Deep Reinforcement Learning

Safe reinforcement learning (RL) aims to learn policies that optimize rewards while satisfying constraints. Predominant approaches rely on soft-constrained policy optimization, which has achieved empirical success but does not provide formal safety guarantees for the learned policy. In contrast, methods with strict guarantees typically rely on explicit certificate functions, whose construction requires the direct synthesis and verification of control-invariant sets, a process that scales poorly with state dimension and often yields overly conservative behavior. In this paper, we present the Provably Safe, yet Scalable RL (PS2-RL) framework, a novel two-phase architecture for learning provably safe policies in a scalable manner, designed to overcome the key bottlenecks of prior methods. Rather than explicitly computing invariant sets, PS2-RL leverages a learned backup policy to forward-integrate the system dynamics, generating an implicit control-invariant set online. In the first phase, the backup policy is trained with our proposed safe-arrival value function, which characterizes the optimal backup policy for invariant-set construction. In the second phase, an RL policy is trained end-to-end through a differentiable projection layer that strictly enforces the safety guarantees induced by the learned backup policy. By maximizing the volume of the implicit control-invariant set in the first phase, the resulting PS2 policy from the second phase is performant and scalable, while maintaining provable safety. Crucially, PS2-RL imposes no restrictions on the underlying RL algorithm and can be plugged into any existing training pipeline. We establish theoretical guarantees for the proposed framework and evaluate it on robotic control tasks with state dimensions up to 10, a regime in which prior provably safe RL methods struggle or become impractical.

Safe reinforcement learning (Safe RL) aims to maximize expected return while satisfying safety constraints, typically modeled as Constrained Markov Decision Processes (CMDPs). While primal-dual methods scale well to deep RL, they often suffer from delayed constraint correction, leading to oscillatory behavior and prolonged safety violations. In this paper, we propose Constraint-Sensitive Policy Optimization (CSPO), a first-order primal-dual method that incorporates local constraint sensitivity into policy updates. CSPO augments the primal objective with a constraint-sensitive correction derived from the shortest signed distance to the safety boundary, enabling smarter recovery steps back to safety, compensating for delayed Lagrange multiplier updates, reducing oscillations near the boundary, and preserving the KKT solutions of the original constrained problem. Experiments on navigation and locomotion benchmarks demonstrate that CSPO achieves faster safety recovery and high reward preservation, resulting in higher constrained returns compared to state-of-the-art primal-dual and penalty-based methods

Auto-bidding is a core component of real-time advertising systems, where decisions must optimize long-term performance under budget and cost constraints, while online exploration is prohibitively risky. Offline reinforcement learning and, more recently, Transformer-based sequence modeling have shown promise for learning bidding policies from logged data, but their unimodal and purely parametric formulations often collapse multiple effective bidding strategies into suboptimal averaged actions and perform unreliably under sparse or long-tail traffic. To mitigate these limitations, we propose DRIVE (Distributional and Retrieval-Augmented Bidding with Value Evaluation), a unified Transformer-based framework that decouples candidate action generation from decision making for offline auto-bidding. DRIVE combines distributional action modeling, retrieval-augmented candidate generation from high-quality historical decisions, and value-based evaluation to select the most promising bid at inference time. Extensive experiments on AuctionNet and additional offline reinforcement learning benchmarks demonstrate that DRIVE consistently improves bidding performance and generalizes well across multiple Transformer-based methods.

Flow-matching and diffusion policies are expressive action generators, but optimizing them with temporal-difference reinforcement learning (RL) remains difficult. Effective policy extraction requires exploiting the critic's action gradient, yet directly backpropagating this signal through a multi-step denoising process can be numerically unstable. Existing methods work around this either by discarding gradient information, distilling the policy into a simpler one-step actor, or repeatedly fine-tuning the denoising policy as the critic improves. We propose QPILOTS, a method that leaves the original policy unmodified and steers the denoising process at inference time. At each denoising step, instead of evaluating the critic on the noisy intermediate action where critic predictions are unreliable, we first project that intermediate state to an estimate of the final clean action and compute the critic gradient there. We introduce two variants: QPILOTS-U uses a fast single-point approximation, while QPILOTS-M draws differentiable posterior samples via a learned auxiliary network. On a standard offline-to-online RL benchmark, QPILOTS achieves the best aggregate performance, reaching an average success rate of 90% across 50 tasks. We also apply QPILOTS to steer a large, frozen, pretrained Vision-Language Action (VLA) foundation model, outperforming or matching prior inference-time approaches across six manipulation tasks in simulation.

Formal safety analysis determines whether a system admits a safe defense; adaptive evaluation characterizes the operating quality sustained under adversarial interaction. Both answers matter because systems with the same safety verdict can impose very different operational burdens. We introduce shielded analysis, a design-time framework that derives these answers from one encoded system while keeping the safety requirement and admissible threat model independently variable. It returns a defensibility certificate and a four-axis defensibility fingerprint spanning structural margin, shield latitude, and adaptive operating quality. Each axis is informative in its own right; their relationships show whether formal and operational assessments agree, diverge, or respond differently to system changes. We instantiate the framework for network defense on a reference segment and four controlled perturbations spanning topology, safety requirements, and adversary capabilities. Every configuration is certified defensible, yet two topology variants with nearly identical structural profiles sustain mean clean-host fractions of 22.7% and 80.7% under adaptive pressure. Shielded analysis turns a safety-game solution into a comparative instrument: it determines whether a defense exists, characterizes what that defense requires, and identifies which system changes strengthen it.

Language model agents are increasingly effective in solving realistic tasks through multi-turn tool use. However, training reliable tool-using agents remains challenging in practice. While reinforcement learning provides an on-policy paradigm for improving agents from their own environment interactions, its effectiveness depends heavily on the training task distribution. When tasks are fixed before training, the task distribution can become increasingly mismatched with the policy's evolving capabilities, causing many rollouts to be spent on uninformative tasks. We propose SENTINEL, a failure-driven reinforcement learning framework that turns the Solver's rollout failures into targeted training tasks. SENTINEL follows a Controller--Proposer--Solver loop: the Controller analyzes failed trajectories and summarizes recurring error patterns, the Proposer generates executable tasks that stress these weaknesses, and the Solver is trained on the targeted tasks. On Tau2-Bench Retail with Qwen3-4B-Thinking-2507, SENTINEL improves Pass^{}1 from 66.4 to 74.9 and outperforms RL on general synthetic tasks across Pass^{}k metrics. These results demonstrate that model failures provide an effective and scalable source of targeted training signal for improving tool-using language model agents.

Quantum circuit routing is a key step in compiling programs for noisy intermediate-scale quantum processors. Routes that appear efficient by standard overhead metrics can still lose fidelity when they pass through poorly calibrated couplers. We study a calibration-aware graph reinforcement-learning router that uses same-day IBM Heron r2 calibration data to choose hardware-edge SWAPs. We train the policy with proximal policy optimization and evaluate it with exact simulated fidelity across nine Munich Quantum Toolkit (MQT) Bench circuits and three calibration snapshots. Across these evaluations, pooled mean exact fidelity is $0.727$, compared with $0.440$ for SABRE-best20 and $0.481$ for target-aware SABRE. We observed that fidelity gains came with higher routed two-qubit counts and were concentrated in 5 qubit and 8 qubit circuit families; under the fixed tree action graph, all 10 qubit families favored SABRE-best20. Overall, our results show that calibration-aware learned routing can improve fidelity beyond gate-count-driven compilation.

Recent reinforcement learning approaches have shown great promise in improving humanoid motion tracking performance and achieving fall recovery under disturbances. However, most existing works treat motion tracking and fall recovery as different tasks and require multi-stage training with specialized recovery rewards and/or separate recovery policies. Moreover, existing reinforcement learning-based methods often terminate training episodes immediately after severe tracking failures, limiting recovery-oriented exploration in unstable or fallen states. To address the above issues, we propose Stubborn, a streamlined and unified reinforcement learning framework to achieve robust humanoid motion tracking and fall recovery. Specifically, Stubborn uses an asymmetric Actor-Critic architecture and consists of three major components. First, a yaw-aligned tracking representation is adopted to reduce sensitivity to global drift and heading disturbances while preserving gravity-related balance information. Second, we introduce a Bernoulli-based probabilistic termination mechanism that enables the policy to encourage exploration of fall-recovery behaviors under varying failure modes. Third, we propose a probabilistic termination and tracking-error-driven strategy that dynamically reshapes the sampling distribution based on tracking performance, increasing the training efficiency for difficult motion segments and unstable states. Extensive comparisons with SOTA methods and ablation studies show that Stubborn achieved competitive performance, and the proposed probabilistic termination mechanism and adaptive sampling strategy contributed to the performance and robustness gains. For real-world demonstrations, please refer to https://aislab-sustech.github.io/Stubborn/.

Reinforcement Learning (RL) with verifiable environments has emerged as a powerful approach for enhancing the reasoning capabilities of Large Language Models (LLMs). While prior research demonstrates that scaling environment quantity improves RL performance, existing manual or individual construction methods suffer from linear scaling limits, thereby hindering scalable reasoning generalization. This paper introduces RACES (\textbf{R}ecursive \textbf{A}utomated \textbf{C}omposition for \textbf{E}nvironment \textbf{S}caling), a framework that conceptualizes verifiable environments as composable building blocks that can be recursively assembled. The key insight is that when the codomain (output type) of one environment matches the domain (input type) of another, they can be automatically fused into a new verifiable environment, enabling recursive composition. RACES is implemented with 300 individual environments and defines a set of composition operators (\textsc{SEQUENTIAL}, \textsc{PARALLEL}, \textsc{SORT}, and \textsc{SELECT}) that induce diverse reasoning patterns. Extensive experiments show that RL training on these composite environments consistently enhances reasoning generalization. Specifically, RACES improves DeepSeek-R1-Distill-Qwen-14B by an average of 3.1 points (from 48.2 to 51.3) and boosts Qwen3-14B performance from 58.8 to 61.1 on six benchmarks, which are unseen during the construction of training environments. Moreover, RACES achieves performance comparable to training on 300 individual environments using only 50 base environments, demonstrating significant efficiency in environment utilization.

Reinforcement learning (RL) has become a key component in modern large language models, yet the rollout stage remains the key bottleneck in RL training pipelines. Although Multi-Token Prediction (MTP) offers a natural solution to accelerate rollouts through speculative decoding, many studies have observed that MTP acceptance rates degrade significantly during RL training, leading to limited speedup performance. To address this bottleneck, we present Bebop, a systematic study of MTP in LLM post-training, and offer practical recipes to integrate MTP into large-scale RL pipelines. First, we reveal that the MTP acceptance rate is fundamentally bounded by the fluctuation of model entropy, which demonstrates a clear negative linear relationship with the rise of entropy in the RL stage. Second, we show that probabilistic rejection sampling largely alleviates the disturbance introduced by entropy in RL compared to greedy draft sampling. We further identify that the conventional MTP training objectives (cross-entropy or KL) are suboptimal in such settings, and therefore we propose a novel end-to-end TV loss that directly optimizes multi-step rejection sampling acceptance rate, yielding ~10% acceptance rate improvements, achieving up to 95% acceptance rates and up to 25% extra inference throughput gains across mathematical reasoning, code generation, and agentic tasks. Third, we test various online MTP training strategies during RL and show that pre-RL MTP training with e2e TV loss and rejection sampling achieves a consistent acceptance rate and speedup throughout the entire RL, eliminating the need for costly online MTP updating. We provide extensive experiments and analysis that validate our findings. Experimental results show our method achieves up to 1.8x end-to-end acceleration in async RL training of Qwen3.5, Qwen3.6, and Qwen3.7 models.

Gradient-based adversarial attacks remain a dominant threat to deep neural networks (DNNs), as they exploit gradient information to efficiently optimize adversarial perturbations. To address this, we investigate whether reinforcement learning (RL) training can disrupt the gradient structure used by attackers by training image classifiers with policy-gradient objectives and epsilon-greedy exploration. Through systematic experiments across CIFAR-10, CIFAR-100, and ImageNet-100 with multiple architectures, we find that RL-trained classifiers significantly disrupt gradient-based adversarial optimization. To explain this, we conduct a comprehensive mechanism analysis using loss landscape visualization, static and dynamic gradient indicators, and predictive entropy. Our analysis reveals that RL acts as an implicit regularizer, producing models with highly unstable gradient directions and smaller gradient magnitudes. This combination makes each PGD step both unreliable in direction and limited in magnitude, causing gradient-based attacks to fail within practical iteration budgets. We further show that combining RL with adversarial training (RL-adv) provides a dual-layer defense operating at two complementary levels: RL degrades gradient information available to attackers (gradient-level defense), while adversarial training strengthens decision boundaries (boundary-level defense). RL-adv achieves the highest robustness across all major attack types evaluated, including gradient-based (PGD, AutoAttack), transfer-based, and query-based attacks, outperforming SL-adv by a significant margin. These findings identify RL-induced gradient disruption as a complementary robustness mechanism and motivate future research on hybrid SL-RL training schedules that combine SL's efficiency with RL's gradient-regularization properties.

Existing methods for exploring cellular automata and other complex systems mostly operate in open loop: they set initial conditions, execute a full simulation, and observe the outcome, without intervening during execution. We introduce a closed-loop framework based on autotelic reinforcement learning, in which an agent autonomously samples diverse goals and learns a goal-conditioned policy to intervene in a complex system through minimal, local perturbations. We instantiate this framework on Lenia, a continuous cellular automaton known for life-like self-organizing patterns, in an agentic system we call CARL, and demonstrate three capabilities. First, CARL discovers stable solitons across a wide range of Lenia update rules at a higher rate than heuristic baselines. Second, it learns to steer the movement direction of existing solitons with few interventions, showing that CARL can control self-organizing patterns, not only create them. Third, humans can use trained agents to guide solitons through maze environments in real time by specifying high-level directional commands that the agent translates into low-level interventions. Trained across diverse goals, update rules, and random initial states, the agents acquire policies that generalize zero-shot to various out-of-distribution conditions. These results suggest a path toward artificial experimentalist agents that, autonomously or with human guidance, discover and control emergent phenomena in complex systems.

Deep Reinforcement Learning (DRL) has shown promise for social navigation, yet its real-world deployment remains hindered by a persistent sim-to-real gap arising from simplified first-order dynamics and context-specific human state estimation pipelines. This work presents a unified framework that addresses these limitations to produce dynamically feasible navigation policies suitable for real-world deployment. First, theoretical analysis reveals that tracking error between simulated and actual robot position decays exponentially with increased control order, motivating the use of higher-order control inputs as DRL action space. A second-order control formulation tailored to differential drive robots is developed, complemented by a stochastic iterative Linear Quadratic Regulator (iLQR) that pretrains the policy via a divergence minimization objective. Second, to avoid the added system complexity of camera-LiDAR fusion, a cluster-based human tracking pipeline using only 2D LiDAR is introduced. Human detections are associated according to both spatial proximity and velocity similarity, enabling reliable differentiation of nearby pedestrians and yielding stable velocity estimates through temporal aggregation. Third, we introduce an unbiased residual gating block to balance reaction- and memory-based behaviors while handling time-varying crowd sizes, both critical for social navigation. The resulting policy, KinematicRL, consistently improves kinematic performance and adapts to varying number of detected humans. Experiments in real-world environments demonstrate that, when combined with the proposed tracking pipeline, KinematicRL can be deployed on a real differential drive robot with minimal modifications.

There are two main Parameter-Efficient Fine-Tuning (PEFT) techniques for Large Language Models (LLMs). While Low-Rank Adaptation (LoRA) introduces additional weights between the LLM layers, Soft Prompting introduces additional fine-tuning-specific raw tokens to an LLM input. However, both require modification to the computational graphs of precompiled, preoptimized LLMs. As a result, neither is fully supported in high-throughput engines like vLLM. We propose fine-tuning with ART (Art-based Reinforcement Training). The method injects information into a frozen Multimodal Large Language Model (MLLM) by optimizing only its raw visual input, thus enabling the soft-token approach on pre-compiled computational graphs. It relies on backpropagation of gradients back into a plain pixel array and thus supports any fine-tuning objective. Moreover, the optimized visual input can be stylized as task-relevant computational artworks. The approach's effectiveness is confirmed for different sizes of a popular open Qwen architecture and for several textual benchmarks. Specifically, ART reaches accuracy competitive with LoRA across mathematics and structured-tool-use benchmarks.

Lifelong embodied navigation in dynamic environments requires robots to form persistent scene understanding from fragmentary observations, which remains difficult for existing methods that rely on explicit maps or scene graphs and struggle to generalize beyond structured settings. We propose AllDayNav, a lifelong self-learning navigation framework that implicitly encodes scene dynamics into the billion-scale parameters of a large model via reinforcement learning, powered by a self-evolving multimodal memory that maintains and updates visual keyframes, semantic descriptions, and temporal context while autonomously generating open-vocabulary instructions, image goals, and structured rewards. Experiments in both synthetic and real-world environments across cross-room, cross-episode, and cross-task scenarios show that AllDayNav achieves success rates approaching $100\%$ and consistently surpasses strong map-based, VLM, and RL baselines in path efficiency and robustness, demonstrating implicit, memory-driven reinforcement learning as a scalable alternative to explicit mapping for reliable lifelong navigation.

Learning-based visual navigation for legged robots typically relies on continuous goal updates from hierarchical state estimation to provide a persistent directional reference. This reliance incurs additional sensory and computational overhead and deviates from fully end-to-end mobile autonomy. Furthermore, under partial observability, policies are prone to learn myopic behaviors, easily becoming trapped in dead ends and complex structural layouts. To address these limitations, we investigate a goal-initialized navigation setting, where the target is provided only once at the beginning of an episode, requiring the robot to operate based on intrinsic spatial memory without subsequent goal updates from external modules. In this work, we propose GUIDE, a fully end-to-end reinforcement learning framework designed to cultivate internal directional awareness. Specifically, GUIDE incorporates a spatial anchor predictor that leverages multi-frequency proprioceptive history to extract egomotion representations, thereby maintaining a persistent long-horizon spatial context for navigation. Concurrently, it utilizes raw depth streams to perceive local environmental geometry. We evaluate the proposed framework across both simulation and real-world scenarios on a quadruped robot. Experiments show that GUIDE learns reliable egomotion and directional awareness, enabling a fully end-to-end deployed policy to safely navigate through dense clutter and structured mazes without subsequent goal guidance or prior maps.

Diffusion policies (DPs) have emerged as expressive policy representations for robot learning, often used with imitation learning methods such as behavioral cloning (BC). However, while their success has largely been confined to BC, direct reinforcement learning (RL) fine-tuning remains challenging because actions are generated through a multi-step denoising process. In this work, we propose MODIP, a framework for the offline-to-online fine-tuning of DPs. Rather than directly applying RL to the DPs, MODIP leverages a world model (WM) to guide policy adaptation and keeps the simplicity and stability of BC. We utilize model predictive control (MPC) to generate high-quality trajectories within the WM, and use them as supervised targets for fine-tuning the DP. To make MPC planning efficient, MODIP uses a terminal state value instead of a policy-dependent state-action value, reducing inference time. Additionally, MODIP trains critics with policy-independent TD targets, reducing training time. Experiments on D4RL (MuJoCo, Kitchen) and RoboMimic tasks show that MODIP improves diffusion policies beyond BC, and is competitive with or outperforms diffusion policy RL fine-tuning methods and strong model-based baselines such as TD-MPC2.

Token-level credit assignment remains a key obstacle for reinforcement learning (RL) in large language models (LLMs), where RL recipes typically treat all tokens equally, failing to distinguish decisive reasoning steps from routine formatting or fluent filler. Recent attempts leverage model-internal signals to assign finer-grained credit, but these are often point-wise heuristics that ignore the global structure of information propagation. We propose FlowTracer, an RL framework that traces answer-targeted reasoning flow on an attention-induced directed acyclic graph in which nodes correspond to tokens and edge capacities come from aggregated attention weights and derives token credit from this global structure. The edge capacities are reweighted to retain only the influence that can reach the answer region, while enforcing local flow conservation so intermediate tokens neither lose nor gain effective mass due to path length or irrelevant branches. On this graph, FlowTracer extracts an information-flow backbone connecting the question to the answer and scores tokens by flow throughput, revealing high-impact hubs and aggregation checkpoints that mediate long-range dependencies. These derived importances are used to shape token-level rewards, enabling learning signals to focus precisely on the tokens that route information toward (or away from) correct answers and delivering consistent performance gains across a range of reasoning tasks.

Current reinforcement learning from human feedback (RLHF) methods primarily rely on scalar rewards from a trained reward model (RM). While effective, scalar rewards are often noisy and fail to capture fine-grained preference differences, whereas RM hidden states encode richer semantic and preference information. We introduce the representation-aware advantage estimation, which leverages RM hidden states and models them as auxiliary signals for better advantage estimation. Specifically, we propose the Graph-based Advantage Estimation (GraphAE), treat each sampled group as a graph, where nodes correspond to responses and edges capture their similarity in the RM hidden space. Then advantages are computed via graph propagation, enabling each sample to incorporate contextual information from its neighbors. GraphAE is lightweight and can be seamlessly integrated into existing group-based RL algorithms. We apply GraphAE to GRPO, GSPO and RLOO, and conduct extensive experiments on different models and benchmarks. Empirical results show consistent improvements across three benchmarks, with gains of up to + 6.3 on Arena-Hard-v0.1, + 8.27 on AlpacaEval 2.0, and + 0.22 on MT-Bench. These results demonstrate that leveraging RM representations leads to more sample efficient and robust RLHF.

The financial market is a typical low signal-to-noise ratio (SNR) setting, which often destabilizes off-policy maximum-entropy methods like Soft Actor-Critic (SAC). Specifically, noisy state representations may produce unreliable Q-value estimates, and bootstrapping amplifies these errors, forming a failure mode we call the "Financial Entropy Trap". In this paper, we propose FPQC-SAC, an efficient and plug-and-play SAC variant that places a compact and bounded Parameterized Quantum Circuit (PQC) before the actor and critic networks to constrain feature propagation at the representation level, rather than filtering raw inputs or regularizing Q-values after bootstrapping. Notably, FPQC-SAC reduces the impact of extreme market fluctuations on Bellman target estimation, while trainable quantum entanglement preserves flexible cross-asset interactions. Empirical evaluations on real-world portfolio management tasks demonstrate that FPQC-SAC substantially enhances out-of-sample stability and cumulative returns by achieving a 66.89% relative gain in cumulative return over standard unconstrained SAC and outperforms the best continuous-control deep reinforcement learning baseline by approximately 27%. Open-source code is available at https://github.com/ZeyuLIU-UST/FPQC-SAC-main.

The cost signal that constrained-RL algorithms optimize against is almost always reactive: the simulator emits a non-zero cost only after a collision has begun, and the Lagrange multiplier of PPO-Lagrangian grows only after the episode budget has been exceeded. At race speeds, where collisions are instantaneous and irreversible, any safety mechanism that waits for cost to accumulate is structurally too late. We present VLM-Safe-RL, a framework that integrates a frozen vision-language model into the CMDP Lagrangian update as an anticipatory cost term. The framework comprises four contributions: (i) Decoupled Dual-Path CLIP, independent reward/cost paths that respect the CMDP's factorization; (ii) VLM-Lagrange, an augmented multiplier update that incorporates a per-step VLM cost as an anticipatory term; (iii) Confidence Gating, a Bayes-optimal weight derived from a logistic noise model on the CLIP margin; and (iv) VLMPPOLag, the composed algorithm. On Safety-Gymnasium FormulaOne L2, our principal evaluation ($n{=}5$ seeds, $10^{6}$ steps, budget $d_{\text{lim}}{=}25$) VLMPPOLag$+$Conf is the only configuration in our default budget comparison that simultaneously retains substantive return ($J_r{\approx}40$) and holds cost within budget on a majority of seeds; the five constraint-aware baselines (PPOLag, CPO, CPPOPID, CPO-CLG, PPOLag-RND) each fail at least one requirement. The mechanism generalizes to held-out MetaDrive Medium (catastrophe rate $41\%{\to}26\%$, 95% bootstrap CI $[-26,-5]$,pp) and shows directionally consistent transfer to Bullet Safety-Gym; we report honestly where it does not (MetaDrive Easy/Hard, Qwen2-VL backbone) and trace the Hard failure to a Lagrangian-regulation pathology rather than the VLM signal itself. To our knowledge, this is the first work to use frozen VLM signals as an anticipatory cost term inside the CMDP Lagrangian update.

While deep Reinforcement Learning (deep-RL) has been increasingly applied to parameter control in evolutionary algorithms, rigorous theoretical analysis of parameter control remains largely restricted to single-parameter settings, owing to the difficulty of deriving effective, interpretable multi-parameter policies amenable to formal study. We demonstrate how deep-RL can be leveraged to overcome this barrier, using the (1+($λ$,$λ$))-genetic algorithm optimizing OneMax, one of the few problems where a super-constant speedup of dynamic control has been formally proven, as a representative case study. We first show that standard approaches struggle to converge in this multi-parameter setting, and introduce algorithm-agnostic enhancements targeting action-space decomposition, reward shifting, and long-horizon discounting. With these in place, we compare common deep-RL methods and find that Double Deep Q-Networks uniquely avoid the policy collapse observed in Proximal Policy Optimization, yielding trajectories suitable for downstream analysis. Crucially, we move beyond the ``black-box'' nature of neural networks by distilling the learned behaviors into a transparent, symbolic control policy. This resulting policy does not only offer interpretability for future theoretical analysis but also yields exceptional performance, consistently outperforming existing baselines across a wide range of problem sizes.

Continual training of deep neural networks under non-stationarity often leads to a progressive loss of plasticity, eventually limiting further learning. We relate plasticity to the empirical Neural Tangent Kernel, and identify dynamical isometry (the condition that layer-wise Jacobian singular values remain close to one) as a key mechanism for preserving plasticity in continual learning. We revisit a class of networks that are almost-everywhere isometric while remaining universal Lipschitz function approximators, demonstrating that near-dynamical isometry is compatible with expressive nonlinear representations. For general architectures, we propose an efficient isometry-promoting regularization scheme and identify a novel mechanism by which it can reactivate dormant ReLU units. Building on this, we introduce AdamO, an Adam-style adaptive optimizer that decouples isometry regularization from gradient updates, analogous to AdamW. We further reinterpret prior plasticity-preserving approaches through the lens of dynamical isometry, showing that they target only a partial measure of isometry. Across supervised and reinforcement-learning continual-learning benchmarks designed to induce plasticity loss, our methods consistently match or outperform existing approaches.

Offline safe reinforcement learning (Safe RL) enables policy learning without online interactions, making it suitable for safety-critical systems such as robotics systems. However, its reliance on static datasets exposes offline Safe RL to data poisoning attacks, where adversaries inject malicious samples that compromise safety and induce unsafe policy behavior. In this work, we propose a new learning paradigm, named safe reinforcement unlearning (Safe-RULE), used as a defense framework to remove the influence of poisoned data without retraining from scratch or requiring access to the original training environment. We further extend reinforcement unlearning to offline Safe RL by explicitly accounting for both task performance and safety constraints during the unlearning process. Experiments across benchmark Safe RL tasks demonstrate that our approach effectively enhances safety performance against data poisoning attacks.

Hindsight relabeling usually turns achieved future states into exact goals, which can overconstrain offline robot learning when task success depends only on a subset of the state. We propose Goal-Set Hindsight Relabeling (GS-HER), a predicate-level generalization of HER in which achieved states certify query-defined goal sets rather than singleton goal states. A binary query specifies which variables define success, making the goal predicate an inference-time input while leaving the underlying offline GCRL algorithm unchanged. Across OGBench tasks and five offline goal-conditioned learners, GS-HER improves performance when full-state goals are bottlenecked by nuisance dimensions and turns hindsight relabeling into a reusable goal interface: one checkpoint can answer multiple robot goal predicates without retraining.

Image and video captioning are fundamental tasks that bridge the visual and linguistic domains, playing a critical role in pre-training Large Vision-Language Models (LVLMs). Current state-of-the-art captioning models are typically trained with Supervised Fine-Tuning (SFT), a paradigm that relies on expensive, non-scalable annotations and often causes models to memorize specific ground-truth answers, limiting their generality and ability to generate diverse, creative descriptions. To overcome these limitations, we propose applying Reinforcement Learning with Verifiable Rewards (RLVR) to the open-ended task of multimodal captioning. We introduce Captioning Reinforcement Learning++ (CapRL++), a novel reference-free training framework that redefines caption quality through its utility: a high-quality caption should enable a non-visual language model to accurately answer questions about the corresponding visual content. CapRL++ employs a decoupled two-stage pipeline where an LVLM generates a caption, and the objective reward is derived from the accuracy of a separate, vision-free LLM answering Multiple-Choice Questions based solely on that caption. Evaluations on more than 20 image and video benchmarks show that CapRL++ improves dense caption quality and strengthens caption-based pretraining across tasks such as spatial and temporal understanding. Pretraining on scalable image and video caption datasets annotated by CapRL++ yields substantial downstream gains. Furthermore, within the Prism Framework for caption quality evaluation, compact models trained with CapRL++ achieve dense captioning performance comparable to substantially larger models such as Qwen2.5-VL-72B and Qwen3-VL-235B-A22B. These results validate that CapRL++ effectively trains models to produce generalizable, high-fidelity descriptions, establishing a robust foundation beyond the limitations of traditional SFT.

Long-horizon agentic tasks pose a fundamental credit assignment challenge for outcome-base reinforcement learning: trajectory-level rewards verify final correctness but provide limited guidance on which intermediate reasoning steps or tool interactions contribute to the outcome. The difficulty is especially pronounced in multi-turn search agents, where successful trajectories may contain misleading actions and failed trajectories may contain valuable evidence-gathering steps. We propose PBSD (Privileged Bayesian Self-Distillation), a Bayes-calibrated self-distillation method for fine-grained credit assignment under sparse final rewards. PBSD measures trajectory quality through the posterior-to-prior probability ratio of the verified answer and applies Bayes' rule to convert this hard-to-estimate answer-side ratio into a tractable likelihood ratio between a standard student model and a privileged answer-conditioned teacher model. Autoregressive decomposition of this Bayesian evidence score yields turn-level signals that identify whether each intermediate turn supports or undermines the verified outcome. Consequently, PBSD provides a principled and elegant reweighting scheme that transforms sparse outcome supervision into Bayes-calibrated turn-level credit signals, while remaining fully compatible with standard policy optimization. Experiments demonstrate that PBSD consistently enhances performance across both in-domain and out-of-domain settings, and effectively transfers knowledge from short-context training to long-context inference, suggesting that its fine-grained credit assignment mechanism facilitates more effective policy learning and yields improved generalization.

Deep reinforcement learning (DRL) frameworks for portfolio optimization have shown promise for their ability to learn allocation rules dynamically from market data. However, these models fail to account for fat-tailed returns, which characterize actual market behavior with more frequent extreme events. Furthermore, historical data is treated homogeneously, without accounting for temporal importance, leading models to fail during regime changes. We propose a new BAVAR-BLED algorithm that combines methods derived from Bayesian-Averaging Vector Autoregressive (BAVAR) and the Black-Litterman model using Elliptical Distributions (BLED) within a TD3 architecture. BAVAR captures a set of vector autoregressive representations that consider multi-scale temporal features, enabling adaptive allocation decisions based on regime-aware estimates of return expectations and dispersion matrices. These estimates serve as prior inputs to BLED, a model that uses Student's t-distributions, allowing for more realistic fat tail return estimates. The BAVAR-BLED algorithm uses transformer networks for view construction and CNNs for risk-aversion estimates, which modify dynamic allocation decisions based on market conditions. An evaluation of 29 Dow Jones Industrial Average constituents over a decade-long market period shows that BAVAR-BLED significantly outperforms state-of-the-art methods, achieving Sharpe and Sortino ratios of 1.72 and 2.70, respectively, and total returns of 57.26%.

Two-stage post-training -- a Stage-1 warm-start (supervised fine-tuning, SFT, or on-policy distillation, OPD) followed by Stage-2 reinforcement learning (RL) -- is increasingly used for vision-language models (VLMs). We ask what Stage-1 actually controls in a small-data study using Qwen2.5-VL-7B with a same-modality 72B VLM teacher for OPD. First, the three warm-starts reach a narrow $53$--$54\%$ band on Geometry3K internal validation, consistent with the narrow range reported by recent specialized methods; this setup provides little evidence that Stage-1 changes the in-domain endpoint. Second, a matched-recipe, early-stopped SFT improves out-of-domain MathVista by $+2.1$ points, reversing the $-9.5$-point drop of an over-trained variant. The clearest difference is the \emph{entropy regime}: OPD enters RL with substantially higher policy entropy than either SFT initialization, and the separation remains visible through the available trajectories. At the in-domain initialization, OPD also has higher answer diversity and pass@16 ($+2.0$ to $+5.2$ points over SFT), although problem-level bootstrap intervals show that the smaller contrast is uncertain. The advantage is absent after RL (endpoint pass@16 values within $1.1$ points) and on MathVista (six models within $1.2$ points). Our contribution is therefore a bounded empirical characterization: Stage-1 is strongly associated with the entropy regime in this setup, but the downstream payoff is small, localized, and not evidence that OPD is a better RL warm-start.

Vision-Language-Action models face significant challenges in real-world deployment due to the entanglement of high-level reasoning with low-level control, and the instability of policy optimization. In this paper, we introduce SyVLA, a robust VLA model trained with diversified experiences. We propose an Intention Decoupling algorithm to isolate control-relevant features from reasoning contexts and a similar-sample guided RL pipeline to stabilize policy updates and mitigate distribution shift. Extensive experiments on real-world robotic tasks and multi-modal benchmarks demonstrate that SyVLA achieves superior task success rates and stronger out-of-distribution generalization compared to existing methods, while effectively preserving core vision-language capabilities. Codes and Datasets is released on \href{https://sy-vla.github.io/}{project page}.

Baichuan-M4 is Baichuan Intelligence's clinical-grade medical large model, designed for continuous care rather than single-turn medical question answering. It is built as a coordinated medical agent system around three pillars: Baichuan-Harness, a unified runtime that keeps reinforcement-learning training and real-world deployment consistent while enforcing action constraints, tool use, long-term patient memory, and multi-agent coordination; a core reasoning model trained with a continuous-care reinforcement-learning framework that integrates span-level reward modeling (SPAR++), reasoning-path compression, curriculum learning, and stabilized policy optimization; and a clinical tool layer for patient-memory management, authoritative evidence-based retrieval, and multimodal medical perception across documents, X-rays, and dermatology. On a cross-dimensional medical evaluation suite, Baichuan-M4 attains leading results in static medical knowledge and safety, dynamic OSCE-style consultation, long-context clinical memory, evidence-based retrieval, medical document OCR, and multimodal image understanding, while lowering the hallucination rate to 3.3%.

Reinforcement Learning from Human Feedback (RLHF) has significantly improved the quality and fluency of large language models in text summarization. However, its impact on affective properties remains insufficiently understood. In this work, we study sentiment drift, a systematic shift toward neutral sentiment in RLHF-based summarization outputs compared to source texts. We conduct extensive experiments across multiple datasets, model architectures, and eight languages to analyze how alignment objectives influence sentiment preservation. Our results show that sentiment drift is a consistent phenomenon that becomes stronger with increased KL regularization strength, indicating a trade-off between alignment stability and affective fidelity. To explain this behavior, we introduce a Policy Attribution framework that decomposes the RLHF objective and quantifies the contribution of its components. Our analysis reveals that KL regularization is the primary driver of sentiment suppression across all settings. Based on these findings, we propose a sentiment-aware modification of the KL regularization term, which selectively reduces constraints on sentiment-bearing tokens. Empirical results demonstrate that this approach mitigates sentiment drift while maintaining summarization quality. Overall, our findings highlight a fundamental limitation of current alignment methods: while they improve factual consistency and safety, they may unintentionally suppress emotional expressiveness. This motivates the development of alignment strategies that explicitly account for affective preservation.

Standard Reinforcement Learning with Verifiable Rewards (RLVR) training allocates a fixed rollout budget to every query, without regard for what each query's difficulty means for the current policy. This leads to two symmetric failure modes: easy queries produce near-zero advantage because the policy already solves them, while unsolvable queries produce no signal because the policy never solves them. Both regimes waste training FLOPs without contributing to a learning gradient. We introduce sorted Group Policy Optimization (sGPO), a compute-efficient strategy that trades a small budget of inference FLOPs for a large reduction in wasted training FLOPs. The key insight is that cheap inference compute can serve as a single offline proxy for query difficulty. By generating a small batch of parallel samples per query under the initial policy, we obtain a model-aware empirical success rate. This motivates setting the training rollout group size to the inverse of this success rate, a practical rule that maximizes sample efficiency by extracting the most advantage per generated rollout. This single profiling pass simultaneously drives data filtering (removing trivial queries and sub-sampling unsolvable ones), adaptive group size allocation, and curriculum construction (scheduling queries from easy to hard). sGPO matches or exceeds baseline performance while reducing total training compute by a factor of three, with the upfront inference profiling cost included.

Reinforcement learning (RL) has become a powerful paradigm for robot learning, particularly in sim-to-real settings, but its broader adoption remains limited by the engineering pipeline surrounding the algorithms. Building tasks, shaping rewards, and tuning hyperparameters require substantial expert effort, making RL workflows costly and difficult to scale. We introduce HARBOR, an agentic framework that frames robot RL automation as a harness-engineering problem: given a simulator codebase and a task specification, it automates the workflow from environment setup to policy training in simulation. HARBOR decomposes such high-level objectives into bounded stages executed by specialized agents through standardized commands, persistent artifacts, executable gates, and reusable knowledge, and scales iteration via decentralized parallel trials and experience learning across runs. We evaluate HARBOR across 6 benchmarks and 16 tasks in total, spanning manipulation, locomotion, and bimanual dexterous control. We demonstrate that HARBOR automates the simulation RL workflow end-to-end, designs rewards, tunes algorithms to match or improve over default configurations, and reduces engineering effort at practical token and wall-clock cost; the resulting policies can also be transferred to real robots.

Conventionally, existing vehicle platooning approaches are designed for connected vehicles, typically including connected autonomous vehicles and connected human-driven vehicles. Non-connected vehicles, such as non-connected autonomous or human-driven vehicles, are not incorporated. As a result, these platooning approaches may not properly reflect real-world mixed traffic conditions at the current stage. To address this limitation, this study proposes a hybrid platooning pattern that conditionally permits non-connected vehicles to join platoons, thereby enhancing platooning diversity and flexibility. However, it was found that the unregulated integration of non-connected vehicles can trigger rapid platoon expansion, significantly amplifying the risk of disturbance propagation in traffic flow. This, in turn, exacerbates the inherent conflict between traffic throughput and stability. To mitigate these challenges, this paper further develops a hybrid platooning control strategy based on deep reinforcement learning (DRL). This strategy integrates vehicle dynamics, platoon topology, and traffic flow states through a multi-level state representation network, enabling a dynamic trade-off between traffic capacity and stability. Numerical simulations demonstrate that the proposed strategy effectively suppresses velocity disturbance propagation by dynamically optimizing platoon structures, thereby significantly enhancing the stability and safety of mixed traffic while reducing fuel consumption and emissions.

Financial portfolio trading is naturally formulated as a reinforcement learning problem, where an agent sequentially rebalances assets under changing market conditions to balance return, risk, and transaction costs. Yet in non-stationary markets, raw OHLCV states and short-horizon return rewards often provide an under-specified learning interface, motivating large language models as a way to inject financial knowledge into state and reward design while constraining open-ended generation. To this end, we propose GIFT, an LLM-guided framework for state-reward interface design in PPO-based financial reinforcement learning. Rather than using the LLM to make trading decisions, GIFT uses Factor-guided State Enhancement to generate state features from financial-factor primitives, Risk-rule-guided Reward Shaping to generate auxiliary rewards from portfolio-risk rules, and Diagnostic-guided Refinement to revise candidate interfaces using PPO rollout diagnostics. After refinement, GIFT fixes the selected state-reward interface before evaluation, with no further LLM queries or interface updates at test time. Comprehensive rolling-window experiments across diverse market regimes and portfolio scenarios demonstrate that GIFT improves learning-signal quality and out-of-sample risk-adjusted portfolio performance over baselines. Code and data are available at: https://github.com/KAG778/GIFT .

Despite being powerful, reinforcement learning with verifiable rewards (RLVR) induces extremely long COT, making it computationally expensive. Since RLVR per-step cost is dominated by long-context rollout generation, sparse attention offers a promising way to accelerate dense rollout. However, sparse rollouts require a delicate stability-efficiency tradeoff: overly aggressive sparsity causes collapse, while overly lenient sparsity gives insufficient speedup. In this work, we study this tradeoff through sparse-to-dense actor-policy mismatch. We first observe that sparse rollout collapse is not driven by uniform degradation across tokens: most sparse tokens align perfectly with dense even under aggressive sparsity. Motivated by this, we hypothesize that sparse rollout training remains stable if the lower tail of per-token actor-policy mismatch stays above a critical threshold throughout the trajectory. We introduce a dynamic sparsity schedule that keeps this tail statistic constant during generation and validate our hypothesis. Across Qwen3 thinking-family models, keeping the tail mismatch statistic near a consistent threshold generally enables stable training. We then use a cost model to find the sparsity schedule for maximum speedup under this mismatch threshold, achieving 2.2x, 2.4x, and 2.0x rollout speedups when training Qwen3-1.7B, Qwen3-4B, and Qwen3-8B. Empirically, we show the thresholds generalize to a larger model (Qwen3-14B) and another RL domain (coding). Finally, our analysis naturally motivates DistillSparse: lightweight LoRA-based distillation on sparse rollout lets more aggressive sparsity reach the same sparse-to-dense mismatch threshold, yielding higher speedup.

Detecting anomalies in large-scale system logs is critical for the reliability and security of modern computing infrastructure. We present LogNEO, a log anomaly detector built on EleutherAI's GPT-Neo (1.3B parameters) and fine-tuned with a novel partial-credit, exponentially decaying position-aware reward scheme combined with cross-entropy regularisation via Proximal Policy Optimisation (PPO). The position-aware reward explicitly models prediction difficulty: early positions receive higher rewards for correct predictions, while later positions incur stronger penalties for errors. LogNEO attains F1-scores of 0.927, 0.913, and 0.984 on the HDFS, BGL, and Thunderbird benchmarks, improving recall by up to 6 percentage points over the prior state-of-the-art LogGPT while maintaining comparable precision. A production microservice deployment over Apache Kafka, Redis, and TensorRT-accelerated inference demonstrates 45 ms end-to-end latency at 15,000 events per second.

Robotic simulators are a cornerstone of modern research in aerial robotics, serving both as a vehicle for the development of new control algorithms and as the data source for training reinforcement learning (RL) policies. Yet, existing quadcopter learning environments often face a trade-off between physical fidelity, multi-agent support, and the throughput required by modern deep RL pipelines. In this paper, we present MuJoCo-Drones-Gym, an open-source Gymnasium-compatible multi-drone environment built on top of the MuJoCo physics engine. MuJoCo-Drones-Gym supports an arbitrary number of Bitcraze Crazyflie 2.x nano-quadcopters and exposes a modular API for selecting (i)~the physics model (rigid-body MuJoCo, explicit Python dynamics, or any subset of ground effect, blade drag, and inter-drone downwash), (ii)~the action interface (per-motor RPMs, collective normalized thrust, velocity setpoints, or PID waypoint commands), and (iii)~the observation space (kinematic state vectors, RGB / depth / segmentation cameras, or neighbourhood adjacency information). A PettingZoo ParallelEnv wrapper enables drop-in multi-agent reinforcement learning, while a suite of seven task environments, hover, velocity tracking, multi-drone hover, waypoint navigation, formation flight, gate racing, and a generic multi-agent template, demonstrates the breadth of the interface. We describe the environment design, the underlying physics and quadcopter dynamics, and illustrate its use through control and learning examples that mirror those of the closely related gym-pybullet-drones project, while taking advantage of MuJoCo's improved contact handling, rendering, and parallelizability.

Path-planning for autonomous vehicles in threat-laden environments is a fundamental challenge because the problem is nonlinear and nonconvex even in simplest scenarios. While traditional optimal control methods can be used to find ideal paths, the computational time is often too slow for real-time decision-making. To solve this challenge, we propose a method based on Deep Deterministic Policy Gradient (DDPG) and model the threat as possibly multiple circular 'no-go' zones. A mission is regarded as a failure if the vehicle enters this restricted zone at any time or does not reach a neighborhood of the destination. The DDPG agent is trained through trial and error in a simulated environment, learning a direct mapping from its current state (position and heading) to a series of feasible actions that guide the agent to safely reach its destination. The reword function has three parts: (a) an attractive field centered at the final destination, (b) some repulsive fields centered at the origins of circular obstacles, and (c) a penalty of control energy consumption (the magnitude of heading change) that indirectly in favor for straight path. The DDPG trains the agent using these incentives to find the largest possible set of starting points wherein a safe path to the destination is guaranteed. This provides critical information for mission planning, showing beforehand whether a task is achievable from a given starting point, assisting pre-mission planning activities. The approach is validated in simulation. A comparison between the DDPG method and a traditional optimal control (pseudo-spectral) method is carried out. The results show that the learning-based agent produces effective paths while being significantly faster, making it a better fit for real-time applications.

Generative policies provide expressive and multimodal action distributions, making them attractive for reinforcement learning (RL) in complex continuous-control tasks. Among them, flow-based policies are especially appealing because they generate actions through deterministic transport maps. However, applying such generative policies to likelihood-based on-policy learning remains limited by the difficulty of evaluating the probability of executed actions. Existing flow RL methods either replace the true action-density ratio with approximate surrogates, which can introduce biased updates, or recover exact likelihoods through dummy-action augmentation, which enlarges the policy space and increases computation. In this work, we propose GenPO++, a reversible generative policy optimization framework that uses history states as auxiliary memory in a high-order reversible ODE solver, yielding exact inversion without changing the original action dimension. The resulting generative policy map has a log-determinant determined only by fixed solver coefficients, enabling exact and Jacobian-free likelihood-ratio computation. This design preserves the expressiveness of generative flow policies while avoiding both action ratio bias and dummy-action overhead. We evaluate GenPO++ on large-scale simulated control, fine-tuning, and real-world robotic manipulation tasks, where it achieves competitive or superior performance over state-of-the-art on-policy RL methods, while improving training stability and computational efficiency.

Reinforcement learning has recently shown promise in improving large language models for Text-to-SQL generation, yet existing methods typically optimize one-shot rewards defined over a single SQL state. Such rewards provide limited guidance for iterative SQL correction and are insufficient to capture the improvement of multi-turn SQL refinement. In this paper, we propose Progress-SQL, a multi-turn reinforcement learning framework with progressive rewards for Text-to-SQL. Our approach introduces an Oracle-guided Diagnostic Tree (ODT), which abstracts SQL queries into clause-level structural profiles and produces diagnostic feedback for next-turn refinement. To provide dense and robust reward signals, we combine ODT-based structural alignment with lexical alignment and define a progressive reward that measures the improvement from the initial SQL to the final SQL. We further incorporate a progression latency reward that favors earlier correctness and an execution status reward that encourages recovery from the invalid SQL. Experiments on BIRD, Spider, and Spider robustness variants demonstrate that our method consistently improves Text-to-SQL performance across both primary and robustness evaluations.

Agentic Large Language Model (LLM) systems decompose complex tasks into workflow Directed Acyclic Graphs (DAGs) whose primitives must be scheduled on heterogeneous clusters. Existing deep reinforcement learning (DRL) schedulers are tied to a fixed cluster size and require retraining whenever the number of servers changes. We propose SCALE (Scalable Cross-Attention Learning with Extrapolation), a DRL scheduler that generalizes to unseen cluster scales without fine-tuning. SCALE employs a cross-attention pointer network where task features query against server features, so the architecture accepts any number of servers by construction. We observe, however, that permutation-invariant architecture alone does not guarantee good performance at new scales - the attention feature undergoes distribution shift as the server count grows. To counter this, we introduce Structured Representation Regularization (SRR): a decorrelation loss combined with a KL penalty toward the standard normal, which keeps feature statistics stable regardless of input size. Trained on 16 nodes and tested directly on 32 and 48 nodes, SCALE reduces average response time by 8.9% at N=48 relative to the same architecture without SRR, confirming that explicit regularization is necessary to close the scale-generalization gap.

Mental health struggles wax and wane, yet clinical and wellness interventions typically operate separately, causing frequent breakdowns at care transitions. We explore reinforcement learning (RL) as a means to build digital health systems that deliver clinical and wellness interventions proactively, as part of a coherent care journey. We ask: what complexities does designing such a system involve? We built a contextual bandit that dynamically selects journaling prompts from clinical and wellness repertoires to optimize for an overarching health goal (sustained journaling) and deployed it in a four-week exploratory study (N=38). We found that, first, many benefits of RL-optimized intervention sequences appeared only after interventions ended, raising the question: Should systems that offer coherent clinical-wellness care journeys include stepping-back periods? If so, when and how? Second, participants most engaged with RL-generated interventions deepened their engagement over time, while those most engaged with a constant intervention tended to burn out and drop out later. It raises the question: When should a system blending clinical and wellness interventions reduce intensity to prevent burnout in versus sustain it to maximize treatment gains?

Deep reinforcement learning (RL) algorithms often suffer from low run-to-run robustness, manifesting as significant performance variation across independent runs of identically configured agents. Although this issue poses a spectrum of challenges across research and practice, relatively few studies develop methods to evaluate it; RL research instead often reports uncertainty in the estimated mean performance. In this paper, we outline the limitations of conventional uncertainty and variation estimates, particularly their misalignment with purpose and the risk of underreporting. We then propose an alternative percentile-based statistic and visualization method, min-max IPR and run-wise percentile highlighting, respectively. These percentile-based tools are easy to interpret and rely on standard properties of sample percentiles, providing rich information about run-to-run performance variation. We demonstrate this through three case studies. First, we show that LayerNorm and penultimate-layer normalizations narrow performance variation in PPO, whereas the variation is mostly unchanged in SAC. Second, we compare PPO, SAC, TD-MPC, and TD-MPC2, and show TD-MPC exhibits the least variation while being the most data efficient among the four. Finally, in a comparison of DQN and Rainbow on five Atari environments, we show that both algorithms exhibit similar levels of performance variation.

Sparse rewards and heterogeneous task sequences remain persistent challenges in Reinforcement Learning (RL), often resulting in slow convergence, weak generalization, and inefficient exploration. We propose Uncertainty-Aware LLM-Guided Policy Shaping (ULPS), a novel framework that integrates a calibrated Large Language Model (LLM) into the RL training loop to provide structured, uncertainty-modulated behavioral guidance. ULPS employs an A*-based oracle to synthesize optimal symbolic trajectories, which are used to fine-tune a BERT-based language model. During training, this model supplies action suggestions whose influence is conditioned on epistemic uncertainty estimated via Monte Carlo (MC) dropout. An entropy-based blending mechanism adaptively balances LLM guidance and the learned policy (via Proximal Policy Optimization, PPO), allowing the agent to prioritize reliable priors while preserving adaptability. We evaluate ULPS on the MiniGridUnlockPickup benchmark and observe consistent improvements in success rate, reward efficiency, and sample complexity over unguided, uncalibrated, and standard RL baselines. ULPS achieves more than 9% improvement in execution accuracy after fine-tuning, requires fewer environment interactions, and yields higher reward AUC. Our results demonstrate that integrating symbolic A* trajectories, pretrained language priors, and uncertainty-aware control offers a principled and effective approach to multi-task reinforcement learning in sparse-reward domains, with potential extensibility to partially observable and multi-agent settings.

Large language models (LLMs) trained predominantly on English data encode substantial world knowledge, yet often fail to express it reliably in other languages, a phenomenon known as cross-lingual factual inconsistency. To study and address this, we introduce PolyFact, a large-scale parallel multilingual factual QA dataset containing 100K Wikidata-grounded facts across 12 typologically diverse languages. Using PolyFact, we compare light continual pretraining (CPT), supervised fine-tuning (SFT), and reinforcement learning via Group Relative Policy Optimization (GRPO) for improving cross-lingual factual recall in Qwen-2.5-7B and OLMo-2-1124-7B. We find that GRPO consistently outperforms SFT, improving both cross-lingual consistency and generalization to unseen languages, while CPT on parallel data yields limited additional gains. Mechanistic analyses further show that GRPO reorganizes multilingual routing by reducing language specialization in MLP layers and attention heads, thereby promoting more shared cross-lingual representations. We release our code, models, and dataset.

Machine learning is increasingly employed for the evaluation of football tactics. However, existing approaches focus on characterising historical actions or analyst-specified counterfactual scenarios. In this work, we seek to go beyond the imitation of historically observed patterns towards discovering new generalisable player configurations and strategies. To tackle this, we focus on optimising corner kick routines, and formulate a decision-making problem in which a central policy makes adjustments to attacking player positions and velocities to maximise first contact shot probability. Unlike classic optimisation that solves for isolated setups, we contribute a reinforcement learning architecture operating on graph-structured data that yields a general policy for adjusting arbitrary starting player positions. Evaluated on over 3,000 Premier League corners, our approach strongly outperforms baseline optimisation techniques under matched inference budgets. Our results suggest that graph reinforcement learning can shift set-piece analysis from historical evaluation and imitation towards reward-driven tactical discovery.

A reinforcement-learning agent maximises its reward, which can diverge from the outcome its designer intended. In physical control the reward rarely closes that gap, and drag reduction in wall turbulence makes it concrete. A mass-conservation projection couples agents' outputs and erases the per-agent credit the policy gradient needs; a memoryless policy cannot resolve the slow near-wall cycle it acts on; and a pressure-gradient reward pays for nominal drag reduction by pumping power through the wall. Two degenerate controllers achieve large drag reductions while total dissipation rises, so the reported figure can mask a more wasteful flow. We trace each fault to its cause and fix it: a differentiable projection that restores credit, a recurrent policy with a widened sensing stencil, and a reward scored on the true wall power. The corrected controller acts on the flow within a closed energy budget, earning a conservative $17\%$ under honest accounting.

Pharmaceutical supply chains (PSCs) struggle with inventory management (IM) due to unpredictable demand patterns and variable lead times associated with restocking. This complexity is further compounded by the finite shelf lives of pharmaceutical products, which necessitate a delicate balance between adequate stock and minimal waste. These intertwined factors create a complex optimization problem that requires sophisticated inventory strategies to ensure both product availability and PSC efficiency. This study aims to develop an optimal inventory replenishment policy for pharmaceutical products that can handle the stochasticity arising from uncertain demand and variable PSC conditions. The objective is to maximize the profitability of the PSC while maintaining a high patient service level. We formulate the problem as a Markov decision process and propose a deep reinforcement learning (DRL) approach, specifically, a hybrid asynchronous advantage actor critic distributed proximal policy optimization (A3C DPPO)algorithm. The A3C DPPO algorithm is tailored to handle the continuous action space inherent in IM. The numerical results demonstrate that the proposed algorithm adaptively updates the inventory replenishment strategy under dynamic scenarios, resulting in lower inventory costs compared to various benchmarks. We also conduct numerical validation using real-world pharmaceutical inventory data to confirm the practical feasibility of the proposed algorithm.

Latent reasoning has emerged as a promising alternative to discrete Chain-of-Thought (CoT) in large language models (LLMs), enabling more expressive reasoning by operating over continuous representations. However, the inherently deterministic nature of continuous representations limits policy exploration in reinforcement learning (RL). To address this, we propose TARPO (Token-Wise Latent-Explicit Reasoning via Action-Routing Policy Optimization), a pure RL framework that adaptively switches between discrete token generation and continuous latent reasoning at each step. TARPO introduces a lightweight action head router that observes the current hidden state and samples a routing decision from a binary mode-selection space, preserving the stochasticity of discrete token sampling from the vocabulary. The LLM backbone and router are jointly optimized end-to-end with a shared group-relative advantage signal. Extensive experiments across Qwen2.5 (from 1.5B to 7B) and Llama-3.1-8B backbones demonstrate that TARPO consistently outperforms existing explicit and latent reasoning RL baselines across diverse benchmarks. Further analysis shows that TARPO learns adaptive token-wise switching behaviors while maintaining stable training dynamics. Our code is available at https://github.com/NKU-LITI/TARPO-master.

In humanoid motion control, model predictive control (MPC) offers physically grounded prediction and constraint handling, while reinforcement learning (RL) enables robust whole-body skills through large-scale simulation. However, using MPC inside RL often requires time-consuming problem construction or excessive training overhead, making such frameworks difficult to justify in practice. This work studies efficient training-time MPC guidance for humanoid locomotion and manipulation, termed MPC-RL. We introduce a centroidal-dynamics MPC reward formulation that leverages guidance from MPC trajectories in training time. To make this practical in massively parallel RL, we develop $π^n$MPC, a parallel-in-horizon and construction-free batched GPU MPC solver that operates directly on time-varying dynamics to avoid high memory usage and pre-compilation. Through a variety of comparative studies and hardware validations, we have found that MPC-RL achieves superior performance in locomotion and manipulation skills. The code base is available at https://github.com/junhengl/mpc-rl.

Scaling reinforcement learning (RL) to diverse multitask settings remains a central challenge. While recent advances in model-based RL achieve strong performance, they rely on planning and complex training pipelines, making it unclear which components are essential for scalability. We revisit this question and argue that the primary driver of scalable multitask RL is not model-based control, but \emph{representation learning}. In particular, we show that combining predictive, model-based representations with high-capacity value function approximation is sufficient to achieve strong performance, even without planning. We evaluate a simple model-free algorithm, MR.Q, coupled with auxiliary predictive objectives into a scalable actor-critic architecture. This approach outperforms a recent world-model-based method and a range of deep RL baselines across a diverse suite of multitask continuous control tasks, while significantly reducing computational overhead and improving wall-clock efficiency. We observe consistent improvements with increased model capacity and show through ablations that predictive representation learning is critical for performance.

Group Relative Policy Optimisation (GRPO) has emerged as an effective reinforcement-learning algorithm for aligning language models on reasoning tasks, but it treats every token position and every sampled rollout symmetrically. We introduce two complementary extensions: (i) Adaptive-Horizon GRPO (AH-GRPO), which weights each token's policy gradient using a cumulative entropy-based discount that reduces the effective horizon when the model is uncertain, and (ii) Selective-Advantage AH-GRPO (SA-AH-GRPO), which applies this discounting only to negative-advantage rollouts, leaving positive-advantage, successful trajectories unattenuated. We evaluate standard GRPO with alpha = 0, AH-GRPO with alpha = 0.5, and SA-AH-GRPO with alpha = 0.5 on the GSM8K mathematical reasoning benchmark using both Qwen 2.5-1.5B-Instruct and Qwen 2.5-3B-Instruct fine-tuned with LoRA. On the 3B model, SA-AH-GRPO achieves Pass@1 = 0.858 at its peak at step 30 and maintains 0.846 at 180 steps, with training variance reduced to 0.0246, a 3.6 times reduction relative to GRPO while matching its peak accuracy. On the 1.5B model, SA-AH-GRPO achieves a peak Pass@1 of 0.686, improving over the zero-shot baseline of 0.637. Our analysis shows that asymmetric discounting preserves the full gradient signal on correct solutions, prevents entropy collapse, and substantially stabilises training, suggesting a principled inductive bias for reinforcement learning with verifiable rewards on structured generation tasks.

Finding optimal solution paths for combinatorial puzzles like the Rubik's Cube, sliding tile puzzles, and Lights Out remains a classical challenge in artificial intelligence. Heuristic search algorithms, such as A* , guarantee path optimality only when using an admissible heuristic-one that never overestimates the true remaining cost-to-go. Deep reinforcement learning (RL) methods like DeepCubeA train deep neural networks to approximate cost-to-go heuristics. However, standard mean-squared error (MSE) training regularly yields overestimations, violating admissibility and compromising solution optimality. In this paper, we introduce a generalizable framework for learning validation-calibrated admissible neural heuristics. We train a value network using an underestimating Admissible Bellman Operator combined with an Asymmetric Loss function to penalize overestimation. To account for residual neural function approximation errors, we propose a post-hoc calibration safety offset computed over validation scrambles. We demonstrate that our calibrated neural heuristics achieve no observed admissibility violations under the evaluation protocol and preserve path optimality in practice while reducing search node expansions by up to 83.0% on a 2 by 2 Rubik's Cube, 19.9% on a 3 by 3 Lights Out grid, and 1.9% on an 8-Puzzle compared to standard analytical baselines.

Lifelong learning is essential for Large Language Model (LLM) agents operating in dynamic, interactive environments. However, existing lifelong learning agents for long-horizon tasks typically depend on discrete skill or past experiences retrieval with static parameters during inference, which prevents them from continuously internalizing test-time feedback like human learners. To bridge this gap, we propose Skill-enhanced Test-Time Co-Evolution (\texttt{LifeSkill}), a two-stage reinforcement learning framework for Online Lifelong Learning Agents. Specifically, we design Verifier-Guided Skill Learning that addresses the lack of direct supervision for skill extraction by rewarding candidate skills according to the average verifier success of multiple skill-conditioned policy rollouts, encouraging the model to generate skills that are useful for solving tasks rather than merely plausible in text. Furthermore, we introduce Online Skill Internalization, which continuously improves the policy model during test-time interaction by transforming skill-conditioned trajectories into reward signals. This enables the agent to directly internalize reasoning capabilities into its parameters, avoiding the context bloat of experience retrieval. Experiments on LifelongAgentBench show that LifeSkill improves average performance by 7 absolute points by comparing with existing lifelong agent baselines.

Temporal credit assignment is central to both biological and artificial intelligence, yet its interaction with non-linear function approximation is poorly understood. We identify a systematic failure mode in deep reinforcement learning (RL) termed Trace-Mediated Peak Bias (TMPB). At intermediate eligibility trace depths, agents irrationally prefer trajectories with high-magnitude reward peaks'' over alternatives with higher cumulative returns. This provides a mechanistic account of the Peak-End Rule: a human memory bias where experiences are judged by their most intense moments rather than integrated utility. We show that TMPB emerges because traces amplify distal Temporal Difference errors into gradient shocks'' that fixed-step-size Stochastic Gradient Descent cannot normalize, leading to global overestimation. Conversely, adaptive optimizers mitigate this pathology via second-moment normalization. Our results suggest that human-like saliency distortions may emerge naturally from the mathematical constraints of credit assignment in distributed systems, and that adaptive optimization is a theoretical necessity for rational value estimation.

This study aims to determine whether the application of Deep Reinforcement Learning (DRL) as a specialized execution overlay can enhance pair trading in highly volatile cryptocurrency markets. Although classical implementations of the strategy have proven successful in traditional equities, they frequently exhibit rigidity and suffer from severe divergence risks when applied to high-variance environments. To address this need, this research introduces novel concepts. To construct a robust system, we developed a hierarchical "Filter-then-Rank" pair selection methodology and a proprietary "Fixed Risk, Adaptive Mean" execution model. The system employs a Proximal Policy Optimization (PPO) agent with a Long Short-Term Memory (LSTM) layer to govern execution decisions within strict deterministic risk management boundaries. Evaluated on 1-hour interval data from the Binance USD-M Futures market, the optimized RL policy achieved an out-of-sample performance that substantially outperformed the heuristic baseline. A stationary circular block bootstrap robustness check confirms that the agent's risk-adjusted outperformance is statistically significant at the 10 percent level. Although falling marginally short of the stricter 5 percent threshold, this result highlights the extreme idiosyncratic variance characteristic of digital assets. Ultimately, this thesis contributes to the quantitative finance literature by introducing a hybrid architecture that combines statistical arbitrage with DRL execution policies. Furthermore, it delivers a novel framework for safe reinforcement learning via deterministic shielding, proving that anchoring a neural policy to statistically robust boundaries successfully mitigates severe divergence risks.

Underground mines present extreme conditions for autonomous robot navigation: GPS is denied, lighting is degraded, and tunnel topology is loop-rich and non-convex. Simulation benchmarks grounded in real production-mine geometry and compatible with GPU-accelerated learning pipelines do not yet exist in the open-source ecosystem. We present MineXplore, an open-source MuJoCo-based navigation benchmark derived from the Leung et al. 2017 Chilean underground copper mine dataset. The environment reconstructs a 104,423 sq.m tunnel network through an six-stage contour-to-MJCF pipeline incorporating octagonal wall cross-sections, LiDAR-sourced jagged wall geometry, three terrain friction zones, a global 5 degree incline, and periodic spot lighting. Geometric fidelity is validated at an Intersection over Union (IoU) of 0.9538 against the source survey map, and surface texture similarity scores 79.4% across six structural dimensions. A single-agent PPO baseline trained via RLlib across five independent random seeds achieves a best rolling coverage of 88.89% (3 of 5 seeds reaching the 90% coverage target), confirming that MineXplore supports stable and reproducible policy learning under realistic underground sensing and topology.

We present AgentJet, a distributed swarm training framework for large language model (LLM) agent reinforcement learning. Unlike centralized frameworks that tightly couple agent rollouts with model optimization, AgentJet adopts a decoupled multi-node architecture in which swarm server nodes host trainable models and run optimization on GPU clusters, whereas swarm client nodes execute arbitrary agents on arbitrary devices. This design provides capabilities that are difficult to support in centralized frameworks: (1) heterogeneous multi-model reinforcement learning, enabling the training of heterogeneous multi-agent teams with multiple LLM as brains; (2) multi-task cocktail training with isolated agent runtimes; (3) fault-tolerant execution that prevents external environment failures from interrupting the training process; and (4) live code iteration, which allows agents to be edited during training by replacing swarm client nodes. To support efficient RL in multi-model, multi-turn, and multi-agent settings, AgentJet introduces a context tracking module with timeline merging, which consolidates redundant context and achieves a 1.5-10x training speedup. Finally, AgentJet introduces an automated research system that takes a research topic as input and autonomously conducts long-horizon, multi-day RL studies on large-scale clusters. By leveraging the swarm architecture, this system reproduces key exploratory workflows of RL researchers without human intervention during execution.