Policy gradient methods for distortion risk measures

We propose policy-gradient algorithms for solving the problem of control in a risk-sensitive reinforcement learning context. The objective of our algorithms is to maximize the distortion risk measure (DRM) of the cumulative reward in an episodic Markov decision process. We derive a variant of the policy gradient theorem that caters to the DRM objective. Using this theorem in conjunction with a likelihood ratio-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.