Risk-Sensitive Reinforcement Learning: a Martingale Approach to Reward Uncertainty

TL;DR

This paper introduces a new risk-sensitive reinforcement learning framework that uses martingale decomposition to measure reward uncertainty, enhancing decision-making in stochastic environments.

Contribution

It presents a novel martingale-based risk measure called chaotic variation and integrates it into model-free RL algorithms for improved reward uncertainty handling.

Findings

Effective in grid world environments

Applicable to portfolio optimization tasks

Enhances sensitivity to reward stochasticity

Abstract

We introduce a novel framework to account for sensitivity to rewards uncertainty in sequential decision-making problems. While risk-sensitive formulations for Markov decision processes studied so far focus on the distribution of the cumulative reward as a whole, we aim at learning policies sensitive to the uncertain/stochastic nature of the rewards, which has the advantage of being conceptually more meaningful in some cases. To this end, we present a new decomposition of the randomness contained in the cumulative reward based on the Doob decomposition of a stochastic process, and introduce a new conceptual tool - the \textit{chaotic variation} - which can rigorously be interpreted as the risk measure of the martingale component associated to the cumulative reward process. We innovate on the reinforcement learning side by incorporating this new risk-sensitive approach into model-free algorithms, both policy gradient and value function based, and illustrate its relevance on grid world and portfolio optimization problems.