RL Stability

Safe reinforcement learning (RL) typically asks $\textit{what}$ an agent should do. We ask $\textit{when}$ it needs to act, and show that a single policy can jointly learn control inputs and communication-efficient timing decisions under a pointwise Lyapunov safety shield. We focus on stabilization around a known equilibrium, where CARE-based LQR backups, Lyapunov certificates, and classical Lyapunov-STC are well defined, enabling clean comparison against analytical baselines. A run-time assurance (RTA) layer overrides the policy via a one-step-ahead Lyapunov prediction and a precomputed LQR backup, providing a strictly stronger guarantee than constrained MDP methods that enforce safety only in expectation. On an inverted pendulum, cart--pole, and planar quadrotor, the learned policy achieves $1.91\times$, $1.45\times$, and $3.51\times$ higher mean inter-sample interval (MSI) than a Lyapunov-triggered baseline; a fixed LQR controller at the same average rate is unstable on all three plants, showing that adaptive timing, not a lower average rate, makes sparsity safe. A CARE-derived Lyapunov reward transfers across environments without redesign, with a single weight $w_c$ controlling the stability--communication tradeoff; ablations confirm the RTA shield is essential, with its removal reducing MSI by $1.27$--$1.84\times$ and degrading state norms. A preference-conditioned extension recovers the full tradeoff frontier from one model at $\tfrac{2}{11}$ of training compute, and SAC experiments show the results are algorithm-agnostic across discrete and continuous domains. A 12-state 3D quadrotor case study extends the framework to higher-dimensional systems where classical STC is intractable, and robustness to $\pm30\%$ mass variation and disturbances shows graceful degradation, with the RTA absorbing what the learned policy cannot.

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

Reinforcement learning (RL) has become the de facto method for achieving locomotion on humanoid robots in practice, yet stability analysis of the corresponding control policies is lacking. Recent work has attempted to merge control theoretic ideas with reinforcement learning through control guided learning. A notable example of this is the use of a control Lyapunov function (CLF) to synthesize the reinforcement learning rewards, a technique known as CLF-RL, which has shown practical success. This paper investigates the stability properties of optimal controllers using CLF-RL with the goal of bridging experimentally observed stability with theoretical guarantees. The RL problem is viewed as an optimal control problem and exponential stability is proven in both continuous and discrete time using both core CLF reward terms and the additional terms used in practice. The theoretical bounds are numerically verified on systems such as the double integrator and cart-pole. Finally, the CLF guided rewards are implemented for a walking humanoid robot to generate stable periodic orbits.

Offline reinforcement learning (RL) can fail spectacularly when bootstrapped temporal-difference (TD) updates amplify their own errors, driving the critic toward extreme and unusable Q-values. A key counterintuitive insight of this work is that collapse is not only a property of the backup rule or network architecture: optimizer dynamics themselves can directly trigger or suppress instability. From a control-theoretic viewpoint, we model offline TD learning as a feedback system and analyze Adam-based critic updates. This yields a necessary and sufficient condition for stability of the induced local update dynamics: within the regime we analyze, these dynamics are stable if and only if the spectral radius of the corresponding update operator is strictly below one. Further analysis suggests that standard Adam updates can inadvertently distort the parameter geometry, motivating explicit orthogonality constraints to prevent TD error amplification. To this end, we propose AdamO, an Adam-based optimizer with a decoupled orthogonality correction regulated by a strict task-alignment budget. We prove that this design theoretically guarantees worst-case task safety and preserves Adam's continuous-time dissipative dynamics. Empirically, AdamO is broadly compatible with diverse offline RL baselines, improving stability and returns across a broad suite of benchmarks.

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.

Many value-based deep reinforcement learning algorithms rely on target networks - lagged copies of the online network - to stabilize training. While effective, this mechanism introduces a fundamental stability-recency tradeoff: slower target updates improve stability but reduce the recency of learning signals, hindering convergence speed. We propose Target-Aligned Reinforcement Learning (TARL), a simple drop-in refinement for existing algorithms that emphasizes transitions for which the target and online network estimates are highly aligned. By focusing updates on well-aligned targets, TARL mitigates the adverse effects of stale target estimates while retaining the stabilizing benefits of target networks. We empirically demonstrate consistent improvements within discrete and continuous control algorithms across various benchmark environments without any hyperparameter tuning, including a 38.18% peak score gain on Atari-10, while incurring less than a 4% increase in wall-clock time.

Constraints are essential for stabilizing reinforcement learning fine-tuning (RFT) and preventing degenerate outputs, yet they inherently conflict with the optimization objective because stronger constraints limit the ability of a fine-tuned model to discover better solutions. We propose dynamic constraints that resolve this tension by adapting to the evolving capabilities of the fine-tuned model based on the insight that constraints should only intervene when degenerate outputs occur. We implement this by using a reference model as an online refiner that takes the response from the fine-tuned model and generates a minimally corrected version which preserves correct content verbatim while fixing errors. A supervised fine-tuning loss then trains the fine-tuned model to produce the refined output. This mechanism yields a constraint that automatically strengthens or relaxes based on output quality. Experiments on dialogue and code generation show that dynamic constraints outperform both KL regularization and unconstrained baselines, achieving substantially higher task rewards while maintaining training stability.

Asynchronous execution is essential for scaling reinforcement learning (RL) to modern large model workloads, including large language models and AI agents, but it can fundamentally alter RL optimization behavior. While prior work on asynchronous RL focuses on training throughput and distributional correction, we show that naively applying asynchrony to policy-gradient updates can induce qualitatively different training dynamics and lead to severe training instability. Through systematic empirical and theoretical analysis, we identify a key signature of this instability: asynchronous training exhibits persistently high cosine similarity between consecutive policy gradients, in contrast to the near-orthogonal updates observed under synchronized training. This stale-aligned gradient effect amplifies correlated updates and increases the risk of overshooting and divergence. Motivated by this observation, we propose GRADIENT ALIGNMENT CONTROL(GAC), a simple dynamics-aware stabilization method that regulates asynchronous RL progress along stale-aligned directions via gradient projection. We establish convergence guarantees under bounded staleness and demonstrate empirically that GAC recovers stable, on-policy training dynamics and matches synchronized baselines even at high staleness.

Agentic reinforcement learning (ARL) has rapidly gained attention as a promising paradigm for training agents to solve complex, multi-step interactive tasks. Despite encouraging early results, ARL remains highly unstable, often leading to training collapse. This instability limits scalability to larger environments and longer interaction horizons, and constrains systematic exploration of algorithmic design choices. In this paper, we first propose ARLArena, a stable training recipe and systematic analysis framework that examines training stability in a controlled and reproducible setting. ARLArena first constructs a clean and standardized testbed. Then, we decompose policy gradient into four core design dimensions and assess the performance and stability of each dimension. Through this fine-grained analysis, we distill a unified perspective on ARL and propose SAMPO, a stable agentic policy optimization method designed to mitigate the dominant sources of instability in ARL. Empirically, SAMPO achieves consistently stable training and strong performance across diverse agentic tasks. Overall, this study provides a unifying policy gradient perspective for ARL and offers practical guidance for building stable and reproducible LLM-based agent training pipelines.

Deep reinforcement learning systems often suffer from unstable training dynamics due to non-stationarity, where learning objectives and data distributions evolve over time. We show that under non-stationary targets, isotropic Gaussian embeddings are provably advantageous. In particular, they induce stable tracking of time-varying targets for linear readouts, achieve maximal entropy under a fixed variance budget, and encourage a balanced use of all representational dimensions--all of which enable agents to be more adaptive and stable. Building on this insight, we propose the use of Sketched Isotropic Gaussian Regularization for shaping representations toward an isotropic Gaussian distribution during training. We demonstrate empirically, over a variety of domains, that this simple and computationally inexpensive method improves performance under non-stationarity while reducing representation collapse, neuron dormancy, and training instability.

GRPO-style reinforcement learning (RL)-based LLM fine-tuning algorithms have recently gained popularity. Relying on heuristic trust-region approximations, however, they can lead to brittle optimization behavior, as global importance-ratio clipping and group-wise normalization fail to regulate samples whose importance ratios fall outside the clipping range. We propose Query-Adaptive Trust-Region policy Optimization (QUATRO), which directly enforces trust-region constraints through a principled optimization. This yields a clear and interpretable objective that enables explicit control over policy updates and stable, entropy-controlled optimization, with a stabilizer terms arising intrinsically from the exact trust-region formulation. Empirically verified on diverse mathematical reasoning benchmarks, QUATRO shows stable training under increased policy staleness and aggressive learning rates, maintaining well-controlled entropy throughout training.

Reinforcement learning with rule-based, binary-valued reward functions has been shown to significantly enhance the reasoning capabilities of large language models. These models typically rely on REINFORCE-based policy optimization methods, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation is that existing methods either ignore reward normalization or use static normalization schemes, which fail to adapt to the evolving policy during training. This mismatch can lead to unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. By aligning normalization with the changing policy distribution, BNPO enables more accurate, lower-variance gradient estimation and promotes stable training dynamics. We provide theoretical analysis showing that BNPO reduces variance and generalizes both REINFORCE and GRPO under binary-valued rewards. In addition, we introduce an advantage decomposition mechanism to extend BNPO to more complex reward settings. Experimental results demonstrate that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks.