Risk-Sensitive Reinforcement Learning: a Martingale Approach to Reward Uncertainty
This work addresses risk sensitivity in reinforcement learning for applications like finance and robotics, though it is incremental as it builds on existing risk-sensitive formulations with a novel decomposition.
The authors tackled the problem of reward uncertainty in sequential decision-making by introducing a risk-sensitive reinforcement learning framework that decomposes cumulative reward randomness using a martingale approach. They demonstrated the framework's relevance on grid world and portfolio optimization problems, achieving competitive performance with specific gains in risk-adjusted metrics.
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.