Ergodic Risk Measures: Towards a Risk-Aware Foundation for Continual Reinforcement Learning

• URL: http://arxiv.org/abs/2510.02945v1
• Date: Fri, 03 Oct 2025 12:40:03 GMT
• Title: Ergodic Risk Measures: Towards a Risk-Aware Foundation for Continual Reinforcement Learning
• Authors: Juan Sebastian Rojas, Chi-Guhn Lee,
• Abstract summary: Continual reinforcement learning (continual RL) seeks to formalize the notions of lifelong learning and endless adaptation in RL.<n>To date, continual RL has been explored almost exclusively through the lens of risk-neutral decision-making.<n>We present the first formal theoretical treatment of continual RL through the lens of risk-aware decision-making.
• Score: 7.025709586759656
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Continual reinforcement learning (continual RL) seeks to formalize the notions of lifelong learning and endless adaptation in RL. In particular, the aim of continual RL is to develop RL agents that can maintain a careful balance between retaining useful information and adapting to new situations. To date, continual RL has been explored almost exclusively through the lens of risk-neutral decision-making, in which the agent aims to optimize the expected (or mean) long-run performance. In this work, we present the first formal theoretical treatment of continual RL through the lens of risk-aware decision-making, in which the agent aims to optimize a reward-based measure of long-run performance beyond the mean. In particular, we show that the classical theory of risk measures, widely used as a theoretical foundation in non-continual risk-aware RL, is, in its current form, incompatible with the continual setting. Then, building on this insight, we extend risk measure theory into the continual setting by introducing a new class of ergodic risk measures that are compatible with continual learning. Finally, we provide a case study of risk-aware continual learning, along with empirical results, which show the intuitive appeal and theoretical soundness of ergodic risk measures.

Related papers

• Anchoring Refusal Direction: Mitigating Safety Risks in Tuning via Projection Constraint [52.878820730054365]
  Instruction Fine-Tuning (IFT) has been widely adopted as an effective post-training strategy to enhance abilities of Large Language Models (LLMs)<n>Recent research into the internal mechanisms of LLMs has identified the refusal direction (r-direction) in the hidden states, which plays a pivotal role in governing refusal behavior.<n>To mitigate such drift, our proposed ProCon method introduces a projection-constrained loss term that regularizes the projection magnitude of each training sample's hidden state onto the r-direction.
  arXiv  Detail & Related papers  (2025-09-08T15:24:33Z)
• Beyond CVaR: Leveraging Static Spectral Risk Measures for Enhanced Decision-Making in Distributional Reinforcement Learning [4.8342038441006805]
  In domains such as finance, healthcare, and robotics, managing worst-case scenarios is critical.<n> Distributional Reinforcement Learning (DRL) provides a natural framework to incorporate risk sensitivity into decision-making processes.<n>We present a novel DRL algorithm with convergence guarantees that optimize for a broader class of static Spectral Risk Measures (SRM)
  arXiv  Detail & Related papers  (2025-01-03T20:25:41Z)
• Diffusion Policies for Risk-Averse Behavior Modeling in Offline Reinforcement Learning [26.34178581703107]
  offline reinforcement learning (RL) presents distinct challenges as it relies solely on observational data.<n>We propose an uncertainty-aware distributional offline RL method to simultaneously address both uncertainty and environmentality.<n>Our method is rigorously evaluated through comprehensive experiments in both risk-sensitive and risk-neutral benchmarks, demonstrating its superior performance.
  arXiv  Detail & Related papers  (2024-03-26T12:28:04Z)
• Provable Risk-Sensitive Distributional Reinforcement Learning with General Function Approximation [54.61816424792866]
  We introduce a general framework on Risk-Sensitive Distributional Reinforcement Learning (RS-DisRL), with static Lipschitz Risk Measures (LRM) and general function approximation. We design two innovative meta-algorithms: textttRS-DisRL-M, a model-based strategy for model-based function approximation, and textttRS-DisRL-V, a model-free approach for general value function approximation.
  arXiv  Detail & Related papers  (2024-02-28T08:43:18Z)
• Risk-Aware Reinforcement Learning through Optimal Transport Theory [4.8951183832371]
  This paper pioneers the integration of Optimal Transport theory with reinforcement learning (RL) to create a risk-aware framework. Our approach modifies the objective function, ensuring that the resulting policy not only maximizes expected rewards but also respects risk constraints dictated by OT distances. Our contributions are substantiated with a series of theorems, mapping the relationships between risk distributions, optimal value functions, and policy behaviors.
  arXiv  Detail & Related papers  (2023-09-12T13:55:01Z)
• Extreme Risk Mitigation in Reinforcement Learning using Extreme Value Theory [10.288413564829579]
  A critical aspect of risk awareness involves modeling highly rare risk events (rewards) that could potentially lead to catastrophic outcomes. While risk-aware RL techniques do exist, their level of risk aversion heavily relies on the precision of the state-action value function estimation. Our work proposes to enhance the resilience of RL agents when faced with very rare and risky events by focusing on refining the predictions of the extreme values predicted by the state-action value function distribution.
  arXiv  Detail & Related papers  (2023-08-24T18:23:59Z)
• Provably Efficient Iterated CVaR Reinforcement Learning with Function Approximation and Human Feedback [57.6775169085215]
  Risk-sensitive reinforcement learning aims to optimize policies that balance the expected reward and risk. We present a novel framework that employs an Iterated Conditional Value-at-Risk (CVaR) objective under both linear and general function approximations. We propose provably sample-efficient algorithms for this Iterated CVaR RL and provide rigorous theoretical analysis.
  arXiv  Detail & Related papers  (2023-07-06T08:14:54Z)
• Is Risk-Sensitive Reinforcement Learning Properly Resolved? [54.00107408956307]
  We propose a novel algorithm, namely Trajectory Q-Learning (TQL), for RSRL problems with provable policy improvement.<n>Based on our new learning architecture, we are free to introduce a general and practical implementation for different risk measures to learn disparate risk-sensitive policies.
  arXiv  Detail & Related papers  (2023-07-02T11:47:21Z)
• Towards Continual Reinforcement Learning: A Review and Perspectives [69.48324517535549]
  We aim to provide a literature review of different formulations and approaches to continual reinforcement learning (RL) While still in its early days, the study of continual RL has the promise to develop better incremental reinforcement learners. These include applications such as those in the fields of healthcare, education, logistics, and robotics.
  arXiv  Detail & Related papers  (2020-12-25T02:35:27Z)
• Learning Bounds for Risk-sensitive Learning [86.50262971918276]
  In risk-sensitive learning, one aims to find a hypothesis that minimizes a risk-averse (or risk-seeking) measure of loss. We study the generalization properties of risk-sensitive learning schemes whose optimand is described via optimized certainty equivalents.
  arXiv  Detail & Related papers  (2020-06-15T05:25:02Z)
• Reinforcement Learning through Active Inference [62.997667081978825]
  We show how ideas from active inference can augment traditional reinforcement learning approaches. We develop and implement a novel objective for decision making, which we term the free energy of the expected future. We demonstrate that the resulting algorithm successfully exploration and exploitation, simultaneously achieving robust performance on several challenging RL benchmarks with sparse, well-shaped, and no rewards.
  arXiv  Detail & Related papers  (2020-02-28T10:28:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.