A Reductions Approach to Risk-Sensitive Reinforcement Learning with Optimized Certainty Equivalents
This work addresses risk-sensitive decision-making in reinforcement learning for applications requiring robust policies, though it is incremental as it builds on existing risk-neutral methods with new theoretical extensions.
The paper tackles risk-sensitive reinforcement learning by proposing two meta-algorithms based on optimism and policy gradients that optimize a family of risk measures called optimized certainty equivalents, leveraging risk-neutral RL algorithms in an augmented MDP to establish novel theoretical bounds and demonstrate empirical success in a proof-of-concept MDP where Markovian policies fail.
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.