A Reductions Approach to Risk-Sensitive Reinforcement Learning with Optimized Certainty Equivalents

Kaiwen Wang, Dawen Liang, Nathan Kallus, Wen Sun
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:63636-63661, 2025.

Abstract

We study risk-sensitive RL where the goal is learn a history-dependent policy that optimizes some risk measure of cumulative rewards. We consider a family of risks called the optimized certainty equivalents (OCE), which captures important risk measures such as conditional value-at-risk (CVaR), entropic risk and Markowitz’s mean-variance. In this setting, we propose two meta-algorithms: one grounded in optimism and another based on policy gradients, both of which can leverage the broad suite of risk-neutral RL algorithms in an augmented Markov Decision Process (MDP). Via a reductions approach, we leverage theory for risk-neutral RL to establish novel OCE bounds in complex, rich-observation MDPs. For the optimism-based algorithm, we prove bounds that generalize prior results in CVaR RL and that provide the first risk-sensitive bounds for exogenous block MDPs. For the gradient-based algorithm, we establish both monotone improvement and global convergence guarantees under a discrete reward assumption. Finally, we empirically show that our algorithms learn the optimal history-dependent policy in a proof-of-concept MDP, where all Markovian policies provably fail.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-wang25bl, title = {A Reductions Approach to Risk-Sensitive Reinforcement Learning with Optimized Certainty Equivalents}, author = {Wang, Kaiwen and Liang, Dawen and Kallus, Nathan and Sun, Wen}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {63636--63661}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/wang25bl/wang25bl.pdf}, url = {https://proceedings.mlr.press/v267/wang25bl.html}, abstract = {We study risk-sensitive RL where the goal is learn a history-dependent policy that optimizes some risk measure of cumulative rewards. We consider a family of risks called the optimized certainty equivalents (OCE), which captures important risk measures such as conditional value-at-risk (CVaR), entropic risk and Markowitz’s mean-variance. In this setting, we propose two meta-algorithms: one grounded in optimism and another based on policy gradients, both of which can leverage the broad suite of risk-neutral RL algorithms in an augmented Markov Decision Process (MDP). Via a reductions approach, we leverage theory for risk-neutral RL to establish novel OCE bounds in complex, rich-observation MDPs. For the optimism-based algorithm, we prove bounds that generalize prior results in CVaR RL and that provide the first risk-sensitive bounds for exogenous block MDPs. For the gradient-based algorithm, we establish both monotone improvement and global convergence guarantees under a discrete reward assumption. Finally, we empirically show that our algorithms learn the optimal history-dependent policy in a proof-of-concept MDP, where all Markovian policies provably fail.} }
Endnote
%0 Conference Paper %T A Reductions Approach to Risk-Sensitive Reinforcement Learning with Optimized Certainty Equivalents %A Kaiwen Wang %A Dawen Liang %A Nathan Kallus %A Wen Sun %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-wang25bl %I PMLR %P 63636--63661 %U https://proceedings.mlr.press/v267/wang25bl.html %V 267 %X We study risk-sensitive RL where the goal is learn a history-dependent policy that optimizes some risk measure of cumulative rewards. We consider a family of risks called the optimized certainty equivalents (OCE), which captures important risk measures such as conditional value-at-risk (CVaR), entropic risk and Markowitz’s mean-variance. In this setting, we propose two meta-algorithms: one grounded in optimism and another based on policy gradients, both of which can leverage the broad suite of risk-neutral RL algorithms in an augmented Markov Decision Process (MDP). Via a reductions approach, we leverage theory for risk-neutral RL to establish novel OCE bounds in complex, rich-observation MDPs. For the optimism-based algorithm, we prove bounds that generalize prior results in CVaR RL and that provide the first risk-sensitive bounds for exogenous block MDPs. For the gradient-based algorithm, we establish both monotone improvement and global convergence guarantees under a discrete reward assumption. Finally, we empirically show that our algorithms learn the optimal history-dependent policy in a proof-of-concept MDP, where all Markovian policies provably fail.
APA
Wang, K., Liang, D., Kallus, N. & Sun, W.. (2025). A Reductions Approach to Risk-Sensitive Reinforcement Learning with Optimized Certainty Equivalents. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:63636-63661 Available from https://proceedings.mlr.press/v267/wang25bl.html.

Related Material