL is currently hindered by critical gaps in contact modeling, actuator latency & jitter, and safe hardware exploration. This study proposes a high-fidelity MuJoCo simulation that explicitly models the discrete roller mechanics of ETH-type omni-wheels, thereby capturing parasitic vibrations and contact discontinuities that have previously been ignored. We also developed a Friction-Aware Reinforcement Learning framework that achieves zero-shot Sim2Real transfer by mastering the coupled rolling, lateral, and torsional friction channels at the wheel-ball and ball-floor interfaces. We designed asRoBallet through subtractive reconfiguration, repurposing key components from an overconstrained quadruped and integrating them into a newly designed structural frame to achieve a robust research platform at low cost. We also developed a generalized iOS ecosystem that transforms consumer electronics into a low-latency interface, enabling a single operator to orchestrate expressive humanoid maneuvers via intuitive natural motion.

Specification-guided reinforcement learning (RL) provides a principled framework for encoding complex, temporally extended tasks using formal specifications such as linear temporal logic (LTL). While recent methods have shown promising results, their ability to generalize across unseen specifications and diverse environments remains insufficiently understood. In this work, we introduce SpecRLBench, a benchmark designed to evaluate the generalization capabilities of LTL-based specification-guided RL methods. The benchmark spans multiple difficulty levels across navigation and manipulation domains, incorporating both static and dynamic environments, diverse robot dynamics, and varied observation modalities. Through extensive empirical evaluation, we characterize the strengths and limitations of existing approaches and reveal the challenges that emerge as specification and environment complexity increase. SpecRLBench provides a structured platform for systematic comparison and supports the development of more generalizable specification-guided RL methods. Code is available at https://github.com/BU-DEPEND-Lab/SpecRLBench.

Recent work in hierarchical reinforcement learning has shown success in scaling to billions of timesteps when learning over a set of predefined option reward functions. We show that, instead of using a single reward function per option, the reward functions can be effectively used to induce a space of behaviours, by letting the controller specify linear combinations over reward functions, allowing a more expressive set of policies to be represented. We call this method Hierarchical Behaviour Spaces (HBS). We evaluate HBS on the NetHack Learning Environment, demonstrating strong performance. We conduct a series of experiments and determine that, perhaps going against conventional wisdom, the benefits of hierarchy in our method come from increased exploration rather than long term reasoning.

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.

Large language model (LLM) agents that follow the sequential "reason-then-act" paradigm have achieved superior performance in many complex tasks.However, these methods suffer from limited exploration and incomplete environmental understanding, as they interact with only a single environment per step. In this paper, we first introduce a novel paradigm that enables an agent to interact with multiple environments simultaneously and share cross-trajectory experiences. Building upon this paradigm, we further propose DPEPO, a reinforcement learning (RL) algorithm that encourages the agent to perform diverse parallel exploration. There are two stages in DPEPO: initial supervised fine-tuning (SFT) imparts basic parallel reasoning and action generation, followed by reinforcement learning stage with a hierarchical reward scheme. We design a parallel trajectory-level success reward and two step-level rewards: Diverse Action Reward and Diverse State Transition Reward, which actively penalize behavioral redundancy and promote broad exploration. Extensive experiments on ALFWorld and ScienceWorld show that DPEPO achieves state-of-the-art (SOTA) success rates, while maintaining comparable efficiency to strong sequential baselines. (Code is available at https://github.com/LePanda026/Code-for-DPEPO)

We present a framework using Relative Entropy Inverse Reinforcement Learning (RE-IRL) to recover investor reward functions from observed investment actions and market conditions. Unlike traditional IRL algorithms, RE-IRL is employed to account for environments where transition probabilities are unknown or inaccessible. To address the challenge of data sparsity, we utilize a $K$-nearest neighbor approach to estimate the observed behavior policy. Furthermore, we propose a statistical testing framework to evaluate the validity and robustness of the estimated results.

Efficiently solving the Job Shop Scheduling Problem in real-world industrial applications requires policies that are both computationally lean and topologically robust. While Reinforcement Learning has shown potential in automating dispatching rules, existing models often struggle with a scalability bottleneck caused by quadratic graph complexity or the architectural overhead of heterogeneous layers. We introduce a unified graph framework that employs feature-based homogenization to project distinct node roles into a shared latent space. This allows a standard homogeneous Graph Isomorphism Network to capture complex resource contention with linear complexity, ensuring low-latency inference for large-scale industrial applications. Our empirical results demonstrate that our framework achieves state-of-the-art performance while exhibiting consistent zero-shot generalization. We identify the job-to-machine ratio as the primary driver of policy effectiveness, rather than absolute problem size. Based on this, we propose a hypothesis of structural saturation, demonstrating that policies trained on critically congested instances ($\mathcal{J} \approx \mathcal{M}$) learn scale-invariant resolution strategies. Agents trained at this saturation point internalize invariant conflict-resolution logic, allowing them to treat massive rectangular instances as a sequential concatenation of saturated sub-problems. This approach eliminates the need for expensive scale-specific retraining and prevents overfitting to statistical shortcuts, providing a robust and efficient pathway for deploying RL solutions in dynamic production environments.

Deep reinforcement learning policies achieve strong performance in complex continuous control environments with nonlinear contact forces. However, these policies often produce chaotic state dynamics, with trivially small changes to the initial conditions significantly impacting the long-term behaviour of the control system. This high sensitivity to initial conditions limits the application of Deep RL to real-world control systems where performance and stability guarantees are often required. To address this issue, we propose Global stabilisation via Intrinsic Fine Tuning (GIFT), a general-purpose training framework which directly optimises the global stability of existing high-performing deep RL policies using a custom reward function. We demonstrate that GIFT increase the stability of the control interaction while maintaining comparable task performance, thereby improving the suitability of deep RL policies for real-world control systems.

We propose a simple yet effective alternative to reward normalization in policy gradient reinforcement learning by integrating a 1D Kalman filter for online reward estimation. Instead of relying on fixed heuristics, our method recursively estimates the latent reward mean, smoothing high-variance returns and adapting to non-stationary environments. This approach incurs minimal overhead and requires no modification to existing policy architectures. Experiments on \textit{LunarLander} and \textit{CartPole} demonstrate that Kalman-filtered rewards significantly accelerate convergence and reduce training variance compared to standard normalization techniques. Code is available at https://github.com/Sumxiaa/Kalman_Normalization.

One-step offline RL actors are attractive because they avoid backpropagating through long iterative samplers and keep inference cheap, but they still have to improve under a critic without drifting away from actions that the dataset can support. In recent one-step extraction pipelines, a strong iterative teacher provides one target action for each latent draw, and the same student output is asked to do both jobs: move toward higher Q and stay near that paired endpoint. If those two directions disagree, the loss resolves them as a compromise on that same sample, even when a nearby better action remains locally supported by the data. We propose DROL, a latent-conditioned one-step actor trained with top-1 dynamic routing. For each state, the actor samples $K$ candidate actions from a bounded latent prior, assigns each dataset action to its nearest candidate, and updates only that winner with Behavior Cloning and critic guidance. Because the routing is recomputed from the current candidate geometry, ownership of a supported region can shift across candidates over the course of learning. This gives a one-step actor room to make local improvements that pointwise extraction struggles to capture, while retaining single-pass inference at test time. On OGBench and D4RL, DROL is competitive with the one-step FQL baseline, improving many OGBench task groups while remaining strong on both AntMaze and Adroit. Project page: https://muzhancun.github.io/preprints/DROL.

Standard supervised classification trains models to imitate the exact labels provided by a perfect oracle. This imitation happens in a single pass, restricting the model to a fixed compute budget even when inputs vary in complexity. Moreover, the rigid training objective forces the model to express absolute certainty on its training data, resulting in overconfident predictions during evaluation. We propose Reinforced Iterative Classification (RIC), which replaces the imitative objective with Reinforcement Learning (RL). RIC deploys a recurrent agent that iteratively updates a predictive distribution over classes, receiving reward for stepwise improvement in prediction quality. The value function provides a natural halting criterion by estimating the remaining scope for improvement. We prove that the iterative formulation recovers the same optimal predictions as cross-entropy while yielding an anytime classifier. On image classification benchmarks, RIC matches the accuracy of supervised baselines with improved calibration and learns to allocate computation adaptively across inputs.

Most reinforcement-learning (RL) controllers used in continuous control are architecturally centralized: observations are compressed into a single latent state from which both value estimates and actions are produced. Biological control systems are often organized differently. Insects, in particular, coordinate navigation, heading stabilization, memory, and context-dependent action selection through distributed circuits rather than a single monolithic controller. Motivated by this contrast, we study an RL policy architecture that decomposes control into interacting modules for sensory encoding, heading representation, sparse associative memory, recurrent command generation, and local motor control, with a learned arbitration mechanism that allocates motor authority across modules. The model is evaluated on a two-dimensional navigation task that require simultaneous food seeking, obstacle avoidance, and predator escape. In a six-seed predator-navigation experiment trained with Proximal Policy Optimization (PPO) for 75 updates, the modular policy achieves the strongest final mean performance among the tested controllers, with final episodic return $-2798.8\pm964.4$ versus $-3778.0\pm628.1$ for a centralized gated recurrent unit (GRU) and $-4727.5\pm772.5$ for a centralized multilayer perceptron (MLP). The modular policy also attains the lowest final value loss and stable PPO optimization statistics while driving module-assignment entropy to $0.0457\pm0.0244$, indicating highly selective control allocation. These results suggest that distributed control can serve as a useful inductive bias for RL problems involving dynamically competing behavioral objectives.

Deep reinforcement learning for quantum circuit optimization faces three bottlenecks: replay buffers that overlook temporal difference (TD) target reliability, curriculum-based architecture search requiring a full quantum-classical evaluation after every edit, and the discard of noiseless trajectories when retraining under hardware noise. We address these limitations by treating replay as a central algorithmic lever. We introduce ReaPER+, an annealed replay rule that transitions from TD-error prioritization to reliability-aware sampling as value estimates mature. ReaPER+ achieves up to 4x higher sample efficiency than fixed PER, ReaPER, and uniform replay, while matching prior on-policy solution quality with up to 32x fewer interactions At 12 qubits, fixed ReaPER reaches the lowest energy error in the fewest steps, while PER and uniform replay find more compact circuits at higher error. On tasks scaling to 20 qubits, ReaPER+ retains its advantage, demonstrating that reliability-aware annealing extends beyond small-system benchmarks. LunarLander-v3 confirms that the ReaPER+ is domain-agnostic, it improves success rates by up to 26.8% over PER and 21.8% over fixed ReaPER, with a 3% AUC gain over both. We further introduce OptCRLQAS, which amortizes quantum-classical evaluations across multiple architectural edits, reducing training wall-clock time by up to 67.5% on 12-qubit without degrading solution quality. Finally, lightweight replay-buffer transfer warm-starts noisy optimization from noiseless trajectories, without weight transfer or $ε$-greedy pretraining, reducing steps to chemical accuracy by 85-90% and final energy error by up to 90% relative to from-scratch learning. Transfer gains increase with system size. Together, these results establish experience storage, sampling, and transfer as decisive levers for sample efficient, noise-aware quantum circuit optimization.

Autonomous underwater vehicles are required to perform multiple tasks adaptively and in an explainable manner under dynamic, uncertain conditions and limited sensing, challenges that classical controllers struggle to address. This demands robust, generalizable, and inherently interpretable control policies for reliable long-term monitoring. Reinforcement learning, particularly multi-task RL, overcomes these limitations by leveraging shared representations to enable efficient adaptation across tasks and environments. However, while such policies show promising results in simulation and controlled experiments, they yet remain opaque and offer limited insight into the agent's internal decision-making, creating gaps in transparency, trust, and safety that hinder real-world deployment. The internal policy structure and task-specific specialization remain poorly understood. To address these gaps, we analyze the internal structure of a pretrained multi-task reinforcement learning network in the HoloOcean simulator for underwater navigation by identifying and comparing task-specific subnetworks responsible for navigating toward different species. We find that in a contextual multi-task reinforcement learning setting with related tasks, the network uses only about 1.5% of its weights to differentiate between tasks. Of these, approximately 85% connect the context-variable nodes in the input layer to the next hidden layer, highlighting the importance of context variables in such settings. Our approach provides insights into shared and specialized network components, useful for efficient model editing, transfer learning, and continual learning for underwater monitoring through a contextual multi-task reinforcement learning method.

Standard reinforcement learning (RL) optimizes policies for reward but imposes few constraints on how decisions evolve over time. As a result, policies may achieve high performance while exhibiting temporally incoherent behavior such as abrupt confidence shifts, oscillations, or degenerate inactivity. We introduce Dynamical Prior Reinforcement Learning (DP-RL), a training framework that augments policy gradient learning with an auxiliary loss derived from external state dynamics that implement evidence accumulation and hysteresis. Without modifying the reward, environment, or policy architecture, this prior shapes the temporal evolution of action probabilities during learning. Across three minimal environments, we show that dynamical priors systematically alter decision trajectories in task-dependent ways, promoting temporally structured behavior that cannot be explained by generic smoothing. These results demonstrate that training objectives alone can control the temporal geometry of decision-making in RL agents.

Test-time reinforcement learning (TTRL) always adapts models at inference time via pseudo-labeling, leaving it vulnerable to spurious optimization signals from label noise. Through an empirical study, we observe that responses with medium consistency form an ambiguity region and constitute the primary source of reward noise. Crucially, we find that such spurious signals can be even amplified through group-relative advantage estimation. Motivated by these findings, we propose a unified framework, Debiased and Denoised test-time Reinforcement Learning (DDRL), to mitigate spurious signals. Concretely, DDRL first applies a frequency-based sampling strategy to exclude ambiguous samples while maintaining a balanced set of positive and negative examples. It then adopts a debiased advantage estimation with fixed advantages, removing the bias introduced by group-relative policy optimization. Finally, DDRL incorporates a consensus-based off-policy refinement stage, which leverages the rejection-sampled dataset to enable efficient and stable model updates. Experiments on three large language models across multiple mathematical reasoning benchmarks demonstrate that DDRL consistently outperforms existing TTRL baselines. The code will soon be released at https://github.com/yuyongcan/DDRL.

Graphical User Interface (GUI) grounding requires mapping natural language instructions to precise pixel coordinates. However, due to visually homogeneous elements and dense layouts, models typically grasp semantic intent yet struggle with achieving precise localization. While scaling sampling attempts (Pass@k) reveals potential gains, static self-consistency strategies derived from geometric clustering often yield limited improvements, as the model's predictions tend to be spatially dispersed. In this paper, we propose replacing static consistency strategies with a learnable selection mechanism that selects the optimal target by critiquing its own proposals rendered on the screenshot. Given the significant disparity between the model's grounding and critiquing capabilities, we propose a co-evolving Propose-then-Critic framework. To jointly optimize these, we introduce a maturity-aware adaptive co-evolutionary reinforcement learning paradigm. This approach dynamically balances the training objectives of proposer and critic, where the diversity of the proposer's outputs enhances critic robustness, while the critic's maturing discrimination capability conversely unlocks the proposer's potential for extensive spatial exploration, fostering the mutual reinforcement and co-evolution of both capabilities, thereby ensuring generalizability to adapt to diverse and complex interface layouts. Extensive experiments over 6 benchmarks show that our method significantly enhances both grounding accuracy and critic reliability.

We introduce SuperIgor, a framework for instruction-following tasks. Unlike prior methods that rely on predefined subtasks, SuperIgor enables a language model to generate and refine high-level plans through a self-learning mechanism, reducing the need for manual dataset annotation. Our approach involves iterative co-training: an RL agent is trained to follow the generated plans, while the language model adapts and modifies these plans based on RL feedback and preferences. This creates a feedback loop where both the agent and the planner improve jointly. We validate our framework in environments with rich dynamics and stochasticity. Results show that SuperIgor agents adhere to instructions more strictly than baseline methods, while also demonstrating strong generalization to previously unseen instructions.

Quality-Diversity (QD) algorithms excel at discovering diverse repertoires of skills, but are hindered by poor sample efficiency and often require tens of millions of environment steps to solve complex locomotion tasks. Recent advances in Reinforcement Learning (RL) have shown that high Update-to-Data (UTD) ratios accelerate Actor-Critic learning. While effective, standard high-UTD algorithms typically utilise target networks to stabilise training. This requirement introduces a significant computational bottleneck, rendering them impractical for resource-intensive Quality-Diversity (QD) tasks where sample efficiency and rapid population adaptation are critical. In this paper, we introduce QDHUAC, a sample-efficient, target-free and distributional QD-RL algorithm that provides dense and low-variance gradient signals, which enables high-UTD training for Dominated Novelty Search whilst requiring an order of magnitude fewer environment steps. We demonstrate that our method enables stable training at high UTD ratios, achieving competitive coverage and fitness on high-dimensional Brax environments with an order of magnitude fewer samples than baselines. Our results suggest that combining target-free distributional critics with dominance-based selection is a key enabler for the next generation of sample-efficient evolutionary RL algorithms.

A popular approach to apprenticeship learning (AL) is to formulate it as an inverse reinforcement learning (IRL) problem. The MaxEnt-IRL algorithm successfully integrates the maximum entropy principle into IRL and unlike its predecessors, it resolves the ambiguity arising from the fact that a possibly large number of policies could match the expert's behavior. In this paper, we study an AL setting in which in addition to the expert's trajectories, a number of unsupervised trajectories is available. We introduce MESSI, a novel algorithm that combines MaxEnt-IRL with principles coming from semi-supervised learning. In particular, MESSI integrates the unsupervised data into the MaxEnt-IRL framework using a pairwise penalty on trajectories. Empirical results in a highway driving and grid-world problems indicate that MESSI is able to take advantage of the unsupervised trajectories and improve the performance of MaxEnt-IRL.

This paper presents a model-based reinforcement learning (RL) framework for optimal closed-loop control of nonlinear robotic systems. The proposed approach learns linear lifted dynamics through Koopman operator theory and integrates the resulting model into an actor-critic architecture for policy optimization, where the policy represents a parameterized closed-loop controller. To reduce computational cost and mitigate model rollout errors, policy gradients are estimated using one-step predictions of the learned dynamics rather than multi-step propagation. This leads to an online mini-batch policy gradient framework that enables policy improvement from streamed interaction data. The proposed framework is evaluated on several simulated nonlinear control benchmarks and two real-world hardware platforms, including a Kinova Gen3 robotic arm and a Unitree Go1 quadruped. Experimental results demonstrate improved sample efficiency over model-free RL baselines, superior control performance relative to model-based RL baselines, and control performance comparable to classical model-based methods that rely on exact system dynamics.

Reinforcement fine-tuning with verifiable rewards (RLVR) has emerged as a powerful paradigm for equipping large vision-language models (LVLMs) with agentic capabilities such as tool use and multi-step reasoning. Despite striking empirical successes, most notably Visual Agentic Reinforcement Fine-Tuning (Visual-ARFT), the theoretical underpinnings of this paradigm remain poorly understood. In particular, two critical questions lack rigorous answers: (i)how does the composite structure of verifiable rewards (format compliance, answer accuracy, tool executability) affect the convergence of Group Relative Policy Optimization (GRPO), and (ii)why does training on a small set of tool-augmented tasks transfer to out-of-distribution domains? We address these gaps by introducing the \emph{Tool-Augmented Markov Decision Process} (TA-MDP), a formal framework that models multimodal agentic decision-making with bounded-depth tool calls. Within this framework, we establish three main results. First, we prove that GRPO under composite verifiable rewards converges to a first-order stationary point at rate $O(1/\sqrt{T})$ with explicit dependence on the number of reward components and group size (\textbf{Theorem1}). Second, we derive a \emph{Reward Decomposition Theorem} that bounds the sub-optimality gap between decomposed per-component optimization and joint optimization, providing a precise characterization of when reward decomposition is beneficial (\textbf{Theorem2}). Third, we establish a PAC-Bayes generalization bound for tool-augmented policies that explains the strong out-of-distribution transfer observed in Visual-ARFT (\textbf{Theorem~3}).

Test-time training (TTT) adapts model parameters on unlabeled test instances during inference time, which continuously extends capabilities beyond the reach of offline training. Despite initial gains, existing TTT methods for LRMs plateau quickly and do not benefit from additional test-time compute. Without external calibration, the self-generated reward signal increasingly drifts as the policy model evolves, leading to both performance plateaus and diversity collapse. We propose TEMPO, a TTT framework that interleaves policy refinement on unlabeled questions with periodic critic recalibration on a labeled dataset. By formalizing this alternating procedure through the Expectation-Maximization (EM) algorithm, we reveal that prior methods can be interpreted as incomplete variants that omit the crucial recalibration step. Reintroducing this step tightens the evidence lower bound (ELBO) and enables sustained improvement. Across diverse model families (Qwen3 and OLMO3) and reasoning tasks, TEMPO improves OLMO3-7B on AIME 2024 from 33.0% to 51.1% and Qwen3-14B from 42.3% to 65.8%, while maintaining high diversity.

In gradient-based learning, a step size chosen in parameter units does not produce a predictable per-step change in function output. This often leads to instability in the streaming setting (i.e., batch size=1), where stochasticity is not averaged out and update magnitudes can momentarily become arbitrarily big or small. Instead, we propose intentional updates: first specify the intended outcome of an update and then solve for the step size that approximately achieves it. This strategy has precedent in online supervised linear regression via Normalized Least Mean Squares algorithm, which selects a step size to yield a specified change in the function output proportional to the current error. We extend this principle to streaming deep reinforcement learning by defining appropriate intended outcomes: Intentional TD aims for a fixed fractional reduction of the TD error, and Intentional Policy Gradient aims for a bounded per-step change in the policy, limiting local KL divergence. We propose practical algorithms combining eligibility traces and diagonal scaling. Empirically, these methods yield state-of-the-art streaming performance, frequently performing on par with batch and replay-buffer approaches.

We study finite-horizon continuous-time policy evaluation from discrete closed-loop trajectories under time-inhomogeneous dynamics. The target value surface solves a backward parabolic equation, but the Bellman baseline obtained from one-step recursion is only first-order in the grid width. We estimate the time-dependent generator from multi-step transitions using moment-matching coefficients that cancel lower-order truncation terms, and combine the resulting surrogate with backward regression. The main theory gives an end-to-end decomposition into generator misspecification, projection error, pooling bias, finite-sample error, and start-up error, together with a decision-frequency regime map explaining when higher-order gains should be visible. Across calibration studies, four-scale benchmarks, feature and start-up ablations, and gain-mismatch stress tests, the second-order estimator consistently improves on the Bellman baseline and remains stable in the regime where the theory predicts visible gains. These results position high-order generator regression as an interpretable continuous-time policy-evaluation method with a clear operating region.

Local prediction-error-based curiosity rewards focus on the current transition without considering the world model's cumulative prediction error across all visited transitions. We introduce Curiosity-Critic, which grounds its intrinsic reward in the improvement of this cumulative objective, and show that it admits a tractable per-step surrogate: the difference between the current prediction error and the asymptotic error baseline of the current state transition. We estimate this error baseline online with a learned critic co-trained alongside the world model; since the critic only has to learn how hard a transition is to predict, its estimate of the irreducible noise floor converges well before the world model saturates, redirecting exploration toward learnable transitions. The reward is higher for learnable transitions and collapses toward zero for stochastic ones, thereby separating epistemic (reducible) from aleatoric (irreducible) prediction error online. Prior prediction-error curiosity formulations, from Schmidhuber (1991) to learned-feature-space variants, emerge as special cases corresponding to specific approximations of this error baseline. Experiments on a stochastic grid world show that Curiosity-Critic outperforms prediction-error, visitation-count, and Random Network Distillation methods in training speed and final world model accuracy.

Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove that this solution ensures monotonic performance improvement. To handle parameterized policy classes, we develop a policy optimization algorithm called Bounded Policy Optimization (BPO) that minimizes an advantage-weighted divergence between the policy and the analytic optimal solution from BRRL. We further establish a lower bound on the expected performance of the resulting policy in terms of the BPO loss function. Notably, our framework also provides a new theoretical lens to interpret the success of the PPO loss, and connects trust region policy optimization and the Cross-Entropy Method (CEM). We additionally extend BPO to Group-relative BPO (GBPO) for LLM fine-tuning. Empirical evaluations of BPO across MuJoCo, Atari, and complex IsaacLab environments (e.g., Humanoid locomotion), and of GBPO for LLM fine-tuning tasks, demonstrate that BPO and GBPO generally match or outperform PPO and GRPO in stability and final performance.

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.

Search agents achieve strong question-answering performance through multi-turn interactions with search engines, with Group Relative Policy Optimization (GRPO) being a widely used training algorithm. However, GRPO-style algorithms still face several challenges in multi-hop search settings. First, correct intermediate steps are often penalized when the final answer is wrong. Second, training is highly unstable, often causing degradation of natural language ability or even catastrophic training collapse. Our analysis attributes these issues to coarse-grained advantage assignment and an imbalance between positive and negative advantages. To address these problems, we propose CalibAdv, an advantage calibration method specifically designed for search agents that enables more accurate and more stable modeling of penalties and rewards. Specifically, CalibAdv leverages the correctness of intermediate steps to downscale excessive negative advantages at a fine-grained level. It then further rebalances positive and negative advantages to improve training stability. Importantly, CalibAdv adopts a lightweight design that calibrates advantages from standard rollout signals, making it simple and easy to deploy. Extensive experiments across three models and seven benchmarks demonstrate that CalibAdv improves both model performance and training stability. Our code is available at https://github.com/wujwyi/CalibAdv.