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

Oct 7, 2026stat.ML

Safe Meta-Policy Design with Risk Control

Models can be retrained as new data arrive, but deploying every new version risks replacing a good policy with a worse one. We study how to plan policy updates (i.e., meta-policy) before future candidates are trained, balancing the benefits of improvement against the risk of performance regression. Our offline meta-policy maximizes expected cumulative value subject to a budget on the expected number of updates that perform worse than the policies they replace. We estimate the value and risk of possible switches from historical learning trajectories, represent an update schedule as a path in a directed acyclic graph, and select a schedule using dynamic programming. A leading-order analysis identifies the signal-to-noise ratio of policy improvement as a key driver of update frequency, waiting times, and risk allocation: clearer improvements support earlier, more frequent updates, while noisier improvements call for longer waits or greater risk expenditure. Their asymptotic rates also reveal a diminishing marginal cost of achieving greater safety over time. Experiments on synthetic and clinical trial data illustrate the performance--risk tradeoff and compare our method with alternative baselines.

Wenbin Zhou, Michael Lingzhi Li, Shixiang Zhu

Heinz College of Information Systems and Public Policy, Carnegie Mellon University · Technology and Operations Management, Harvard Business School

Safe RL Risk-Sensitive RL

Oct 7, 2026cs.LG

Safe on Average, Unsafe in the Tail: When Is the Episodic-Cost Tail Controllable?

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.

Samuel Tetteh, Cody Fleming

Iowa State University Ames, Iowa, USA

Safe RL Constrained RL Risk-Sensitive RL

Oct 6, 2026cs.LG

Variance-Averse $n$ -Step Offline Reinforcement Learning for Sparse Long-Horizon Environments

Generative actors are transforming offline reinforcement learning (RL) by enabling expressive policy classes that model complex action distributions. However, this expressiveness also exposes a key challenge in heterogeneous datasets: generative policies can reproduce unreliable action modes whose return distributions exhibit high variance, occasionally yielding high returns by chance but lacking consistency. Consequently, maximizing the expected

Q

-value alone is insufficient for identifying reliable actions. We propose VAN-Flow (Variance-Averse

n

-step Flow), a framework that promotes reliable actions in generative offline RL. VAN-Flow combines (i) a categorical distributional critic, (ii) a variance-averse expectation operator that smoothly reweights atom probabilities to favor actions with both high returns and low dispersion, and (iii) a flow-matching generative actor guided via rejection sampling. Unlike CVaR or mean-variance objectives, the operator redistributes probability mass over the categorical return distribution without hard truncation or auxiliary penalty terms. Across more than 40 tasks from D4RL and OGBench, VAN-Flow consistently outperforms strong baselines, with the largest gains in long-horizon and high-variance regimes where reliable action selection becomes critical.

Guhyeon Kang, Minhae Kwon

Department of Electrical and Computer Engineering Sungkyunkwan University, Republic of Korea

Distributional RL Risk-Sensitive RL Offline RL RL for Generative Models

Oct 5, 2026cs.RO

Risk-Sensitive Crowd Navigation with Adaptive Ellipsoidal Conformal Prediction

Safe crowd navigation under distribution shift requires uncertainty representations that capture structured human-motion prediction errors and safety objectives that account for rare but consequential failures. Existing uncertainty-aware methods typically represent prediction errors using isotropic regions, which can be either overly conservative or poorly aligned with directional motion uncertainty. We introduce a risk-aware navigation framework that uses anisotropic conformal ellipsoids to translate structured prediction uncertainty into an episode-level conditional value-at-risk (CVaR) signal that regulates the Lagrangian safety penalty. In particular, adaptive ellipsoidal conformal prediction (AECP) captures directional prediction errors and adaptively calibrates uncertainty regions under distribution shift, while the resulting CVaR-regulated navigation policy is optimized using Lagrangian proximal policy optimization. We evaluate our proposed method under both in-distribution settings and out-of-distribution (OOD) settings involving shifts in pedestrian motion patterns. Compared with state-of-the-art baselines, our method maintains competitive in-distribution performance while improving success rates by 5.68-7.44 percentage points and reducing collision rates by 5.44-6.64 percentage points across OOD settings. We further deploy the trained policy without fine-tuning on a physical robot with onboard perception and CPU-only inference, showing that the full pipeline is feasible in physical crowd navigation.

Ruihan A. Li, Ziyao Guo, Yingying Li

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL

Distribution Shift Robustness Robot Navigation Conformal Prediction Risk-Sensitive RL

Oct 1, 2026cs.AI

PPO-HRAP: Proximal Policy Optimization with a Hybrid Regime-Aware Policy for Risk-Controlled Trading

Reinforcement learning for trading often struggles to balance upside participation with drawdown control. Profit-only policies can collapse toward passive long exposure on upward-drifting assets, while aggressively risk-penalized rewards can become too defensive during volatile periods. This paper proposes PPO-HRAP, a hybrid regime-aware policy that combines Proximal Policy Optimization with an interpretable regime prior. The agent observes both market features and portfolio-state variables, receives a reward combining portfolio log return, VIX-conditioned drawdown-increase penalty, target-exposure deviation, and turnover cost, and executes a blended action between the PPO actor output and a regime-derived target exposure. On the held-out 2020-2022 SPY test window, PPO-HRAP achieves 27.62% total return, 8.48% annualized return, 0.6447 Sharpe ratio, 0.8588 Sortino ratio, and 0.4592 Calmar ratio, while reducing maximum drawdown from 34.10% for Buy and Hold to 18.47%. Across five SPY seeds, PPO-HRAP remains stable with mean total return

0.2725 \pm 0.0109

and mean Sharpe ratio

0.6219 \pm 0.0565

. Single-run cross-asset tests on QQQ and DIA further show that the proposed method ranks first on total return and Sharpe ratio for all three reported assets. These results suggest that blending learned actions with a volatility-aware regime prior is a practical way to improve risk-adjusted trading behavior, although the current policy still incurs high turnover and cross-asset robustness beyond SPY remains limited to single-run evidence.

Duong Hien Chi Kien, Thanh Trung Huynh

College of Engineering and Computer Science, VinUniversity Ha Noi, Viet Nam

Reinforcement Learning Risk-Sensitive RL Proximal Policy Optimization Reward Design for RL Algorithmic Trading

Sep 30, 2026cs.LG

Exploring More, Reasoning Better: Stepwise Risk-Sensitive GRPO for Diffusion Language Models

Diffusion large language models (dLLMs) generate text by denoising a sequence or successive blocks, allowing several tokens to be revealed in parallel. Reinforcement learning with verifiable rewards (RLVR) reuses terminal feedback across these decisions, even as their conditioning context changes. We propose stepwise risk-sensitive GRPO (StepRS-GRPO), which varies the risk coefficient of the group-advantage transformation across denoising states while retaining the underlying trainer. For binary rewards, we show that this transformation is exactly a prompt- and state-dependent rescaling of centered outcome advantages. A capability-based calibration suggests a coefficient scale, while endpoint and interpolation ablations guide schedule selection. Across multiple dLLM backbones and mathematical reasoning benchmarks, StepRS-GRPO improves both pass@1 accuracy and pass@k coverage over centered GRPO, while increasing answer diversity. In our ablation studies, mass-matched controls support the contributions of state allocation and schedule direction, and the gains persist after matching the root mean square (RMS) of the advantages to that of centered GRPO. Reasoning-trace diagnostics further show that the diversity gains from StepRS-GRPO extend beyond final-answer strings.

Yue YU, Bowen Zuo, David Crandall +2

Indiana University · University of California, Riverside

RL for Language Model Reasoning Group Relative Policy Optimization Risk-Sensitive RL RL for Diffusion Models Diffusion Language Models LLM Reasoning

Sep 30, 2026cs.LG

Robust Risk-Sensitive Reinforcement Learning from Corrupted Human Feedback

Reinforcement learning with human feedback (RLHF) learns from human comparisons, which can be corrupted or deliberately manipulated. This paper studies online risk-sensitive RLHF with static conditional value-at-risk (CVaR) under adversarial preference-label flips. We consider additive linear rewards and a fixed-reference protocol with one comparison per episode and at most

C

flipped labels over

K

episodes. We propose weighted streamed-preference CVaR RLHF (WSP-CVaR-RLHF), which combines uncertainty-weighted reward estimation with optimistic augmented-state CVaR planning. For known transitions and normalized rewards, we establish the regret bound

\widetilde{O}\left(\frac{d}κ\sqrt{\frac{K}α}+\frac{dC}{κα}\right)

up to lower-order terms, where

d

is the reward-feature dimension,

α

is the CVaR level, and

κ

characterizes the preference link. The bound separates the clean statistical cost from the penalty caused by corrupted feedback. We further extend the analysis to unknown tabular transitions, where the trajectory distribution entering the CVaR objective must be learned together with the reward. We address the resulting coupled uncertainty using rectangular transition confidence sets, joint optimistic planning, and a history-level CVaR simulation argument. Experiments under four adversarial attacks demonstrate that WSP-CVaR-RLHF consistently reduces cumulative regret relative to its unweighted robust counterpart while preserving confidence-set coverage.

Xinyi Ni, Lifeng Lai

Department of Electrical and Computer Engineering, University of California, Davis, CA 95616, USA

Risk-Sensitive RL Robust RL Preference-Based RL RL from Human Feedback

Sep 29, 2026cs.AI

Character Training for Risk-Averse Agents

Risk aversion in resources could prevent misaligned AI agents from causing catastrophic harm. Misaligned but risk-averse agents would tend to favor safer strategies like making deals with humans over riskier strategies like rebelling. We train agents to be risk averse through character training, finding that persona traits provide a robust mechanism for instilling risk preferences. To do this, we construct a model constitution describing constant absolute risk aversion (CARA) over an agent's resources and instill it through on-policy distillation. Despite never seeing the benchmark's decision format during training, character-trained models are competitive with baselines trained directly on it, and generalise better than them out of distribution on two of our four models. We also modulate different aspects of the constitution, finding that token budget and model choice are the most influential aspect of character training to instill risk aversion. We conclude from these results that character training is a promising and scalable way to instil broad dispositions, which we can use to our advantage in mitigating risk from misaligned AI agents.

Arav Dhoot, Punya Syon Pandey, Jamie Johnson +3

UK AI Security Institute · Resolution

Risk-Sensitive RL AI Agent Safety LLM Agent Training

Sep 27, 2026cs.AI

RSD-Poker: Structure-Adaptive and Shift-Robust Risk-Utility Certification for Residual Policies in Imperfect-Information Games

Residual policy adaptation provides a lightweight way to modify a strong reference policy, but a shared scale and a fixed subgroup partition can hide heterogeneous degradation and become fragile when the deployment mixture of information states changes. We introduce RSD-Poker, a structure-adaptive and shift-robust certification framework that freezes a bank of residual families and scales, learns a policy-visible partition on an independent structure split, and freezes that partition before calibration labels are joined. Each candidate-group pair receives a weighted simultaneous upper certificate for anchor-relative risk and a lower certificate for weak-response utility. A robust group-to-candidate map is then selected over a predeclared uncertainty set of deployment group proportions. Under independent calibration units drawn from each frozen group's law, a candidate bank and partition fixed before calibration, and invariant within-group conditionals, the selected map satisfies its declared mixture-robust risk budget and utility certificate with probability at least

1-ζ_{risk}-ζ_{util}

. The information contract supports both a teacher-backed transform and a teacher-free observation-only student. The retained deterministic 24-state audit remains an exact replay diagnostic: empirical-zero selects

α=0.08

, raising the weak-response proxy from 4.2082 to 4.2889 with

0/12

held-out threshold crossings. On stratified held-out states, the learned-partition dual selector raises weak utility from 4.4074 under global dual certification to 4.4936 and lowers held-out violation from 0.0215 to 0.0078; its mixture-robust variant reaches violation 0.0059. Across five observation-only checkpoints, risk-calibrated residuals attain weak utility

4.3659\pm0.0177

and violation rate

0.0178\pm0.0057

.

Miaobo Hu, Shuhao Hu, Xiaobo Guo +5

School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China · Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

Distribution Shift Robustness Imperfect-Information Games Risk-Sensitive RL Distributionally Robust RL Residual Policy Learning

Sep 23, 2026cs.LG

Robust Adversarial Reinforcement Learning with Risk Sensitivity and Critic Consistency Regularization

Reinforcement learning (RL) achieves strong performance in sequential decision-making but remains brittle under dynamic uncertainty and distributional shifts. Robust Adversarial Reinforcement Learning (RARL) improves robustness via worst-case perturbations, but existing approaches frequently suffer from unstable optimization and degraded value estimation. In particular, overly aggressive adversaries can drive the agent toward uninformative failure states, while adversarial perturbations amplify disagreement between double critics and introduce biased value targets. We propose a unified framework, RACER (Risk-sensitive robust Adversarial critic ConsistEncy-regularized Reinforcement learning), that revisits adversarial RL from a risk-sensitive perspective. First, we introduce a state-dependent adversarial objective that adaptively regulates perturbation strength, suppressing harmful disturbances while preserving informative exploration. Second, we propose critic consistency regularization to reduce disagreement between Q-value estimators and stabilize learning. Comprehensive experiments on challenging continuous control benchmarks demonstrate that RACER consistently improves performance, robustness, and training stability over strong robust RL baselines.

Jiaxi Wu, Tiantian Zhang, Yuxing Wang +2

Shenzhen International Graduate School, Tsinghua University Shenzhen, China

Reinforcement Learning Risk-Sensitive RL Robust RL Consistency Regularization

Sep 11, 2026cs.LG

Certifying Lower Bounds for Risk-Sensitive Reinforcement Learning under Adversarial State Perturbations

Reinforcement learning (RL) agents deployed in real-world environments are often vulnerable to adversarial perturbations in state observations, creating risks in safety-critical applications. Certification methods can improve robustness against adversarial perturbations by providing lower bounds on expected cumulative rewards. Existing certification methods, however, mainly focus on risk-neutral objectives. In this paper, we extend certification methods to risk-sensitive objectives by establishing lower bounds on the exponential utility of cumulative rewards under

l_{p}

-norm-bounded state adversarial perturbations (

1\leq p <\infty

). By introducing a

\phi

-divergence relaxation of the perturbation set, we formulate the risk-sensitive certification problem as a convex optimization and derive its dual to obtain a tractable approximation of the certified lower bound. We further propose an empirical method that improves certified lower bounds by selecting the training risk-aversion parameter

\beta

independently of the risk level used during evaluation. Experiments on both OpenAI Gym environments and a machine replacement problem show that, compared to risk-neutral training, risk-averse training generally yields policies with higher certified lower bounds, particularly under larger perturbation budgets. Moreover, under both risk-neutral and risk-averse evaluation settings, increasing risk aversion during training leads to non-monotonic certification performance, where certified lower bounds initially improve but eventually decrease due to overly conservative policies.

Tong Li, Saunak Kumar Panda, Yisha Xiang

Department of Industrial and Systems Engineering, University of Houston, 4302 University Dr, Houston, 77004, TX, USA. · Department of Decision and Information Science, University of Houston, 4302 University Dr, Houston, 77004, TX, USA.

Risk-Sensitive RL Adversarial Perturbations Certified Robustness Robust RL

Sep 9, 2026cs.RO

A Risk-Sensitive and Uncertainty-Aware Decision-Making and Control Framework for Safe and Robust Autonomous Driving

Reinforcement learning (RL) has demonstrated considerable potential for autonomous driving decision-making. However, its deployment in urban autonomous driving, particularly at highly interactive unsignalized intersections, remains challenging, as learned policies may struggle to maintain both safety and robust decision-making in complex traffic situations. Conventional safety-filtering approaches typically employ fixed conservative constraints, which may improve safety at the cost of excessive intervention and degraded traffic efficiency. To address these limitations, we propose a Risk-sensitive and Uncertainty-aware Decision-making and Control (RUDC) framework for safe and robust autonomous driving. RUDC couples risk-sensitive distributional RL with ensemble-based policy uncertainty quantification, jointly accounting for tail risks in return distributions and uncertainty in learned policies. An uncertainty-aware high-order control barrier function (HOCBF)-based safety correction mechanism adaptively adjusts constraint strictness according to policy uncertainty, while a learnable residual predictor compensates for CBF model mismatches and discretization errors. Extensive simulations at unsignalized intersections demonstrate that RUDC achieves a favorable balance among safety, efficiency, and robustness, outperforming representative safe RL baselines under both nominal and challenging OOD and long-tail scenarios while satisfying real-time requirements.

Zhuoren Li, Ran Yu, Weiqi Zhang +4

College of Automotive and Energy Engineering, Tongji University, Shanghai 201804, China · Department of Data and Systems Engineering, The University of Hong Kong, Hong Kong

Control Barrier Functions Autonomous Driving Risk-Sensitive RL Safe RL Robust RL

Sep 8, 2026cs.LG

Risk-Conditioned Fine-Tuning of Large Language Models

Large Language Models (LLMs) are increasingly deployed in settings where rare but severe harmful generations can have significant consequences. Existing Risk-Averse RLHF addresses this issue by optimizing Conditional Value-at-Risk (CVaR), but it trains policies for fixed risk levels and therefore cannot adjust the desired degree of risk aversion at inference time. In this paper, we propose risk-conditioned RLHF, a framework that trains a single policy that provides a continuous risk-control interface, enabling users to select different degrees of risk aversion without retraining or deploying multiple risk-specific models. Experiments across multiple benchmarks demonstrate that a single risk-conditioned policy can adapt to different risk levels at inference time, enabling more flexible and risk-aware LLM deployment.

Zixuan Liu, Fangzheng Wu, Brian Summa +1

Department of Computer Science, Tulane University, New Orleans, LA, 70118, USA

Risk-Sensitive RL LLM Safety RL Fine-Tuning

Sep 7, 2026cs.AI

Mini-Batch Risk-Averse Deep Q-Learning: A Robot Navigation Case Study

We study the control of Markov decision processes in which the quality of a policy is evaluated by a dynamic, time-consistent Markov risk measure rather than by an expected discounted cost. The main obstacle to combining such measures with reinforcement learning is that a transition risk mapping depends on the transition kernel in a nonlinear way, and therefore cannot be estimated from a single observed transition. We remove this obstacle by employing mini-batch transition risk mappings: the mapping is applied to the empirical measure of

N

independent next-state samples, and the result is averaged. The resulting mapping is again coherent. However, as an expected value of a function of

N

next-state values, it admits an unbiased one-sample estimator. We embed this mapping into a double deep Q-network, analyze the two sources of estimation bias that arise, and obtain a risk-averse Q-learning method applicable to state spaces far beyond the reach of tabular schemes. The method is applied to an underwater robot navigation problem, in which a vehicle must visit collection points, gather stochastic information payloads, and deliver them at transmission points, while exposed at each step to the risk of destruction. A hierarchical decomposition delegates path execution to an exact graph search and confines learning to the high-level ``collect or transmit'' decision. A low-dimensional feature map, invariant under the symmetries of the problem, replaces the raw state--configuration encoding. In experiments on

300

held-out environments, the resulting policies transfer to instance sizes never seen in training, and already

N=2

reduces the upper semideviation of the outcome distribution while simultaneously improving its mean whenever the simulator is misspecified---an empirical counterpart of the duality between coherent risk measures and distributional robustness.

Aayush Patel, Andrzej Ruszczyński

Department of Management Science and Information Systems, Rutgers University

Deep Q-Learning Robot Navigation Risk-Sensitive RL Policy Learning

Sep 3, 2026cs.LG

Risk and Anomaly Identification for Distribution Network Optimal Operation Based on Reinforcement Learning and Uncertainty Quantification

Reliable operation of modern distribution networks requires timely identification of operational risks and anomalous events under pervasive uncertainty. In practice, operators must identify risks that are inherent in stochastic yet in-distribution conditions, and anomalies that correspond to out-of-distribution behaviors such as unusual load patterns, extreme weather or cyber-physical attacks. This paper addresses this joint risk and anomaly identification problem for optimal distribution network operation and proposes a deep reinforcement learning framework that is explicitly uncertainty aware. We integrate distributional and Bayesian deep reinforcement learning to realize a second- order uncertainty quantification scheme that decomposes total uncertainty into aleatoric and epistemic components, which are respectively used to characterize inherent risk and out-of- distribution anomalies. The resulting epistemic estimates drive both exploration during training and out-of-distribution detec- tion with fallback control during deployment, whereas aleatoric estimates are used to characterize intrinsic operational risk. Simulation results demonstrate the performance of our DRL agent and the effectiveness of the uncertainty quantification.

Ziqi Zhang

College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China

Risk-Sensitive RL OOD Detection Power Systems

Sep 2, 2026cs.LG

Tail-Likelihood Reinforcement Learning

Reinforcement learning typically optimizes average reward. For generative policies, the average can hide an important distinction: two policies can achieve the same mean reward while having very different chances of producing a rare but high-reward rollout. This matters as sampling increases during training and inference, since its benefit depends on retaining probability mass on high-reward outcomes. We propose to optimize this coverage directly. Rather than considering only expected reward, we consider all of its upper tails: for each reward threshold, how likely is the policy to exceed it? This turns a continuous reward into a family of binary success events. We introduce Tail-Likelihood Reinforcement Learning (TailRL), which maximizes the log-probability of exceeding a randomly chosen reward threshold. Its gradient gives more weight to rare, high-reward rollouts and can be interpreted as a mixture of Best-of-k gradients. TailRL requires only a simple modification to the advantage function, making it compatible with existing reinforcement learning pipelines. Across object localization, maze navigation, GUI grounding, and code optimization, TailRL leverages rare high-reward training samples to avoid suboptimal solutions and yields models that benefit more from additional samples at inference time.

Shrinivas Ramasubramanian, Daman Arora, Fahim Tajwar +11

Carnegie Mellon University · Together AI · University of California, Berkeley +2

Risk-Sensitive RL RL for Generative Models Policy Learning

Aug 5, 2026cs.LG

Adaptive Finite-Budget Training for CVaR Risk-Aware Q-Learning

Risk-aware Q-learning (RaQL) provides a model-free, two-timescale estimator for dynamic risk objectives, but its finite-budget behavior remains fragile: fixed inner-loop hyperparameters can produce unstable value estimates, persistent Bellman residuals, and inefficient sample reuse. This paper proposes an adaptive training controller for Conditional Value-at-Risk (CVaR) RaQL and evaluates it on a daily Bitcoin trading task. The controller preserves the original CVaR estimator and Bellman fixed point; instead, it redesigns the training procedure through six coordinated mechanisms: per-cell inner-step sizing, outer-rate-matched decay synchronization, a short early correction for the VaR-like inner variable, a coverage-first-then-greedy sample allocation rule, progressive suffix aggregation of mature inner estimates, and data-driven calibration of key scales from online-observable quantities. Across 20 random seeds and 856,000 inner-transition samples, the controller reduces the mean empirical CVaR Bellman residual by approximately 85% relative to the fixed-parameter baseline (MeanBEQ: 1.2202 to 0.1854; MeanBEV: 1.1624 to 0.0535) and maintains stability across CVaR levels, discount factors, and training budgets. On the chronological out-of-sample test set, the learned policy attains a Sharpe ratio of 0.9281 with a maximum drawdown of 6.46% after transaction costs. Although buy-and-hold yields a higher cumulative return (35.43% vs. 23.61%), the adaptive policy achieves far lower volatility (9.57% vs. 47.93%), drawdown, and CVaR loss. These results demonstrate that adaptive finite-budget training design, applied solely to the training procedure without altering the risk objective, can materially improve the reliability and risk-adjusted performance of risk-aware Q-learning in financial applications.

Yifan Wu, Junjie Lei, Wenjie Huang

Department of Data and Systems Engineering The University of Hong Kong Hong Kong, Hong Kong SAR

Reinforcement Learning Q-Learning Risk-Sensitive RL Conditional Value-at-Risk Finance

Aug 4, 2026cs.AI

Taming the Implicit: Dual-Channel Risk-Aware Reinforcement Fine-Tuning for Continual Multimodal Post-Training

Reinforcement fine-tuning (RFT) is widely believed to inherently resist catastrophic forgetting in continual post-training of multimodal large language models. Under pronounced task distributional shifts, however, forgetting across representative RFT algorithms escalates sharply. This stems from the implicit reward-variance regularization inherent to RFT, which proves incapable of suppressing uncontrolled optimization risk. We propose Risk-Aware Policy Optimization (RAPO), the first dual-channel framework for explicit risk governance in continual RFT. On the policy channel, Risk-Aware Policy Scaling adaptively calibrates per-sample update magnitude via rollout reliability and Fisher-inspired local predictive sensitivity; on the data channel, Risk-Aware Dynamic Bucket Sampling reorganizes training batches through dynamic risk stratification, steering optimization toward informative yet stable samples. As a plug-and-play strategy requiring no cross-task memory, RAPO generalizes to any RFT algorithm without modification. On the public MLLM-CL benchmark, RAPO reduces final forgetting by 79.8% relative to its RLOO backbone while retaining new-task competitiveness.

Yibei Liu, Jiajun Chen, Qianle Zhang +4

University of Electronic Science and Technology of China · Zhejiang University · South China University of Technology +1

Multimodal Large Language Models Risk-Sensitive RL RL Post-Training Continual Learning for VLMs Catastrophic Forgetting

Aug 3, 2026cs.LG

Finite-Time Analysis of Discounted Exponential-Utility Reinforcement Learning

Discounted exponential utility provides a principled criterion for risk-sensitive sequential decision-making, but its nonlinear structure complicates reinforcement learning. A recent work \citep{thoppe2026reinforcement} addressed this difficulty by introducing a Bellman-compatible surrogate and two model-free fixed-point algorithms for optimizing it over stationary policies. However, their main convergence results are asymptotic. In this work, we establish finite-time rates of

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

for the aforementioned two algorithms under asynchronous Markovian sampling, where

n

is the iteration index and

\tilde{O}

hides logarithmic expressions. Importantly, we employ parameter-free choices for the stepsize parameter to derive these rate results. For the algorithmically simpler one-timescale method, the main challenge is that its update equation is not directly aligned with the contraction geometry of its underlying power-law operator. We overcome this mismatch by exploiting the boundedness, monotonicity, and homogeneity of the operator to obtain a local pseudo-contraction property for the relative-error dynamics. We then use a Moreau-envelope-based Lyapunov function and Polyak--Ruppert averaging to obtain the stated convergence rate with parameter-free stepsizes. For the two-timescale method, the main challenge is to control a tracking error on the faster timescale. These results provide the first finite-time guarantees for model-free discounted exponential-utility reinforcement learning.

Ankur Naskar, Vivek T A, Aditya Kumar +2

Indian Institute of Science, Bengaluru, India · Indian Institute of Technology Madras, Chennai, India

Reinforcement Learning Risk-Sensitive RL Model-Free RL

Jul 29, 2026cs.LG

Efficient Heteroscedastic Bayesian Optimization for Risk-Aware AutoRL

Reinforcement learning (RL) has shown remarkable success across a wide range of complex tasks. However, RL outcomes can be highly stochastic, and both expected performance and variability often depend on hyperparameter (HP) configurations. We propose efficient and risk-averse heteroscedastic Bayesian Optimization (ERAHBO), a Bayesian optimization method that models both the mean and variance of learning outcomes as functions of the HP configurations. ERAHBO aims to identify HP configurations that achieve high average return while reducing variability across training runs, and it improves the sample efficiency of the HP optimization via adaptive re-sampling rather than a fixed budget per HP. Empirical evaluations across diverse RL algorithms and environments demonstrate that ERAHBO generally outperforms both risk-neutral and risk-averse baselines, delivering improved sample efficiency for risk-averse returns.

Mingxuan Che, Tsung-Yuan Tseng, Theresa Eimer +2

Leibniz University Hannover · CARIAD SE · University of Wuppertal +2

Bayesian Optimization Risk-Sensitive RL Hyperparameter Optimization

Jul 26, 2026cs.RO

Anticipatory Risk-Guided Reinforcement Learning for Safe Flight Through Dynamic Clutter

Safe quadrotor navigation in cluttered and dynamic environments depends not only on instantaneous geometric perception, but more critically on anticipating collision risks induced by relative motion. Conventional modular pipelines frequently suffer from perception latency, while end-to-end learning methods relying on implicit scalar rewards often struggle to extract reliable spatio-temporal features without physics-grounded supervision. To address this, we propose an anticipatory risk-guided reinforcement learning framework. Leveraging privileged simulator states, we construct a directionally aligned future collision risk map based on the Closest Point of Approach (CPA). Through an asymmetric actor-critic architecture, the network is trained to self-predict this structured risk, which explicitly guides the visual policy during deployment. A lightweight spatio-temporal encoder extracts motion cues directly from onboard depth sequences, bypassing explicit object tracking or optical flow estimation. Extensive simulated and real-world experiments demonstrate that our method effectively improves safety margins and flight efficiency in dense dynamic clutters compared to existing baselines. Furthermore, the learned policy achieves robust zero-shot Sim-to-Real transfer on a physical quadrotor, relying purely on abstracted spatio-temporal depth sequences and its self-predicted risk priors, validating the effectiveness of our approach and its robust generalization from simulation to reality.

Yuchao Mei, Guohao Zhang, Luxia Ai +2

National Key Laboratory of Science and Technology on Multi-spectral Information Processing, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China

Collision Avoidance Risk-Sensitive RL Quadrotor Control Visual RL Dynamic Obstacle Avoidance

Jul 25, 2026cs.LG

Online Policy Evaluation for MDPs with Dynamic UBSR Measures

Developing efficient function-approximation methods for policy evaluation is a fundamental challenge in risk-aware reinforcement learning. Existing approaches either focus on restrictive classes of risk measures or rely on access to a simulator, limiting their applicability in fully online settings. In this work, we propose computationally efficient online learning algorithms for policy evaluation in Markov decision processes (MDPs) with dynamic utility-based shortfall risk (UBSR) measures under linear function approximation. Specifically, we introduce the UBSR-TD algorithm, establish conditions under which it converges almost surely, and develop several variants designed to accelerate convergence. Our formulation shows that existing policy evaluation algorithms for risk-neutral MDPs can be readily adapted to dynamic UBSR settings by incorporating a loss function into the temporal-difference error. Numerical experiments support our theoretical findings, and an application to a perishable inventory management problem with shelf-life uncertainty demonstrates the practical effectiveness of the proposed methods.

Weikai Wang, Erick Delage

GERAD & Department of Decision Sciences, HEC Montr´eal, Canada

Policy Evaluation Risk-Sensitive RL Temporal-Difference Learning

Jul 22, 2026cs.AI

Long-Term Sequential Decision Making under Risk

We study finite-horizon MDP planning under \emph{root-based} (resolute) risk objectives that apply a rank-dependent functional to the distribution of total returns. Such objectives are non-linear in the return distribution and generally break Bellman optimality, so direct optimization by scenario-tree enumeration is intractable. We propose \textbf{ERQDP}, an enumeration-free and sampling-free method that solves a rank--quantile surrogate via exact DP (Dynamic Programming), evaluates candidate policies exactly by DP over return Probability Mass Functions (PMFs) on a discretized return grid (with an explicit rounding bound), and refines the surrogate in an anytime loop that reports an explicit upper--lower gap (certificate) for the target objective up to discretization budgets. Across tested benchmarks, ERQDP returns certified solutions or explicit residual gaps, enables fast risk-parameter sweeps with substantial runtime gains, and supports both risk-averse and risk-seeking behaviors.

Irmaan, Mirzanejad, Nadjet Bourdache +1

Mohammad · Université de Caen Normandie, ENSICAEN, CNRS, Normandie Univ, GREYC UMR 6072, France

Markov Decision Processes Dynamic Programming Risk-Sensitive RL Decision-Making under Uncertainty

Jul 18, 2026cs.LG

Learning from World Feedback: Why Model Uncertainty Fails as a Risk Signal in Model-Based RL

The RLxF programme argues that learning signals should come from world feedback rather than from internal model proxies. We instantiate this position in safe model-based control and distil it into three concrete design principles. Empirically, across four world-model architectures spanning a 2x MSE range, MPC planning is statistically equivalent (TOST, n=200), and dynamics-based uncertainty penalties increase collision rates from 26% to 34%: the standard MBRL safety proxy is anti-correlated with safety in this regime. Replacing the model-internal proxy with three world-feedback signals (a sensor-derived margin via minimum lidar, a temporal signal via time-to-collision, and an outcome-supervised feedback model g_psi trained on prior collision labels, structurally analogous to outcome-trained reward models in RLHF) reduces collisions to 1-14% without retraining the world model or the planner. The mechanism is structural: model uncertainty has support over state-prediction space, whereas task risk has support over constraint boundaries, with empirical correlation r < 0.15. From this we extract three RLxF principles (ground risk in world outcomes, validate proxies before deployment, and substitute outcome-trained feedback models when direct world signals are unavailable) and argue they apply equally to model-based control and to verifier-based or RLHF approaches in LLM alignment.

Zhaohui Wang

Viterbi School of Engineering, University of Southern California, Los Angeles, CA, USA.

Risk-Sensitive RL Model Predictive Control Safe RL Model-Based RL

Jul 15, 2026cs.LG

A Noise-Robust Elicit-to-Optimize Framework for Distortion Riskmetrics via Inverse Reinforcement Learning

We propose a noise-robust elicit-to-optimize framework that integrates inverse reinforcement learning (IRL) and reinforcement learning (RL) for eliciting agents' risk preferences and optimizing policies under a broad class of risk objectives characterized by distortion riskmetrics. On the elicitation side, we propose an adaptive Bayesian IRL method that infers agents' latent risk objectives from their noisy observed decisions, explicitly allowing agents to take stochastic and suboptimal actions. We establish the existence of a finite set of distinguishing questions that identifies the preferred distortion riskmetric within the candidate class and prove that the convergence rate of the algorithm is of order

O(\exp(-cm+O(\sqrt{m\log m})))

under general settings, where

c>0

is a constant and

m

denotes the number of algorithm iterations. On the optimization side, we develop a model-free RL algorithm for optimizing policies under conditional distortion riskmetrics. By representing the objective as an integral of the conditional cost quantile function with respect to the distortion function, the method unifies distortion-riskmetric objectives. We optimize diverse risk objectives by extending the Proximal Policy Optimization (PPO) algorithm with policy, value, and quantile neural networks, where the quantile network estimates the full conditional cost quantile function and enables numerical evaluation of general risk objectives. A comprehensive empirical study demonstrates the framework's elicitation accuracy and effectiveness in complex financial environments.

Yang Liu, Yuhao Liu, Yunran Wei

School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen), China. · School of Mathematics and Statistics, Carleton University, Canada.

Reinforcement Learning Risk-Sensitive RL Finance

Jul 14, 2026cs.LG

SteinGate: Tail-Sensitive Safe Reinforcement Learning via Stein Discrepancy

Safe reinforcement learning typically enforces safety by bounding expected cumulative costs, a criterion that often fails to detect rare but catastrophic tail events. To overcome these limitations, this paper introduces SteinGate, a boundary-aware distributional safety certificate that replaces fragile tail fitting with a robust consistency check using Kernelized Stein Discrepancy while accounting for boundary atoms induced by clipped costs. SteinGate evaluates whether observed policy rollout costs remain consistent with a safe reference distribution, providing a non-parametric safety certificate. This certificate is used to dynamically adapt the learning regime: favoring reward-improving policy updates when rollouts remain consistent with the safe reference and switching to recovery behavior when the cost tail deviates. Experiments on continuous-control benchmarks demonstrate that SteinGate significantly reduces both the frequency and severity of constraint violations during training while maintaining competitive returns relative to state-of-the-art baselines.

Yassine Chemingui, Chenhua Fan, Honghao Wei +1

School of Electrical Engineering and Computer Science, Washington State University, Pullman, Washington, USA

Constrained RL Risk-Sensitive RL Safe RL

Jul 13, 2026cs.AI

Auditing the Risk Claims of Distributional Reinforcement Learning

Distributional reinforcement learning agents learn full return distributions that are increasingly read at face value: for interpretability, risk-sensitive control, and safety monitoring. We ask a question theory anticipates but that has not been measured directly: are the risk claims of a trained distributional agent true? Our audit combines a decision-relevant screening metric (the excess Wasserstein gap between the top two actions, which equals the mass by which first-order stochastic dominance is violated), ground truth from snapshot-restart Monte Carlo, and a statistical harness (permutation nulls, bootstrap refutation, FDR control) without which the audit itself manufactures false conclusions. Across QR-DQN, C51, and IQN on MinAtar (33 runs), 40-95% of the strongest claimed risk trade-offs are refuted at 95% confidence, the placement of the strongest claims is statistically indistinguishable from truth-blind, and essentially no claim is confirmable: for these agents, the learned "risk" reflects a training artifact rather than environment stochasticity. The artifact is structural (fully formed early in training, uncorrelated with final score, idiosyncratic to each seed) and appears unchanged at full-Atari scale, with every top Breakout claim of a pretrained near-state-of-the-art QR-DQN refuted. Positive controls of known magnitude confirm 96-100% of real claims (correlation 0.89-0.92): the reading measures the agents, not the audit. Acting on the heads' CVaR advice at their most-flagged states ranges from beneficial to significantly worse than chance. Neither training for risk nor ensembling removes the artifact, and recalibration passes the audit only by nullifying the claims: the head is uninformative, not merely miscalibrated. We release the toolkit and document two silent pitfalls that produced convincing but wrong audits of our own.

Hari Prasad

Distributional RL Algorithmic Auditing Risk-Sensitive RL

Jul 10, 2026cs.LG

Risk-Aware General-Utility Markov Decision Processes

We study general-utility Markov decision processes (GUMDPs) with risk-aware objectives. In this framework, an agent aims to optimize a risk measure of the distribution of objective values, where the objective function depends on the frequency of visitation of states induced by the agent's policy. First, we motivate, propose, and formalize risk-aware GUMDPs, which enable agents and decision makers to trade off expected performance by risk aversion while benefiting from the rich set of objectives that can be cast under the framework of GUMDPs. We focus our attention on the entropic risk measure (ERM). Second, we show how we can solve risk-aware GUMDPs with ERM objectives by resorting to online planning techniques. In particular, we propose an approach based on Monte Carlo Tree Search (MCTS) to provably solve risk-aware GUMDPs up to any desired accuracy. Third, we provide a set of experimental results showcasing that our approach is successful when optimizing for a spectrum of risk-aware behaviors in the context of GUMDPs under diverse tasks (standard MDPs, maximum state entropy exploration, imitation learning, and multi-objective MDPs).

Pedro P. Santos, Fábio Vital, Alberto Sardinha +1

INESC-ID · Instituto Superior Técnico, University of Lisbon · Pontifical Catholic University of Rio de Janeiro

Markov Decision Processes Markov Models Risk-Sensitive RL Interval Markov Decision Processes

Jul 7, 2026cs.LG

Deep Reinforcement Learning for Reliability Based Bi-Objective Portfolio Optimization

Portfolio optimization under uncertainty is inherently a multi-objective decision problem involving complex interactions among return, risk, market dynamics, and practical investment constraints. Existing reliability based portfolio optimization approaches primarily rely on static optimization frameworks and often fail to capture sequential decision making, tail risk, and market frictions such as transaction costs. To address these limitations, we propose a deep reinforcement learning framework for multi-objective reliability based portfolio optimization (MORP-DRL). The proposed framework jointly optimizes expected return and downside risk using three complementary risk measures: variance, Conditional Value-at-Risk (CVaR), and Entropic Value-at-Risk (EVaR). To model uncertainty and heavy-tailed market behavior, asset returns are represented using GARCH(1,1), Extreme Value Theory, and a t-copula dependence structure, while realistic scenarios are generated through quasi-Monte Carlo simulation. A Proximal Policy Optimization (PPO) based strategy is developed under practical constraints including transaction costs and portfolio bounds, and is benchmarked against NSGA-II. Experiments on ten global equity indices across pre-COVID, COVID, and post-COVID market regimes demonstrate that MORP-DRL achieves competitive risk-return performance, reduced downside risk during periods of market stress, and scalability to high-dimensional portfolio settings.

Sounaq Das, Tanmay Sen, Raghu Nandan Sengupta +1

Indian Institute of Management Amritsar · Amritsar, India · SQC & OR Unit +7

Multi-Objective Reinforcement Learning Risk-Sensitive RL Portfolio Optimization

Jun 26, 2026cs.LG

RS-Diffuser: Risk-Sensitive Diffusion Planning with Distributional Value Guidance

Offline reinforcement learning enables policy learning from fixed datasets without additional environment interaction, making it appealing for safety-critical applications where online exploration is costly or unsafe. Diffusion-based decision-making methods have recently achieved strong performance in offline RL by modeling rich, multimodal trajectory distributions. However, existing diffusion planners are typically risk-neutral and therefore may overlook rare but catastrophic outcomes that are crucial in real-world deployment. In this work, we propose RS-Diffuser, a risk-sensitive offline diffusion planning framework that combines diffusion-based trajectory generation with distributional value critics. RS-Diffuser learns a diffusion planner over future state trajectories, a separate inverse dynamics model for action decoding, and a Monte Carlo distributional critic that estimates the full return distribution of candidate plans through quantile regression. At sampling time, we incorporate a risk-sensitive guidance signal into the denoising process, using gradients computed from tail-aware objectives such as Conditional Value at Risk to steer generation toward desired risk profiles. As a result, a single trained model can flexibly produce risk-averse, risk-neutral, or risk-seeking behaviors by changing only the inference-time risk parameter. Extensive experiments on risk-sensitive D4RL and risky robot navigation benchmarks demonstrate that RS-Diffuser achieves state-of-the-art performance, improving both overall return and worst-case robustness while reducing safety violations.

Shiqiang Gong

Northwestern Polytechnical University

Distributional RL Diffusion-Based Planning Risk-Sensitive RL Offline RL