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This arXiv paper is squarely about reinforcement learning, a core machine learning subfield, so it passes the topic gate. It studies offline risk-sensitive RL using optimized certainty equivalents, deriving pessimistic value-iteration and least-squares algorithms with suboptimality bounds in tabular and linear-function-approximation settings. For practitioners, the useful takeaway is theoretical: it clarifies how the choice of risk utility affects how hard learning from fixed datasets becomes, which matters for safety-critical decision-making where live experimentation is expensive.
Provably Efficient Risk-Sensitive Offline Reinforcement Learning via Optimized Certainty Equivalents
arXiv:2610.21870v1 Announce Type: cross Abstract: Risk-sensitive reinforcement learning (RL) addresses decision-making under uncertainty and adverse outcomes. Learning risk-sensitive policies from fixed datasets is important when additional interaction with the environment is costly. Existing work on risk-sensitive RL focuses on online settings or specific risk measures, leaving a general theoretical understanding of its offline setting underdeveloped. In this work, we investigate efficient offline risk-sensitive RL using the optimized certainty equivalent (OCE), a general class of risk measures. We consider two formulations: dynamic-OCE RL, which applies OCE recursively at each step, and static-OCE RL, which applies a single OCE to the cumulative rewards. Under the tabular setting, we develop pessimistic value-iteration algorithms for both formulations and establish tight sublinear suboptimality bounds, explicitly capturing how risk sensitivity, encoded by utility functions, affects learning difficulty. Moreover, we establish minimax suboptimality lower bounds to characterize the problem's fundamental limits. To handle large state spaces, we further develop pessimistic least-squares value-iteration algorithms that incorporate the general OCE risk criterion into linear function approximation. We establish utility-dependent sublinear guarantees with explicit dependence on the feature dimension $d$. To our knowledge, we provide the first offline algorithms along with the first upper and lower suboptimality bounds for both dynamic- and static-OCE RL.
Abstract:Risk-sensitive reinforcement learning (RL) addresses decision-making under uncertainty and adverse outcomes. Learning risk-sensitive policies from fixed datasets is important when additional interaction with the environment is costly. Existing work on risk-sensitive RL focuses on online settings or specific risk measures, leaving a general theoretical understanding of its offline setting underdeveloped. In this work, we investigate efficient offline risk-sensitive RL using the optimized certainty equivalent (OCE), a general class of risk measures. We consider two formulations: dynamic-OCE RL, which applies OCE recursively at each step, and static-OCE RL, which applies a single OCE to the cumulative rewards. Under the tabular setting, we develop pessimistic value-iteration algorithms for both formulations and establish tight sublinear suboptimality bounds, explicitly capturing how risk sensitivity, encoded by utility functions, affects learning difficulty. Moreover, we establish minimax suboptimality lower bounds to characterize the problem's fundamental limits. To handle large state spaces, we further develop pessimistic least-squares value-iteration algorithms that incorporate the general OCE risk criterion into linear function approximation. We establish utility-dependent sublinear guarantees with explicit dependence on the feature dimension $d$. To our knowledge, we provide the first offline algorithms along with the first upper and lower suboptimality bounds for both dynamic- and static-OCE RL.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Optimization and Control (math.OC); Machine Learning (stat.ML)
arXiv:2610.21870 [cs.LG]
(or arXiv:2610.21870v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.21870 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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