Risk-Sensitive RL

RL: Reinforcement Learning

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10 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Latest papers 58

Jun 12, 2026cs.LG

Utility-Constrained Policy Optimization

Constrained MDPs (CMDPs) are a widely adopted framework for incorporating safety into RL agents; however, the framework does not support risk-sensitive constraints. This can be problematic: For example, CMDPs allow for optimal solutions that, in order to satisfy the risk-neutral constraints, mix infrequent catastrophic behaviors and frequent, overly conservative ones. Moreover, prior empirical results suggest that enforcing stricter, risk-sensitive constraints can improve performance even under risk-neutral evaluation. The natural framework to incorporate risk-sensitive constraints is utility-constrained MDPs (UCMDPs), but no practical solutions for this problem existed. In this work, we introduce a simple yet powerful methodology for UCMDPs and constrained RL. Besides allowing for risk-sensitive constraints, our framework does not require us to fix constraint limits in advance of training the agent, provided that a sensible range is known. This increases policy flexibility and, in practice, allows for adjustments to these limits at no extra training cost. Besides benefiting from the generality of the framework, our agent shows strong performance in practice, consistently matching or outperforming existing baselines in several Safety Gymnasium benchmark tasks.

Mehrdad Moghimi, Bernardo Avila Pires

York University Toronto, Canada · Google DeepMind London, United Kingdom

Constrained RL Risk-Sensitive RL Safe RL

Jun 11, 2026cs.MA

Safety-Contract Graph Multi-Agent Reinforcement Learning for Autonomous Network Security Response

Autonomous network-security response systems promise to reduce Security Operations Centre (SOC) reaction latency, but reward-only multi-agent reinforcement learning (MARL) can improve security reward while remaining non-deployable. We present a safety-contract graph MARL framework and instantiate it as ACD

^3

-GAT (Adaptive Constrained Counterfactual Decisioning with a Graph Attention Network encoder), an architecture that separates simulator observations from reusable operational budgets, constrained optimization, graph state encoding, and counterfactual action screening. We evaluate the method in CAGE Challenge 4, where agents operate under budgets for Mean Time to Recover (MTTR), false-positive response, and firewall change-management disruption. Across the benchmark, every unconstrained method violates the SOC downtime budget in 100% of evaluated episodes, with mean downtime proxy costs of 311-430 against a budget of 50. This complements prior CAGE Challenge 4 findings by showing that reward-only learning lacks operational discipline. Constrained MAPPO-GAT (C-MAPPO-GAT) isolates Lagrangian operational-cost control and budget-aware screening, while ACD

^3

-GAT adds budget context, CVaR tail-risk estimation, opponent-belief state, and Graph Counterfactual Risk Propagation (G-CRP). The replicated comparison includes three 200-episode seeds for IPPO, MAPPO-GAT, C-MAPPO-GAT, and ACD

^3

-GAT. C-MAPPO-GAT reduces downtime violation from 100% to 0.3% and mean downtime cost from 355.4 to 15.5 relative to MAPPO-GAT. ACD

^3

-GAT reduces mean downtime cost to 48.2 with a 13.8% violation rate, placing it on the safety-contract frontier rather than at the most conservative compliance point. Topology-seed and coupled adaptive Red-process stress tests preserve this contrast and show lower worst adaptive degradation for safety-constrained policies than reward-only MAPPO-GAT.

Jose Luis Lima de Jesus Silva

Oxaala Tecnologias, Rua Dinah Silveira de Queirós, 06, Quinta do Candeal, Horto Florestal, Salvador, 40296-160, Bahia, Brazil · Universidade Federal da Bahia, Instituto de Geociências, Rua Barão de Jeremoabo, s/n, Ondina, Salvador, Bahia, 40170-115, Brazil

Autonomous Cyber Defense Risk-Sensitive RL Cooperative MARL Multi-Agent Reinforcement Learning

Jun 4, 2026cs.LG

OrderGrad: Optimizing Beyond the Mean with Order-Statistic Policy Gradient Estimation

Policy-gradient methods usually optimize expected return, but many real world applications care about distributional properties of returns: tail risk, outlier robustness, or best-of-K discovery. We introduce OrderGrad, a family of likelihood-ratio and reparameterization gradient estimators for order-statistic objectives. OrderGrad optimizes finite-sample L-statistics, i.e., weighted averages of sorted rewards or costs, recovering objectives such as VaR, CVaR, trimmed means, medians, and top-m/best-of-K criteria by changing only the rank weights. For any fixed sample size and rank-weight vector, OrderGrad provides an unbiased gradient estimator for the corresponding order-statistic objective. The method is implemented as a simple reward transformation that can then be used in an otherwise standard policy-gradient or reparameterized update. We study the resulting estimator's variance behavior and evaluate it on tasks where mean optimization is mismatched to the deployment objective, including LLM math post-training and other tasks. OrderGrad provides a unified, plug-and-play route to risk-averse, robust, and exploratory learning. Code: https://github.com/paavo5/ordergrad

Paavo Parmas, Yongmin Kim, Kohsei Matsutani +5

The University of Tokyo

Stochastic Optimization Risk-Sensitive RL Policy Gradient Methods RL for Generative Models Policy Learning

Jun 3, 2026cs.LG

Scenario Generation for Risk-Aware Reinforcement Learning with Probably Approximately Safe Guarantees

Guaranteeing safety is critical to the deployment of reinforcement learning (RL) agents in the real-world, especially as policies learned using deep RL may demonstrate susceptibility to transition perturbations that result in unknown or unsafe behaviour. A method of policy verification is to construct probabilistic barrier-certificates by sampling policy trajectories with respect to safety constraints, thereby demarcating known safe behaviour from unknown behaviour. Obtaining tight upper and lower bounds on the probability of violation of these constraints may be difficult if the policy is susceptible to transition uncertainty or perturbation that places the agent in insufficiently explored states. To address this, we approximate the distribution of the encountered state-space using a variational autoencoder (VAE) and construct upper and lower-bound barrier-certificates using latent characteristics of states to optimize for regions of known, safe behaviour with high confidence. We frame this in our work as a dual optimization problem where the lower-bound barrier-certificate presents a more conservative estimate of the safe region than the upper-bound barrier-certificate. Sampling states that lie within the set difference of the two during training, i.e. the non-robust region, allows us to tighten the upper and lower bounds to provide sharper probabilistic guarantees on safety. Within our study, we describe the guarantees placed and demonstrate the tightness of our bounds experimentally.

Mohit Prashant, Arvind Easwaran

Nanyang Technological University

Control Barrier Functions Risk-Sensitive RL Safe RL Robust RL

May 28, 2026cs.AI

Uncertainty-Aware and Temporally Regulated Expert Advice in Reinforcement Learning for Autonomous Driving

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

Ahmed Abouelazm, Felix Klingebiel, Philip Schörner +1

FZI Research Center for Information Technology, Germany · Karlsruhe Institute of Technology, Germany

Reinforcement Learning Risk-Sensitive RL RL Exploration RL for Autonomous Driving

May 23, 2026cs.LG

Evolving Robustness--Exploration Trade-off in Online Reinforcement Learning via Quantile Bayesian Risk MDPs

In online reinforcement learning, data scarcity creates epistemic uncertainty that makes robustness important early in learning, whereas sufficient exploration is needed to learn the true-environment optimal policy. We study this time-varying robustness--exploration trade-off through a quantile Bayesian risk-aware Markov decision process (BR-MDP), in which the quantile level controls how posterior uncertainty enters the Bellman backup. We characterize this control through an asymptotic normality result for the difference between the quantile BR-MDP value and the value in the true environment. The result implies that upper/lower-tail quantiles induce optimism/pessimism towards epistemic uncertainty, and the magnitude of the optimism/pessimism decreases as data accumulate. Building on this characterization, we propose an online Bayesian risk-aware algorithm with an adaptive quantile schedule that emphasizes robustness early and gradually encourages exploration of less-visited state--action pairs. We establish sublinear Bayesian regret bounds with respect to both the true optimal value and the optimal BR-MDP robust value. Numerical experiments demonstrate strong performance in both exploration-demanding and exploration-costly environments.

Meichen Song, Yuhao Wang, Enlu Zhou

School of Industrial and Systems Engineering Georgia Institute of Technology Atlanta, GA 30332, USA

Reinforcement Learning Bayesian RL Risk-Sensitive RL RL Exploration Robust RL

May 20, 2026cs.LG

On the Sample Complexity of Discounted Reinforcement Learning with Optimized Certainty Equivalents

We study risk-sensitive reinforcement learning in finite discounted MDPs, where a generative model of the MDP is assumed to be available. We consider a family or risk measures called the optimized certainty equivalent (OCE), which includes important risk measures such as entropic risk, CVaR, and mean-variance. Our focus is on the sample complexities of learning the optimal state-action value function (value learning) and an optimal policy (policy learning) under recursive OCE. We provide an exact characterization of utility functions

u

for which the corresponding OCE defines an objective that is PAC-learnable. We analyze a simple model-based approach and derive PAC sample complexity bounds. We establish that whenever

u

does not have full domain

\text{dom}(u)\neq \mathbb{R}

, the corresponding problem is not PAC-learnable. Finally, we establish corresponding lower bounds for both value and policy learning, demonstrating tightness in the size

SA

of state-action space, and for a more restricted class of utilities, we derive lower bounds that makes the dependence on the effective horizon

\frac{1}{1-γ}

explicit. Specifically, for

\text{CVaR}_τ

we show that the correct dependence on

τ

is

\frac{1}{τ^2}

, thus improving by a factor of

\frac{1}τ

over state-of-the-art although our bound has a suboptimal dependence on

\frac{1}{1-γ}

.

Oliver Mortensen, Mohammad Sadegh Talebi

Department of Computer Science, University of Copenhagen.

Reinforcement Learning Risk-Sensitive RL Sample-Efficient RL Conditional Value-at-Risk

May 20, 2026cs.RO

DiffCVaR: Reinforcement Learning for Risk Adaptation via Differentiable CVaR Barrier Functions

Planning through crowded environments under uncertain obstacle motions remains difficult, as stochastic interactions often induce overly conservative behavior or reduced efficiency. To address this challenge, we propose an end-to-end risk adaptation framework for crowd navigation under obstacle-motion uncertainty modeled by a Gaussian mixture model. The framework combines reinforcement learning~(RL) with a differentiable quadratic-program safety layer based on Conditional Value-at-Risk~(CVaR) barrier functions, jointly learning nominal control input, risk level, and safety margin and enforcing explicit probabilistic safety constraints. This design enables context-aware adaptation, promoting efficient behavior while invoking caution only when necessary. We conduct extensive evaluations in dynamic, uncertain, and crowded environments across varying obstacle densities and robot models, and further assess generalization under three out-of-distribution cases. Comparisons across optimization-based, RL-based, and integrated RL and optimization methods are provided, and the proposed method is shown to deliver the strongest overall performance in safety, efficiency, and generalization under uncertainty.

Xinyi Wang, Taekyung Kim, Bardh Hoxha +2

Department of Robotics, University of Michigan, Ann Arbor, MI, 48109, USA · Toyota Motor North America, Research & Development, Ann Arbor, MI, 48105, USA · Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

Control Barrier Functions Risk-Sensitive RL Safe RL Conditional Value-at-Risk Robot Collision Avoidance

May 19, 2026cs.RO

SafeAlign-VLA: A Negative-Enhanced Safe Alignment Framework for Risk-Aware Autonomous Driving

End-to-end autonomous driving systems excel in common scenarios but struggle with safety-critical long-tail cases. Vision-Language-Action (VLA) models are promising due to their strong reasoning capabilities. However, most VLA-based approaches rely on positive expert demonstrations, rarely exploiting negative samples, leading to insufficient understanding of risky behaviors and safety boundaries. To address this limitation, we propose SafeAlign-VLA, a unified negative-enhanced safe alignment framework that incorporates negative data into supervised learning and reinforcement learning. First, we develop a counterfactual safety pairing paradigm to generate structured safety labels and counterfactual positive trajectories from risky scenarios via counterfactual reasoning. Then, a two-stage training strategy is adopted: negative-enhanced supervised fine-tuning for failure feedback and trajectory correction, followed by anchor-based group relative policy optimization that uses positive and negative trajectories as contrastive anchors to steer sampling and penalize high-risk behaviors via group-relative advantages. Experiments on NAVSIM and DeepAccident validate the proposed framework. SafeAlign-VLA achieves 89.1 PDMS on the NAVSIM v1 testset, improving over the baseline without negative data by 1.3%. On DeepAccident, it reduces the collision rate to 3.36%, while achieving 84.2% language accuracy and 85.8% risk prediction accuracy. These results demonstrate the effectiveness of the proposed negative-enhanced safe alignment framework for safe and robust autonomous driving.

Kefei Tian, Yuansheng Lian, Kai Yang +2

aCollege of Transportation, Tongji University, Shanghai, 200092, China · bDepartment of Civil Engineering, Tsinghua University, Beijing, 100084, China · cSchool of Vehicle and Mobility, Tsinghua University, Beijing, 100084, China +1

End-to-End Autonomous Driving Risk-Sensitive RL Vision-Language-Action Models Autonomous Driving Planning

May 15, 2026stat.ML

Pessimistic Risk-Aware Policy Learning in Contextual Bandits

We study risk-aware offline policy learning, aiming to learn a decision rule from logged data that is optimal under general risk criteria. This problem is crucial in high-stakes domains where online interaction is infeasible and adverse outcomes must be carefully controlled. However, existing literature on offline contextual bandits either centers on expected-reward criteria or restricts risk considerations to policy evaluation instead of optimization. In this work, we propose a unified distributional framework for optimizing Lipschitz-continuous risk functionals, a broad class of risk measures encompassing mean-variance, entropic risk, and conditional value-at-risk, among others. By developing novel empirical concentration inequalities for importance sampling-based distributional estimators, our analysis derives data-dependent suboptimality bounds with an

\tilde{\mathcal{O}}(1/\sqrt{n})

rate, without relying on restrictive uniform overlap assumptions. This rate is minimax optimal and matches that of risk-neutral offline policy optimization, indicating that optimizing general Lipschitz risk criteria incurs no additional statistical cost relative to the expected-reward.

Yilong Wan, Yuqiang Li, Xianyi Wu

Risk-Sensitive RL Contextual Bandits Statistical Learning Theory

May 14, 2026cs.LG

Action-Conditioned Risk Gating for Safety-Critical Control under Partial Observability

Many safety-critical control problems are modeled as risk-sensitive partially observable Markov decision processes, where the controller must make decisions from incomplete observations while balancing task performance against safety risk. Although belief-space planning provides a principled solution, maintaining and planning over beliefs can be computationally costly and sensitive to model specification in practical domains. We propose a lightweight risk-gated reinforcement learning approximation for risk-sensitive control under partial observability. The method constructs a compact finite-history proxy state and learns an action-conditioned predictor of near-term safety violation. This predicted candidate-action risk is used in two complementary ways: as a risk penalty during value learning, and as a decision-time gate that interpolates between optimistic and conservative ensemble value estimates. As a result, low-risk actions are evaluated closer to reward-seeking estimates, while high-risk actions are evaluated more conservatively. We evaluate the approach in two safety-critical partially observable domains: automated glucose regulation and safety-constrained navigation. Across adult and adolescent glucose-control cohorts, the method improves overall glycemic tradeoffs and substantially reduces runtime relative to a belief-space planning baseline. On Safety-Gym navigation benchmarks, it achieves a more favorable reward-cost balance than unconstrained RL and several standard safe-RL baselines. These results suggest that action-conditioned near-term risk can provide an effective local signal for approximate risk-sensitive POMDP control when full belief-space planning is impractical.

Yushen Liu, Yin-Jen Chen, Ziyi Chen +4

University of Virginia · Google · University of Maryland, College Park +3

Safety-Critical Control Partially Observable RL Risk-Sensitive RL Feedback Control Safe RL

May 13, 2026cs.RO

Safety-Constrained Reinforcement Learning with Post-Training Reachability Verification for Robot Navigation

Safe navigation for mobile robots demands policies that remain reliable under the high-consequence perception uncertainty of cluttered environments. Yet most existing safe reinforcement learning (RL) methods assess safety through average cumulative cost. Such metrics can mask dangerous tail-risk behaviors. To address this, we propose a framework that trains risk-sensitive policies through Conditional Value-at-Risk (CVaR) constrained optimization on an off-policy TD3 backbone and evaluates their safety margins post-training through neural network reachability verification. During training, the policy is optimized under CVaR constraints on cumulative costs, promoting sensitivity to high-cost tail outcomes rather than average behavior alone. After training, we compute action reachable sets under bounded observation uncertainty using Taylor Model analysis, yielding a safety rate metric that quantifies the proportion of evaluated states at which the policy's reachable action set remains within prescribed safety margins. A key finding is that policies trained with CVaR constraints maintain larger safety margins from obstacles across evaluated states. This makes them significantly more amenable to formal reachability verification. Experiments across ten navigation scenarios and six baselines show that our method achieves a 98.3% success rate, the highest safety verification rate among all compared methods, while revealing that average cost rankings and reachability-based safety rankings can diverge. This indicates that reachability verification captures risks which are missed by empirical cost metrics alone. We further validate our approach on a physical Clearpath Jackal robot, demonstrating successful sim-to-real transfer.

Qisong He, Xinmiao Huang, Jinwei Hu +4

University of Liverpool, Liverpool, UK. · Universit´e Grenoble Alpes, Grenoble, France.

Constrained RL Risk-Sensitive RL Safe Robot Navigation Robot Safety

May 13, 2026cs.LG

Tight Sample Complexity Bounds for Entropic Best Policy Identification

We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the number of samples required to identify an approximately optimal policy. Precisely, known lower bounds scale in

Ω(e^{|β| H})

where

H

is the horizon of the MDP, while the state-of-the-art upper bound achieves at best

O(e^{2|β| H})

(arXiv:2506.00286v2) using a generative model. We show that this extra exponential factor can be traced to overly loose concentration control for exponential utilities. To close this open gap, we revisit the analysis of this problem through a forward-model based algorithm building on KL-based exploration bonuses that we adapt to the entropic criterion. The improvement we get is due to two main novel technical innovations. We leverage the smoothness properties of the exponential utility to derive sharper concentration bounds, and we propose a new stopping rule that exploits further this tightness to obtain a sample complexity that matches the lower bound.

Amer Essakine, Claire Vernade

ENS Paris Saclay · University of Technology Nuremberg

Reinforcement Learning Risk-Sensitive RL Policy Learning Sample-Efficient RL

May 8, 2026cs.LG

Reinforcement Learning for Exponential Utility: Algorithms and Convergence in Discounted MDPs

Reinforcement learning (RL) for exponential-utility optimization in discounted Markov decision processes (MDPs) lacks principled value-based algorithms. We address this gap in the fixed risk-aversion setting. Building on the Bellman-type equation for exponential utility studied in \cite{porteus1975optimality}, we derive two Q-value-style extensions and show that the associated operators are contractions in the

L_\infty

and sup-log/Thompson metrics, respectively. We characterize their fixed points and prove that the induced greedy stationary policy is optimal for the exponential-utility objective among stationary policies. These structural results lead to two model-free algorithms: a two-timescale Q-learning--style algorithm, for which we establish almost-sure convergence and provide finite-time convergence rates via timescale separation, and a one-timescale algorithm governed by a sublinear power-law operator. Since the latter does not admit a global contraction in standard metrics, we prove its convergence using delicate arguments based on local Lipschitzness, monotonicity, homogeneity, and Dini derivatives, and provide a scalar finite-time analysis that highlights the challenges in obtaining convergence rates in the vector case. Our work provides a foundation for value-based RL under exponential-utility objectives.

Gugan Thoppe, L. A. Prashanth, Ankur Naskar +1

Computer Science and Automation, Indian Institute of Science, Bengaluru · Computer Science and Engineering, Indian Institute of Technology Madras, Chennai · Tata Consultancy Services Limited, Hyderabad

Markov Decision Processes Reinforcement Learning Q-Learning Risk-Sensitive RL Model-Free RL

May 8, 2026cs.LG

Actor-Critic Algorithm for Dynamic Expectile and CVaR

Optimizing dynamic risk with stochastic policies is challenging in both policy updates and value learning. The former typically requires transition perturbation, while the latter may rely on model-based approaches. To address these challenges, we propose a surrogate policy gradient without transition perturbation under softmax policy parameterization. We further develop model-free value learning methods for dynamic expectile and conditional value-at-risk by leveraging elicitability. Finally, inspired by Expected SARSA and Expected Policy Gradient, a model-free off-policy actor-critic algorithm is constructed. Empirical results in domains with verifiable risk-averse behavior show that our algorithm can learn risk-averse policy and consistently outperforms other existing methods.

Yudong Luo, Erick Delage

1GERAD & Department of Decision Sciences, HEC Montr´eal, Canada · 2Mila - Quebec AI Institute, Canada

Reinforcement Learning Risk-Sensitive RL Actor-Critic Methods Conditional Value-at-Risk Off-Policy RL

May 7, 2026cs.LG

Learning Material-Aware Hamiltonian Risk Fields for Safe Navigation

Risk-aware navigation should be selective: a policy should expose evasive degrees of freedom only when the local scene admits a lower-risk feasible maneuver, and suppress them when no safer alternative exists. We show that adding one context-energy term to a port-Hamiltonian navigation policy produces a learned force channel with exactly this falsifiable signature. When the local risk field contains a feasible lower-risk direction, the induced context force activates toward it; when the apparent escape is blocked or not yet available, a route-aware gate suppresses lateral force rather than hallucinating an unsafe maneuver. A CVaR tail-risk objective focuses gradient updates on rare but consequential risk transitions. We validate the selectivity signature across four settings. In the primary delayed-required-escape benchmark, route-aware CVaR reduces premature force activation from 0.950 to 0.180 versus DWA while raising success from 0.480 to 0.810 with zero replans. On real off-road terrain (RELLIS-3D), route-aware enrichment achieves correct activation rate 0.837 and false activation rate 0.114, compared to 0.378/0.752 for scalar risk gradients. On static semantic maps (DFC2018), enrichment reduces catastrophic failure from 0.60 to 0.10 and oscillation by 90.7% while preserving path efficiency. In highway traffic, collisions drop from 100% to 0% when a lane escape is feasible; when no escape exists, the policy suppresses the lateral maneuver. The selectivity property follows from the gradient structure of the context energy rather than from training-time tuning.

Aditya Sai Ellendula, Yi Wang, Chandrajit Bajaj

Department of Computer Science, University of Texas at Austin, Austin, TX 78712, USA · Oden Institute, University of Texas at Austin, Austin, TX 78712, USA

Collision Avoidance Dynamical Systems Autonomous Driving Risk-Sensitive RL Safe Robot Navigation Port-Hamiltonian Systems

May 7, 2026cs.LG

RVPO: Risk-Sensitive Alignment via Variance Regularization

Current critic-less RLHF methods aggregate multi-objective rewards via an arithmetic mean, leaving them vulnerable to constraint neglect: high-magnitude success in one objective can numerically offset critical failures in others (e.g., safety or formatting), masking low-performing "bottleneck" rewards vital for reliable multi-objective alignment. We propose Reward-Variance Policy Optimization (RVPO), a risk-sensitive framework that penalizes inter-reward variance during advantage aggregation, shifting the objective from "maximize sum" to "maximize consistency." We show via Taylor expansion that a LogSumExp (SoftMin) operator effectively acts as a smooth variance penalty. We evaluate RVPO on rubric-based medical and scientific reasoning with up to 17 concurrent LLM-judged reward signals (Qwen2.5-3B/7B/14B) and on tool-calling with rule-based constraints (Qwen2.5-1.5B/3B). By preventing the model from neglecting difficult constraints to exploit easier objectives, RVPO improves overall scores on HealthBench (0.261 vs. 0.215 for GDPO at 14B,

p < 0.001

) and maintains competitive accuracy on GPQA-Diamond without the late-stage degradation observed in other multi-reward methods, demonstrating that variance regularization mitigates constraint neglect across model scales without sacrificing general capabilities.

Ivan Montero, Tomasz Jurczyk, Bhuwan Dhingra

Apple

RL for Language Models Risk-Sensitive RL Multi-Objective Language Model Alignment Reward Design for RL

May 5, 2026cs.LG

Quantile Geometry Regularization for Distributional Reinforcement Learning

Quantile-based distributional reinforcement learning methods learn return distributions through sampled quantile regression, but their bootstrapped target quantiles may induce distorted or degenerate distribution estimates. We propose Robust Quantile-based Implicit Quantile Networks (RQIQN), a lightweight Wasserstein distributionally robust enhancement boosted from a quantile estimation perspective. We first reinterpret a snapshot of IQN loss as a collection of local empirical quantile estimation problems over sampled current fractions. We then robustify each local slot with a Wasserstein distributionally robust quantile estimation formulation, yielding a closed-form, fraction-dependent correction to the Bellman target. This correction directly addresses distributional degeneration: its median antisymmetry preserves the risk-neutral quantile average, while its monotonicity enlarges upper-lower quantile gaps and counteracts collapsed distributional spread. RQIQN thus regularizes quantile geometry without changing the underlying value objective or requiring additional sample set reconstruction. Finally, we empirically show that the proposed RQIQN outperforms other existing quantile-based distributional reinforcement learning algorithms in risk-sensitive navigation and Atari games.

Zhaofan Zhang, Minghao Yang, Rufeng Chen +2

Information Hub, AI Thrust Hong Kong University of Science and Technology (Guangzhou) Guangzhou, Guangdong, China

Distributional RL Quantile Regression Risk-Sensitive RL Distributionally Robust Optimization Distributionally Robust RL

May 4, 2026cs.MA

MARS-DA: A Hierarchical Reinforcement Learning Framework for Risk-Aware Multi-Agent Bidding in Power Grids

The increasing penetration of renewable energy has introduced substantial volatility into wholesale electricity markets, complicating the optimal bidding strategies for power producers. Traditional Reinforcement Learning (RL) approaches often struggle to balance profit maximization with risk management, frequently overfitting to specific market conditions or failing to account for the stochastic spread between Day-Ahead (DA) and Real-Time (RT) settlements. To address these challenges, this paper makes two primary contributions. First, we introduce and open-source a high-fidelity gymnasium environment for two-settlement electricity market bidding. Grounded in extensive empirical data from the PJM Interconnection, the environment explicitly models the interplay between DA commitments and RT deviations, providing a standardized testbed for general and risk-sensitive agents. Second, we propose MARS-DA (Multi-Agent Regime-Switching for Day-Ahead markets), a novel hierarchical framework that orchestrates distinct sub-policies for risk management and profit seeking. MARS-DA utilizes a top-level Meta-Controller to dynamically blend the actions of two specialized base agents: a "Safe Agent" that optimizes for reliable DA allocation and a "Speculator Agent" that targets volatile RT arbitrage opportunities. Extensive experiments demonstrate that MARS-DA achieves superior risk-adjusted returns compared to state-of-the-art baselines while maintaining robust regime alignment during periods of extreme market volatility.

Jiayi Chen, Xuan Zhang, Guiling Wang

Department of Computer Science, New Jersey Institute of Technology

Hierarchical RL Risk-Sensitive RL Multi-Agent Reinforcement Learning Power Systems

May 1, 2026cs.LG

Reinforcement Learning with Markov Risk Measures and Multipattern Risk Approximation

For a risk-averse finite-horizon Markov Decision Problem, we introduce a special class of Markov coherent risk measures, called mini-batch measures. We also define the class of multipattern risk-averse problems that generalizes the class of linear systems. We use both concepts in a feature-based

Q

-learning method with multipattern

Q

-factor approximation and we prove a high-probability regret bound of

\mathcal{O}\big(H^2 N^H \sqrt{ K}\big)

, where

H

is the horizon,

N

is the mini-batch size, and

K

is the number of episodes. We also propose an economical version of the

Q

-learning method that streamlines the policy evaluation (backward) step. The theoretical results are illustrated on a stochastic assignment problem and a short-horizon multi-armed bandit problem.

Andrzej Ruszczynski, Tiangang Zhang

Department of Management Science and Information Systems, Rutgers University

Markov Decision Processes Reinforcement Learning Markov Models Q-Learning Risk-Sensitive RL

Apr 28, 2026cs.CL

Frictive Policy Optimization for LLMs: Epistemic Intervention, Risk-Sensitive Control, and Reflective Alignment

We propose Frictive Policy Optimization (FPO), a framework for learning language model policies that regulate not only what to say, but when and how to intervene in order to manage epistemic and normative risk. Unlike standard alignment methods that optimize surface-level preference or task utility, FPO treats clarification, verification, challenge, redirection, and refusal as explicit control actions whose purpose is to shape the evolution of belief, commitment, and uncertainty over time. We formalize alignment as a risk-sensitive epistemic control problem in which intervention decisions are selected based on their expected effect on downstream epistemic quality rather than on immediate reward alone. We introduce a compact taxonomy of frictive interventions, a structured friction functional that operationalizes multiple alignment failure modes, and a unified family of FPO methods spanning reward shaping, preference pairing, group-relative ranking, and risk-conditioned trust regions. We further propose an evaluation framework that measures epistemic competence directly through clarification behavior, calibration, contradiction repair, refusal proportionality, and information efficiency. Together, these results provide a formal and algorithmic foundation for learning agents that are aligned not only in outcome, but in epistemic conduct.

James Pustejovsky, Nikhil Krishnaswamy

Brandeis University · Waltham, MA, USA · Colorado State University +1

RL for Language Models Language Model Safety Evaluation LLM Safety Alignment Risk-Sensitive RL

Apr 17, 2026cs.GT

The Price of Paranoia: Robust Risk-Sensitive Cooperation in Non-Stationary Multi-Agent Reinforcement Learning

Cooperative equilibria are fragile. When agents learn alongside each other rather than in a fixed environment, the process of learning destabilizes the cooperation they are trying to sustain: every gradient step an agent takes shifts the distribution of actions its partner will play, turning a cooperative partner into a source of stochastic noise precisely where the cooperation decision is most sensitive. We study how this co-learning noise propagates through the structure of coordination games, and find that the cooperative equilibrium, even when strongly Pareto-dominant, is exponentially unstable under standard risk-neutral learning, collapsing irreversibly once partner noise crosses the game's critical cooperation threshold. The natural response to apply distributional robustness to hedge against partner uncertainty makes things strictly worse: risk-averse return objectives penalize the high-variance cooperative action relative to defection, widening the instability region rather than shrinking it, a paradox that reveals a fundamental mismatch between the domains where robustness is applied and instability originates. We resolve this by showing that robustness should target the policy gradient update variance induced by partner uncertainty, not the return distribution. This distinction yields an algorithm whose gradient updates are modulated by an online measure of partner unpredictability, provably expanding the cooperation basin in symmetric coordination games. To unify stability, sample complexity, and welfare consequences of this approach, we introduce the Price of Paranoia as the structural dual of the Price of Anarchy. Together with a novel Cooperation Window, it precisely characterizes how much welfare learning algorithms can recover under partner noise, pinning down the optimal degree of robustness as a closed-form balance between equilibrium stability and sample efficiency.

Deep Kumar Ganguly, Chandradithya S Jonnalagadda, Pratham Chintamani +1

Technical University of Munich (TU Munich) · Brown University · Indian Institute of Technology Tirupati (IIT Tirupati)

Cooperative Game Theory Multi-Agent Coordination Non-Stationary RL Game Theory Risk-Sensitive RL Robust RL+2

Mar 11, 2026cs.LG

Safe RLHF Beyond Expectation: Stochastic Dominance for Universal Spectral Risk Control

Safe Reinforcement Learning from Human Feedback (RLHF) typically enforces safety through expected cost constraints, but the expectation captures only a single statistic of the cost distribution and fails to account for distributional uncertainty, particularly under heavy tails or rare catastrophic events. This limitation is problematic when robustness and risk sensitivity are critical. Stochastic dominance offers a principled alternative by comparing entire cost distributions rather than just their averages, enabling direct control over tail risks and potential out-of-distribution failures that expectation-based constraints may overlook. In this work, we propose Risk-sensitive Alignment via Dominance (RAD), a novel alignment framework that replaces scalar expected cost constraints with First-Order Stochastic Dominance (FSD) constraints. We operationalize this constraint by comparing the target policy's cost distribution to that of a reference policy within an Optimal Transport (OT) framework, using entropic regularization and Sinkhorn iterations to obtain a differentiable and computationally efficient objective for stable end-to-end optimization. Furthermore, we introduce quantile-weighted FSD constraints and show that weighted FSD universally controls a broad class of Spectral Risk Measures (SRMs), so that improvements under weighted dominance imply guaranteed improvements in the corresponding spectral risk. This provides a principled mechanism for tuning a model's risk profile via the quantile weighting function. Empirical results demonstrate that RAD improves harmlessness over baselines while remaining competitive in helpfulness, and exhibits greater robustness on out-of-distribution harmlessness evaluations.

Yaswanth Chittepu, Ativ Joshi, Rajarshi Bhattacharjee +1

University of Massachusetts Amherst

Constrained RL LLM Safety Alignment Risk-Sensitive RL Decision-Making under Uncertainty

Feb 10, 2026cs.LG

Reinforcement learning with an expectile-based objective

We consider the policy evaluation and control in a finite horizon reinforcement learning (RL) setting under an expectile-based objective. First, we derive the mean-squared error (MSE) and concentration bounds for the classic estimator of expectiles based on independent and identically distributed (i.i.d.) samples. To the best of our knowledge, expectiles have not been analyzed in the non-asymptotic regime and the bounds we derive may be of independent interest. Next, we analyze a Monte Carlo type estimator of expectile of the Markov chain underlying a given policy. We derive upper bounds that hold in expectation as well as with high probability for this estimator. Further, we show the order-optimality of our estimator by deriving a lower bound on expectile-based policy evaluation. For the problem of control, we adopt a policy gradient approach and derive a policy gradient theorem for expectiles. Using this result, we propose a gradient estimator with a

O\left(1/m\right)

mean-squared error bounds, where

m

is the number of trajectories. Further, under standard assumptions for policy gradient-type algorithms, we establish smoothness of the expectile-sensitive objective, in turn leading to stationary convergence rate bounds for the overall risk-sensitive policy gradient algorithm that we propose. Finally, we conduct numerical experiments to show the utility of expectiles on popular RL benchmarks.

Shrey Rakeshkumar Patel, Sumedh Gupte, Soumen Pachal +2

Indian Institute of Technology Madras · TCS Research, India

Reinforcement Learning Risk-Sensitive RL Policy Gradient Methods

Feb 3, 2026cs.LG

Reward Redistribution for CVaR MDPs using a Bellman Operator on L-infinity

Tail-end risk measures such as static conditional value-at-risk (CVaR) are used in safety-critical applications to prevent rare, yet catastrophic events. Unlike risk-neutral objectives, the static CVaR of the return depends on entire trajectories without admitting a recursive Bellman decomposition in the underlying Markov decision process. A classical resolution relies on state augmentation with a continuous variable. However, unless restricted to a specialized class of admissible value functions, this formulation induces sparse rewards and degenerate fixed points. In this work, we propose a novel formulation of the static CVaR objective based on augmentation. Our alternative approach leads to a Bellman operator with: (1) dense per-step rewards; (2) contracting properties on the full space of bounded value functions. Building on this theoretical foundation, we develop risk-averse value iteration and model-free Q-learning algorithms that rely on discretized augmented states. We further provide convergence guarantees and approximation error bounds due to discretization. Empirical results demonstrate that our algorithms successfully learn CVaR-sensitive policies and achieve effective performance-safety trade-offs.

Aneri Muni, Vincent Taboga, Esther Derman +2

Universit´e de Montr´eal, Quebec, Canada · Mila - Quebec AI Institute, Quebec, Canada · GERAD & Department of Decision Sciences, HEC Montr´eal, Quebec, Canada

Markov Decision Processes Q-Learning Risk-Sensitive RL Conditional Value-at-Risk

Jan 30, 2026cs.LG

Cantelli Constrained Policy Optimization

We introduce Canary, a risk-averse method designed to optimize Value-at-Risk (VaR) constrained reinforcement learning (RL) problems. We employ Cantelli's inequality to obtain a tractable, conservative and smooth bound on the VaR constraint based on the first two moments of the cost return. This yields a constraint estimator that remains stable with tight violation thresholds in dense cost regimes. Extending the trust-region framework of the Constrained Policy Optimization (CPO) method, we further provide worst-case bounds for both policy improvement and constraint violation during the training process. Empirically during training, Canary is the only method that reliably satisfies the VaR constraint in every environment tested.

Rohan Tangri, Jan-Peter Calliess

Machine Learning Research Group, University of Oxford, Oxford, United Kingdom

Policy Optimization Constrained RL Risk-Sensitive RL

Jul 31, 2024cs.LG

ProSpec RL: Plan Ahead, then Execute

Imagining potential outcomes of actions before execution helps agents make more informed decisions, a prospective thinking ability fundamental to human cognition. However, mainstream model-free Reinforcement Learning (RL) methods lack the ability to proactively envision future scenarios, plan, and guide strategies. These methods typically rely on trial and error to adjust policy functions, aiming to maximize cumulative rewards or long-term value, even if such high-reward decisions place the environment in extremely dangerous states. To address this, we propose the Prospective (ProSpec) RL method, which makes higher-value, lower-risk optimal decisions by imagining future n-stream trajectories. Specifically, ProSpec employs a dynamic model to predict future states (termed "imagined states") based on the current state and a series of sampled actions. Furthermore, we integrate the concept of Model Predictive Control and introduce a cycle consistency constraint that allows the agent to evaluate and select the optimal actions from these trajectories. Moreover, ProSpec employs cycle consistency to mitigate two fundamental issues in RL: augmenting state reversibility to avoid irreversible events (low risk) and augmenting actions to generate numerous virtual trajectories, thereby improving data efficiency. We validated the effectiveness of our method on the DMControl benchmarks, where our approach achieved significant performance improvements. Code will be open-sourced upon acceptance.

Liangliang Liu, Yi Guan, BoRan Wang +5

1The Faculty of Computing, Harbin Institute of Technology, Harbin, China · 2The Artificial Intelligence Institute, Harbin Institute of Technology, ShenZhen, China · 3The Artificial Intelligence Institute, Harbin Institute of Technology, Harbin, China

Reinforcement Learning Risk-Sensitive RL Sample-Efficient RL Model-Based RL

May 23, 2024cs.LG

On the Approximation and Convergence of Distributional Policy Gradient Algorithms for Risk-Sensitive Reinforcement Learning

Risk-sensitive reinforcement learning (RL) is crucial for maintaining reliable performance in high-stakes applications. While traditional RL methods aim to learn a point estimate of the random cumulative cost, distributional RL seeks to estimate the entire distribution of it, leading to a unified framework for handling different risk measures. However, developing policy gradient methods for risk-sensitive distributional RL is inherently more complex as it often involves finding the gradient of a probability measure. This paper introduces a new distributional policy gradient framework for risk-sensitive RL, where we derive an analytical gradient of the probability measure of the cumulative cost. For practical implementation, we further design a categorical distributional policy gradient algorithm (CDPG) that approximates arbitrary distributions using a categorical family supported on fixed points. Using Conditional Value-at-Risk (CVaR) as the objective, we prove that the proposed CDPG converges to stationary points and establish its iteration complexities under inexact policy evaluation. Through experiments in a stochastic Cliffwalk environment, we demonstrate the effectiveness of the proposed algorithm and highlight the benefits of incorporating risk sensitivity into distributional RL.

Xian Yu, Minheng Xiao, Lei Ying

Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH, USA · Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA

Stochastic Optimization Distributional RL Risk-Sensitive RL Policy Gradient Methods