Policy Gradient for Coherent Risk Measures

TL;DR

This paper extends policy gradient methods to a broad class of coherent risk measures, enabling risk-sensitive reinforcement learning with both static and dynamic measures through unified algorithms.

Contribution

It introduces a unified policy gradient framework for all coherent risk measures, generalizing previous methods focused on specific risk metrics.

Findings

Unified approach to static and dynamic risk measures

Combines sampling with convex programming for static measures

Uses actor-critic style algorithms for dynamic measures

Abstract

Several authors have recently developed risk-sensitive policy gradient methods that augment the standard expected cost minimization problem with a measure of variability in cost. These studies have focused on specific risk-measures, such as the variance or conditional value at risk (CVaR). In this work, we extend the policy gradient method to the whole class of coherent risk measures, which is widely accepted in finance and operations research, among other fields. We consider both static and time-consistent dynamic risk measures. For static risk measures, our approach is in the spirit of policy gradient algorithms and combines a standard sampling approach with convex programming. For dynamic risk measures, our approach is actor-critic style and involves explicit approximation of value function. Most importantly, our contribution presents a unified approach to risk-sensitive reinforcement learning that generalizes and extends previous results.