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

2024-03-10

AI Summary

This paper studies risk-sensitive reinforcement learning (RL), targeting optimization of risk measures in the optimized certainty equivalent (OCE) class—such as conditional value-at-risk (CVaR), entropy risk, and mean–variance—for cumulative rewards. Methodologically, it introduces the first general reduction framework for OCE risk optimization, transforming the problem into a risk-neutral RL task via an augmented Markov decision process (MDP). Theoretically, it establishes the first finite-sample CVaR regret bounds for non-Markovian, rich-observation MDPs and block MDPs. Algorithmically, it proposes two meta-algorithms—one based on optimism and the other on policy gradients—that ensure monotonic improvement and global convergence for risk-sensitive policy optimization. Empirically, on a conceptual MDP, the learned history-dependent policies strictly dominate all Markovian policies; moreover, the theoretical guarantees extend to block MDPs, and experiments validate both the efficacy and robustness of the proposed methods.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Social networks and social learning

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.

Problem

• Optimize risk-sensitive RL using optimized certainty equivalents (OCE).
• Develop meta-algorithms for risk-sensitive RL in augmented MDPs.
• Establish novel OCE bounds in complex, rich-observation MDPs.

Innovation

• Optimized Certainty Equivalents for risk-sensitive RL
• Meta-algorithms: optimism and policy gradients
• Reductions approach leveraging risk-neutral RL theory