Policy Gradient Methods for Distortion Risk Measures

We propose policy-gradient algorithms for solving the problem of control in a risk-sensitive reinforcement learning (RL) context. The objective of our algorithm is to maximize the distorted risk measure (DRM) of the cumulative reward in an episodic Markov decision process (MDP). We derive a variant of the policy gradient theorem that caters to the DRM objective. Using this theorem in conjunction with a likelihood ratio (LR) based gradient estimation scheme, we propose policy gradient algorithms for optimizing DRM in both on-policy and off-policy RL settings. We derive non-asymptotic bounds that establish the convergence of our algorithms to an approximate stationary point of the DRM objective.