Constrained RL

Safe reinforcement learning commonly places safety and task performance in the same policy objective, where they can introduce competing updates. Safety filters separate them at action execution, but classical designs require an analytic safety function and dynamics model, and standard minimal-intervention filters are myopic to long-horizon task return because they minimize only instantaneous action deviation. Hard projections are also undefined when no safe action exists. We present FAITH, a feasibility-aware, model-free framework that approximates the optimal state-action safety value and amortizes minimal-intervention filtering with a feedforward network. The task policy optimizes the task return through the filtered dynamics, which recovers the feasible constrained problem without a competing safety term in the task-policy update. When no action satisfies the learned safety condition, the same filter approaches the action with minimum predicted peak harm. On a double integrator example and a Safety Gym environment, FAITH achieves the highest return among methods with no feasible-start violations and matches the lowest harm from infeasible starts. On a 29-DoF humanoid, it reaches a 99.95% safety rate while retaining 97% of the unfiltered return in Walking-Avoid, and obtains the highest measured safety rate in Push-Avoid by learning to sacrifice balancing and fall away from the protected region. The same policies are also demonstrated on a real-world Unitree G1 humanoid.

Reinforcement learning in safety-critical domains requires maximizing task performance while strictly adhering to safety constraints. Existing safe reinforcement learning paradigms typically force a trade-off: they either require a priori knowledge to provide strict safety guarantees (e.g., safety filters), or they enable joint learning but only satisfy safety constraints on average. In this work, we propose a novel Bellman operator that unifies performance and safety objectives into a joint value function. We show that temporal difference learning with the joint Bellman operator converges under a two-timescale stochastic approximation framework. On the fast timescale, the safety value of the learning joint policy is estimated, while the joint value is estimated on the slow timescale. Convergence is ensured by formulating the limiting dynamics as an occupation-averaged differential inclusion, and showing that it asymptotically converges to a set of limiting optimal safety-constrained task value functions. Theoretically, once converged, the resulting optimal policy maximizes task return while maintaining safety at all times. Empirical evaluations on continuous control tasks with neural approximations demonstrate stable convergence with near-zero safety violations at test time.

We study episodic constrained Markov decision processes with adversarial losses under stochastic hard constraints. Specifically, starting from a known strictly feasible policy with margin $d$, we seek to obtain optimal regret while satisfying the expected cost constraints in every episode. In this setting, Stradi et al. (2025) show that a carefully designed mixing rule attains regret of order $\widetilde{\mathcal{O}}(\sqrt{T}/\min\{d,d^2\})$. Interestingly, they also provide a lower bound of order $Ω(\sqrt{T}/ρ)$ for the same setting, where $ρ$ is the Slater margin of the offline problem and can be much larger than $d$. In this work, we build on their approach to obtain optimal regret dependence on these margins. Specifically, we propose MA-OPS, an algorithm that combines an optimistic search for the Slater margin with a pessimistic evaluation of the selected policies to safely learn a policy with a large feasibility margin. This policy is then used to minimize regret while satisfying the constraints at every episode. In particular, we show that MA-OPS attains regret $\widetilde{\mathcal{O}}(\sqrt{T}/ρ+ 1/(dρ))$. Finally, we provide a matching lower bound, showing that the dependence on $T$, $d$, $ρ$ in the regret bound is optimal up to logarithmic factors.

Deep reinforcement learning agents reach strong performance in real-time strategy games but can be brittle against opponents outside their training distribution. Separating strategic command selection from learned unit control allows different strategies to be selected for different opponents while reusing the same execution policy. This requires an executor that can follow different commands and measurable criteria for assessing whether it does so. We introduce a constrained command-conditioned Proximal Policy Optimization (PPO) policy, the executor, for MicroRTS, a real-time strategy environment. Discrete commands specify strategic objectives and behavioral requirements for economy, army composition, military posture, and worker policy over multiple environment steps; the executor determines the unit-level actions used to fulfill them. A Thompson-sampling bandit acts as the strategist, selecting command tuples from an estimate of the opponent's strategy built from in-game observations rather than opponent identity. In a controlled comparison with a flat PPO baseline trained with the same architecture, budget, curriculum and self-play league, the strategist-executor system wins significantly more often against three of the four strongest opponents on a training map, including the two strongest held-out ones (0.55 to 0.97 and 0.01 to 0.34), with no significant difference against the others.

Safe reinforcement learning seeks policies that maximize return while satisfying constraints on cumulative cost. Most methods impose these constraints on expected episodic cost. Consequently, standard evaluations report mean episodic cost without characterizing how cost is distributed across episodes. A policy that satisfies the mean-cost criterion may therefore remain unsafe in its worst episodes. Mean-cost reporting neither identifies this tail violation nor shows whether it can be brought within budget while preserving return. In this work, we measure the episodic-cost tail using $\mathrm{CVaR}_{0.1}$, the average cost of the worst $10\%$ of episodes. We classify a policy as tail-safe when $\mathrm{CVaR}_{0.1}$ is within the safety budget. This allows us first to identify policies that are safe on average but unsafe in the tail and then to study whether their tail violations can be controlled while preserving return. To identify tail-unsafe policies, we evaluate five standard algorithms on three Safety-Gymnasium navigation tasks. We then examine four constraint families on dense-hazard navigation and assess tail control across four navigation and four locomotion tasks.

Learning from demonstrations (LfD) provides a framework for inferring unknown constraints from locally optimal, constraint-satisfying expert behavior. Existing approaches largely fall into two paradigms, constrained inverse optimal control (CIOC) and inverse constrained reinforcement learning (ICRL). CIOC exploits optimality conditions such as the Karush--Kuhn--Tucker (KKT) conditions but typically assumes known dynamics and structured constraint representations. Meanwhile, ICRL accommodates complex unknown constraints and unknown transition dynamics but often requires extensive online exploration, during which unsafe constraint violations may occur. In this work, we introduce Counterfactual KKT (CF-KKT), a constraint learning framework that leverages learned dynamics and locally optimal demonstrations to recover unknown constraints without requiring known dynamics or additional risky exploration, thereby combining the data efficiency and safety advantages of CIOC with the flexibility of ICRL. First, we use a locally learned differentiable dynamics model to impose KKT-inspired optimality conditions directly on the demonstrations. Second, we use the learned dynamics to generate reward-improving counterfactual behaviors near the demonstrations, revealing behaviors that would be preferable in the absence of the unknown constraint and thus providing synthetic infeasible data. When the constraint parameterization is known, the same learned-dynamics framework enables direct CIOC-based parameter recovery, and we characterize its sensitivity to dynamics misspecification. Across high-dimensional robotic control tasks, our approach learns neural constraint representations with improved safety and data efficiency relative to state-of-the-art offline ICRL baselines.

When multiple agents share a cost budget, a common Lagrange multiplier can enforce the aggregate constraint but does not determine how its penalty should be allocated across agents. Uniform penalties ignore heterogeneity in the rewards agents sacrifice, while agent-specific multipliers may still rely on the same aggregate cost signal. We introduce Lagrangian Responsibility Allocation (LiRA), which learns each agent's share of a common multiplier by optimizing social welfare over a finite training horizon. The multiplier enforces the aggregate budget, while responsibility shares redistribute its influence without modifying the original rewards or constraints. For convex games under standard regularity conditions, varying these shares induces a smooth family of normalized generalized Nash equilibria in which active constraints remain at their budgets while welfare varies. To optimize responsibility before convergence, we derive a welfare gradient that accounts for both learning updates and the induced change in data distribution. Across CityLearn, MABIM, Harvest, and MetaDrive, spanning 3 to 400 agents, LiRA improves average social welfare by up to 29% over uniform and agent-specific multiplier baselines. Grid and driving costs remain within budget, inventory violations decrease, and Harvest makes more effective use of available budget.

Planar graphs are central to applications across science and engineering, yet existing generators provide limited support for goal-directed generation under hard structural and geometric feasibility constraints. We propose a dataset-free method for generating planar graph embeddings by combining parametric graph grammars with safe reinforcement learning to optimize generic task-specific objectives while satisfying constraints during construction. We formulate the generation process as a constrained Markov decision process, where the graph grammar defines the state and action spaces. We further introduce an action projection that maps sampled actions toward state-dependent safe sets, improving constraint satisfaction during training. In contrast to classical graph generators and deep generative models, which typically offer limited goal-directed control or rely on weak constraint satisfaction, our method constructs feasible planar graph embeddings directly during generation. We also introduce a benchmark suite for constrained and goal-directed planar graph generation, together with classical and deep generative baselines. Across all benchmark tasks, our method consistently outperforms baselines while satisfying the formulated constraints.

Diffusion policies provide expressive action distributions for continuous-control reinforcement learning. However, safety-aware online diffusion policy optimization remains underexplored, particularly methods that use predictive reachability information without an explicit dynamics model. We propose Reachability-Aware Diffusion Policy Optimization (RADPO), a model-free method that combines predictive first-hit safety estimation with cumulative-cost budget feedback. RADPO learns a discounted first-hit reachability value that captures the discounted risk of a cost event, assigns larger weight to events that occur sooner, and uses this signal to shape the reward. A separate dual-like multiplier adjusts the shaping strength according to realized episodic costs relative to a prescribed budget. The diffusion actor improves through weighted denoising regression on candidate actions scored by the reward critic. Our approach requires neither a learned dynamics model, action gradients through the critics, nor differentiation through the reverse diffusion sampler. We establish theoretical properties of the reachability value and show that accumulated reachability penalty provides a conservative surrogate for future discounted cumulative cost. Across ten continuous-control safety tasks, RADPO achieves competitive reward-cost trade-offs, with substantial reductions in constraint violations on several tasks relative to the compared baselines. Our theoretical and empirical analysis supports that combining reachability with cumulative budget feedback is a viable approach to safety-aware diffusion policies.

We study episodic adversarial linear constrained Markov decision processes (CMDPs) with unknown transitions, where both the loss and constraint functions may vary adversarially across episodes. The best previous algorithm achieves $\widetilde{\mathcal{O}}(K^{3/4})$ regret and cumulative constraint violation, leaving a gap to the optimal $\widetilde{\mathcal{O}}(\sqrt{K})$ dependence on the number of episodes $K$. We close this gap by proposing a new primal dual algorithm that achieves $\widetilde{\mathcal{O}}(\sqrt{K})$ regret and cumulative constraint violation without assuming Slater's condition. We further extend the algorithm to achieve the same $\widetilde{\mathcal{O}}(\sqrt{K})$ guarantees for regret and hard constraint violation, which does not allow constraint violations to cancel across episodes. The main challenge is that learning linear CMDPs requires uniform concentration over a value function class with a controlled covering number, whereas standard techniques in constrained online learning, such as policy mixing, can make this class more complex. Our algorithm combines adaptive Follow the Regularized Leader (FTRL), contracted value estimation, and an exponential Lyapunov function. An adaptive dual regularizer offsets the dependence on the dual weights in the primal regret bound, removing the need for policy mixing. We further show that the normalization in the FTRL update bounds the policy parameters independently of the magnitudes of the dual weights, which explains why the resulting policy class remains compatible with uniform concentration. Under feature access, the computational complexity is independent of the size of the state space.

We study infinite-horizon average-reward constrained Markov decision processes (CMDPs) under the weakly communicating assumption. Existing high-probability guarantees for this setting either require computationally inefficient algorithms or have suboptimal dependence on the number of interactions $T$. We propose, to the best of our knowledge, the first computationally efficient algorithm that achieves $\widetilde{\mathcal{O}}(\sqrt{T})$ regret and cumulative constraint violation with high probability in the tabular setting. The $\sqrt{T}$ dependence is optimal up to logarithmic factors. Our approach incorporates cumulative constraint violation into the state and defines a reshaped reward through differences of a Huber potential. The added state determines the penalty on further violations while the reward function remains fixed on the augmented state space. Since the added state has known deterministic dynamics, only the original transition kernel needs to be estimated. The bounded slope of the Huber potential keeps the per-step reward bounded, and the potential differences telescope to relate the reshaped return to the original cumulative reward and the terminal potential. These properties allow us to apply finite-horizon approximation and optimistic value iteration with clipping, as used in unconstrained average-reward MDPs, without worsening the regret rate in $T$.

Constrained multi-agent control requires more than predicting rewarding actions: an action can cease to be executable as contact windows, shared capacity, and deadlines change. We introduce VERA, a centralized-training, decentralized-execution framework that separates feasibility estimation from credit assignment. Each actor predicts a five-dimensional verifiable feasibility representation (VFR). After an action is proposed, exact action-conditioned margins available only during training supervise that representation, while a counterfactual group-relative advantage (CGRA) ranks candidate representation-action pairs. Execution uses one actor pass and no privileged state. In a dynamic space-air-ground integrated network (SAGIN), VERA obtains 55.33% +/- 3.60% success with 0.45% +/- 0.81% coverage violation, within 1.33 percentage points of a privileged-mask reference. With rewards matched over ten paired seeds, VERA improves success over the strongest baseline by 8.74 percentage points (p=0.023) and reduces violation by 52.19 percentage points (p=5.7e-8). A ten-seed 4-by-2 factorial attributes a 14.16-16.48 percentage-point gain to CGRA across handcrafted, learned, random, and latent representations; evaluation on seven unseen topologies preserves a 24.33-30.02 percentage-point advantage over multi-agent proximal policy optimization. From 10 to 40 users, success remains 50.1-53.8%, and VFR adds only 0.026 ms to a central processing unit (CPU) actor step. Cross-domain tests further identify the governing condition: counterfactual credit succeeds when candidate scores respect shared constraints and fails under incompatible reward geometries. These results establish action-conditioned feasibility as an auditable training interface and counterfactual credit as a geometry-dependent optimization mechanism.

Constrained Reinforcement Learning has recently gained increasing attention in the field of Safe Autonomous Driving, where the general mechanism is to maximize the expected reward while keeping the overall action risk bounded. In this way, the safety issues arising in AD can be mitigated through constrained actions. However, existing Constrained RL methods still lack dynamics on the imposed constraints. For instance, the action cost adopted by the existing Primal-Dual/soft-constrained methods is often defined as static state-to-cost mapping, and the safe-action projection in hard-constrained methods relies on the static projection with the fixed feasible region boundary estimated from offline demonstrations. The above drawback tightly couples the imposed constraints to the training scenarios, leaving the AD policy hard to handle different interaction scenarios, due to the improper state-level action-cost and the static projection boundary. Consequently, in this paper, we propose Brain-SAD, a brain-inspired safe autonomous driving control framework with dynamic fear-oriented constraints. By perceiving the current vehicle-interaction scene, Brain-SAD generates dynamic fear signal as fear reaction to online decide long-term policy for regular interaction or short-term policy for urgent-collision defense. In such two policy, the above fear-reaction will be constructed as the dynamic fear constraints, respectively reflecting the overall fear cost directly coupled with action-impact, and the dynamic fear boundary of the feasible region derived from different risky neighbors, both of which will in turn serve for the online policy optimization. Experimental results show that Brain-SAD outperforms existing methods, achieving higher success rate in shorter task-completion and collision-recovery time, and exhibits stronger reliability across continuous intersections of fluctuating complexity.

The tragedy of the commons poses a multi-agent safety problem: reward-seeking agents can deplete a shared resource, and cooperation among its users does not itself specify how much must be preserved. We make preservation an explicit requirement by formulating a regenerative commons as a constrained Markov game or a constrained multi-agent MDP with a designer-specified depletion budget. We develop a nonstationary Lagrangian framework that constructs a policy sequence from solutions of unconstrained games or cooperative control problems. Extending earlier time-average constructions, we introduce average-epoch solution concepts for reset episodes with discounted rewards and terminal costs. We prove a reward-independent feasibility certificate, cooperative feasibility and approximate optimality against feasible policy mixtures, and an extension to unbiased sampled costs. For self-interested agents, a constrained Nash certificate quantifies the price-dispersion term introduced by deviations that redistribute budget across epochs. Under the stated assumptions on solver accuracy and multiplier updates, these results give constrained policy-sequence guarantees using solutions of unconstrained problems. Experiments with constrained IPPO and MAPPO in a Gordon-Schaefer fishery examine how depletion budgets shape stock retention, harvest rewards, and price adaptation.

Power system operation is a safety-critical sequential decision-making problem, making it a natural testbed for reinforcement learning (RL). However, existing RL environments for power systems are often narrow in scope and computationally limited by CPU-based simulation workflows, making large-scale evaluation difficult. We introduce PowerZooJax, a JAX-based benchmark suite for RL in power system operation. It provides five constrained Markov decision process tasks spanning generation, transmission, distribution, distributed energy resources, and data center microgrid. By rewriting power flow, economic dispatch, market clearing, and device dynamics as JAX computation graphs, PowerZooJax keeps the entire training and evaluation loop on the GPU. Experiments show substantial speedups over CPU-based simulations and demonstrate standardized evaluation of policy returns, safety violations, and out-of-distribution stress conditions. Our open-source benchmark is available at: https://github.com/powerzoojax/PowerZooJax.

Greenhouse climate control balances economic return with maintaining temperature, humidity and CO2 within crop-adapted growth ranges. Conventional reinforcement learning (RL) greenhouse controllers use fixed reward penalties to limit climate constraint violations, yet such heuristic penalties cannot explicitly constrain long-term cumulative violations. Poorly tuned weights either lead to overly conservative policies and lower yields, or fail to suppress persistent climate deviations that harm photosynthesis and induce crop diseases. To address this issue, we formulate greenhouse climate regulation as a Constrained Markov Decision Process (CMDP) and use a Lagrangian safe RL framework RCPO-PPO to separate economic optimization and cumulative safety constraints, enabling adaptive penalty adjustment without manual tuning. To handle strong nonlinear, time-varying coupling between greenhouse microclimate and crop growth, Kolmogorov-Arnold Networks (KANs) replace Multi-Layer Perceptrons (MLPs) as policy and value approximators for improved nonlinear representation. Sinusoidal cyclic time features are embedded in observations to capture diurnal environmental periodicity. Simulations use a classic winter lettuce greenhouse model driven by 40-day real weather disturbances. Compared with vanilla penalty-based PPO, our method cuts cumulative climate violations by 18.65% and raises lettuce economic profit by 2.91%, keeping violations stable near the safety threshold. This decoupled CMDP optimization with KAN-based policy representation mitigates long-term climate risks and boosts planting profits, offering a constraint-aware control strategy for precision greenhouse cultivation.

We study finite-time concentration and convergence rates for projected two-time-scale stochastic approximation driven by a controlled Markov chain. The averaged fast map is contractive, while the slow iterate is projected onto a compact convex polyhedron. The associated projected ordinary differential equation may have a discontinuous vector field at the boundary, preventing a direct application of standard analyses based on Lipschitz vector fields. Using the Skorokhod map, we establish explicit high-probability bounds for tracking the moving fast equilibrium and the projected slow dynamics. These bounds separate martingale fluctuations, Markov-noise residuals, and the bias due to time-scale separation. A Lipschitz Lyapunov function satisfying a uniform decrease condition over fixed time intervals yields almost-sure convergence, with explicit last-iterate rates when the decrease admits a power lower bound. Under uniform Lyapunov contraction, polynomial step sizes yield joint fast-tracking and slow Lyapunov-error exponents arbitrarily close to $1/3$. Under the additional assumption that the reduced slow update map is a Euclidean contraction, logarithmically separated step sizes improve the joint rate to $O(n^{-1/2}\log n)$ almost surely, including for boundary equilibria. The same rate holds under a distinct geometric condition involving a strictly attracting face of a box and a fast equilibrium that is constant on that face. An actor-critic application achieves an almost-sure value-gap rate of $O(n^{-1}\log n)$ relative to the optimum within the constrained policy class. Further applications include projected TD(0) and projected stochastic gradient descent. We also extend the analysis to projection of the fast recursion under Euclidean contractivity.

Humanoid robots promise versatile mobility in cluttered, human-centric environments, but real deployment demands principled safety. Classical model-based gait generators yield interpretable motions but often lack the robustness and adaptability of modern reinforcement learning (RL) based approaches. We propose a model-informed reinforcement learning framework anchored to the analytical Angular Momentum Linear Inverted Pendulum (ALIP) template. We provide a step-to-step safety certificate for ALIP stepping via a discrete exponential control barrier function (DECBF) and use it as (i) a training-time shaping signal and (ii) a runtime action filter that minimally adjusts swing-foot placement to satisfy template-level constraints. Full-order safety is evaluated empirically on the Digit humanoid in MuJoCo with a whole-body controller stack. Compared to an unconstrained baseline, our approach reduces safety-violation events in the reported external-disturbance trial, while larger lateral-velocity transients reveal a safety-tracking tradeoff.

This paper addresses the problem of safe offline reinforcement learning, which involves training a policy to satisfy safety constraints using an offline dataset. This problem is inherently challenging as it requires balancing three highly interconnected and competing objectives: satisfying safety constraints, maximizing rewards, and adhering to the behavior regularization imposed by the offline dataset. To tackle this trilogy challenge, we propose Q-learning Penalized Transformer policy (QPT), a \emph{training--inference consistent} framework that bridges conditional sequence modeling with constraint-aware value estimation. QPT trains a Transformer policy that generates actions conditioned on trajectory context and target return/cost, retaining strong behavior regularization. To inject explicit safety semantics during learning, we augment sequence-model training with a Q-shaped penalty using learned reward and cost Q-functions to favor high return under low constraint violation. At inference, the same Q-functions enforce the cost threshold and choose the highest-reward feasible action, closing the loop between training and deployment. We provide a principled analysis under stylized near-deterministic CMDPs, characterizing how Q-penalized conditional generation improve safety and performance. Empirically, QPT consistently outperforms strong safe offline RL baselines across 38 tasks on the DSRL benchmark, and exhibits robust zero-shot adaptation to different constraint thresholds.

Safe reinforcement learning seeks policies that maximise task performance while satisfying safety constraints. In driving benchmarks, however, collision costs typically appear only at the time of collision, providing no advance warning of an approaching hazard. Frozen vision--language models can provide dense semantic feedback, yet it remains unclear whether their scores anticipate collisions and which component drives an observed safety improvement. Episodic cost can also favour policies that make little task progress. To address these gaps, we propose VLM-Safe-RL, a framework that integrates frozen CLIP signals into PPO-Lagrangian through reward shaping and an augmented multiplier update. On MetaDrive Hard, which combines the densest traffic with the largest map, the catastrophe rate falls from 31.6% to 19.4%. FormulaOne-L2 analysis finds no evidence that the CLIP signals anticipate collisions and shows that the VLM term has a negligible effect on the Lagrange multiplier. These findings show a conditional reduction in observed catastrophe rate without evidence of collision anticipation.

A nascent family of methods that forgoes the policy gradient and reweights a supervised regression instead has garnered momentum in reinforcement learning for diffusion and flow models. DiffusionNFT, FlowAWR, and RAM are representative regimes with contrasting motivations. It is yet opaque what, if anything, they share. We substantiate that each is the solution of one divergence-constrained reward-maximization problem, and they are differentiated only by the convex generator that defines the constraint. Under the unified modeling framework, we unravel the relaxations that prior art made during building the advantage-embedded regression target: approximating the KKT condition and posterior normalizer for the linear and exponential tilt shapes DiffusionNFT and FlowAWR respectively, while preserving the exact sparsemax projection onto the probability simplex for linear tilt leads to another superior model type in this work. Beyond the theoretical underpinnings, we further empirically investigate the design space and shed light on the training recipe for regression-style diffusion RL. Retaining the merits discovered during our exploration gives rise to DiffusionRFT, our paradigm that converges faster, trains more stably, and attains the top performance.

Online safe reinforcement learning (RL) seeks policies that maximize reward while satisfying safety constraints. A popular line of research in safe RL relaxes safety to a soft expected-cost constraint and solves the resulting Constrained Markov Decision Process via primal-dual Lagrangian updates that only enforce safety on average. To address this limitation, hard, state-wise constraints are introduced and often imposed through Hamilton-Jacobi (HJ) reachability. Yet such constraints require solving different objectives in the feasible and infeasible regions: reward maximization in the former, recovery toward the feasible regions in the latter. The resulting target action distributions are inherently multimodal, and this structure poses a fundamental challenge for the Gaussian or deterministic actors used in existing HJ-based safe RL, which often collapse onto suboptimal modes. Diffusion policies provide the expressiveness needed to represent such distributions, and recent work on Q-score matching offers a route to training them for online RL by score regression -- but has been applied only to reward maximization. We propose Safe Score Matching (SSM), an off-policy actor-critic method that adapts Q-score matching to hard-constrained safe RL by gating a two-branch score target with HJ reachability: inside the feasible set, the denoising process degenerates to Q-score matching on actions classified as viable by the HJ critic; outside, a recovery branch biases denoising toward regions with lower worst-case violation. On quadrotor and fixed-wing trajectory-tracking and stabilize-and-avoid benchmarks, SSM attains the best or near-best task performance with low false-safe rates, whereas the primal-dual baseline admits more unsafe behavior and reachability-based baselines tend to be more conservative; on Safety-Gymnasium velocity tasks, SSM attains the lowest cost with competitive reward.

Embodied AI systems, particularly humanoid robots deployed in real world scenarios require whole-body control policies that are both task-responsive and physically smooth. However, smoothness is not uniform across the body: lower body must remain sufficiently reactive, while the upper body must be tightly regulated to preserve stability. Existing reinforcement learning approaches typically impose smoothness through auxiliary terms in the reward function, which compete with task objectives, treating the body as uniform and provide no direct control over the physical quantities responsible for smooth behavior. We introduce DeCap (Decoupled Constraint-aware policy), a constrained reinforcement learning algorithm that decouples whole-body smoothness into separate upper- and lower-body constraint groups, each formulates smoothness as explicit constraints on physical motion limits. To improve constraint satisfaction near feasibility boundaries, DeCap incorporates a bounded barrier penalty that activates proactively as limits are approached and remains bounded at the constraint limit. On real-world humanoid whole-body control task, DeCap reduces upper-body action rate by 2.50x and acceleration by 2.18x relative to reward-based smoothness policies, while also improving lower-body smoothness and reducing transient motion. We demonstrate that a fixed set of smoothness constraints transfers across diverse terrains, alleviating the need of extensive reward tuning.

Language models now generate symbolic music from text, and research has focused on musicality. However, many applications require a score that meets explicit constraints, which models struggle to satisfy jointly: on MusicConstraintBench, our benchmark of 2,180 items over eight families of programmatically verifiable constraints, Llama-3.1-70B satisfies 0.630 of single-constraint items but only 0.044 of four-constraint ones. As a remedy, we introduce MusicRLVR, which trains a language model with group relative policy optimisation (GRPO) on verifier rewards alone, needing no human annotation, reward model or music-domain supervised fine-tuning. MusicRLVR incorporates (1) a hard validation gate that rejects malformed scores, (2) graded per-family credit that, unlike a binary reward, separates partially correct outputs, and (3) an all-satisfied bonus for meeting every constraint at once. Extensive experiments show that, in under four hours of training, MusicRLVR raises Qwen3-4B-Instruct-2507 from 0.160 to 0.797 on mixed constraints, outperforming Llama-3.1-70B, and generalises to unseen property combinations, out-of-range parameters and more constraints than any training prompt. The recipe transfers to Qwen3-8B, and neither trained model loses significant accuracy on general benchmarks.

Battery energy storage system (BESS) dispatch must preserve operational feasibility while declining price spreads reduce the margin available to pay for cycling. We study a proximal policy optimization (PPO) controller whose pre-selection physical action mask and emergency projection are separated from a causal, forecast-informed economic advisory. All forecast-dependent methods receive the same causal 24-step forecast and grid-side settlement. Across five PPO seeds, advice-on net profit is 30.59 and 18.04 USD per 336-hour T1 and T2 window, versus 36.77 and 22.94 USD for proxy-cost MPC; PPO remains below this reference in both periods. Advice raises T2 profit from 16.45 to 18.04 USD while reducing throughput, but is immaterial in T1. On disjoint weekly blocks, PPO is stable under daily, weekly, and blended seasonal forecasts, weakens under persistence, and remains below proxy-cost MPC. Paired diagnostics localize changes to the observed 5-10 USD/MWh regime with mixed SoC-dependent effects. An M0-M6 ablation shows that mask removal sends thousands of infeasible requests to projection, while removing both physical layers exposes ramp violations. The evidence separates economic screening from feasibility enforcement without claiming formal safety, lifecycle-optimal aging, or RL dominance.

Meta-reinforcement learning (meta-RL) enables agents to adapt to unseen tasks with limited experience. Despite its promise, the application of meta-RL in real-world tasks is hindered by safety requirements, which have been underexplored in prior work. In this paper, we propose a safe meta-RL framework that explicitly accounts for safety during adaptation. Our key insight is to reason about safety in the information space, which captures both the physical state and the agent's belief over the underlying task. Within this space, we introduce a safety value function that measures the probability of the agent avoiding unsafe regions indefinitely. We show that this function satisfies a self-consistency condition and a Bellman equation, which make it learnable via meta-RL. Based on this formulation, we develop a safe meta-RL algorithm that learns the safety value function and leverages it for safety filtering and constrained policy optimization. Experiments on meta-RL benchmarks demonstrate the effectiveness of the proposed method.

Safe reinforcement learning (RL) is commonly formalized as a Constrained Markov Decision Process (CMDP), in which an agent maximizes expected reward while keeping its expected cumulative cost below a specified safety bound. Existing safe RL benchmarks predominantly report whether an algorithm is safe on average, following this expectation-based guarantee. We argue that this convention is insufficient to reliably characterize an algorithm's true safety: it fails to capture how often and how severely the safety bound is violated, whether this holds consistently across tasks and safety bounds, and whether training-time behavior is representative of behavior of the final converged policy. Therefore, we introduce (i) evaluation metrics for safe RL that address each of these concerns and in addition allow for aggregation across tasks and safety bounds. We furthermore define (ii) a safety tier system to systematically categorize and compare algorithms in terms of safety and reliability at both training and for a final policy. Using this framework, we provide (iii) an empirical safety evaluation across multiple safety navigation tasks. Our results show that aggregate metrics, distributional reporting, and task- and safety bound-specific results each reveal information the other metrics cannot. We therefore recommend reporting all three jointly, rather than compressing this information into a single value, as is common practice. We provide SafeRLEval, an open-source evaluation suite to support the reliable characterization of safety in future safe RL research.

Data-driven driving simulators command accelerations and steering rates from a fixed grid without constraining the realized accelerations and jerks. As a result, reinforcement-learning policies inflate safety metrics through abrupt, last-second maneuvers that lie far outside the range of human driving and would be unacceptable to occupants of a real vehicle, so the metrics measure simulator permissiveness rather than policy quality. Enforcing comfort bounds naively is not enough: lateral limits shrink quadratically with speed, so clamping a static grid saturates it and destroys fine-grained control ("grid collapse"). We propose an adaptive action parameterization that rediscretizes the grid at every step to span exactly the per-step feasible control set, via closed-form inversion of the lateral-jerk constraint. We further present PufferDrive-Editor, a browser-based tool to audit realized kinematics and author kinematically challenging scenes. On the Waymo Open Motion Dataset and a hand-authored slalom, our adaptive model holds comfort violations below 1% while outperforming clipped-grid and direct-jerk baselines in navigability.

Regularization-based methods have become a standard approach for training Deep Reinforcement Learning policies against adversarial input perturbations. In this paper, we unify these methods by deriving new upper bounds on the performance gap between the nominal and worst-case policies. Each upper bound is expressed as an existing regularization objective plus a KL-divergence penalty between the nominal and worst-case policies, which further explains why adding a KL penalty improves robustness in practice. Building on these bounds, we formulate robust training as a constrained optimization problem, showing that existing methods correspond to the special case of a fixed Lagrange multiplier. We instead update the multiplier jointly with the policy to automatically tune the regularization weight. Finally, we conduct extensive adversarial evaluations across several continuous control tasks to validate our theoretical analysis.

Ensuring safety in reinforcement learning under nonstationarity requires anticipating changes in risk before they lead to unsafe behavior. Existing approaches typically rely on safety constraints defined at design time or updated reactively during execution, assuming that such constraints remain valid over time. However, in nonstationary environments with evolving contexts and changing driving layouts, these assumptions may fail. We propose a framework for proactive safety constraint generation based on context forecasting. The approach infers latent environmental context from observations, predicts its future evolution, and constructs safety constraints adapted to anticipated conditions. This enables the agent to proactively avoid unsafe regions instead of reacting only after safety violations occur. We evaluate the method in driving environments with structured context variation. The experiments include a sweep over nonstationarity intensities and additional held-out driving layouts, including highway, intersection, and racetrack scenarios. Results show that proactive constraint generation substantially reduces collisions under both seen and out-of-training nonstationarity intensities and generally remains effective across held-out driving layouts while maintaining usable task performance. These findings suggest that context-based constraint generation is a promising approach for safe reinforcement learning under nonstationarity.