Distributionally Robust Deep Q-Learning

TL;DR

This paper introduces a distributionally robust deep Q-learning algorithm that accounts for model uncertainty in continuous state spaces by using Sinkhorn distance regularization, enhancing policy robustness.

Contribution

It develops a novel deep Q-learning method that incorporates distributional robustness via Sinkhorn distance, addressing model uncertainty in continuous state spaces.

Findings

Effective in portfolio optimization with S&P 500 data

Modifies Deep Q-Network for worst-case transition optimization

Demonstrates tractability and robustness of the approach

Abstract

We propose a novel distributionally robust $Q$-learning algorithm for the non-tabular case accounting for continuous state spaces where the state transition of the underlying Markov decision process is subject to model uncertainty. The uncertainty is taken into account by considering the worst-case transition from a ball around a reference probability measure. To determine the optimal policy under the worst-case state transition, we solve the associated non-linear Bellman equation by dualising and regularising the Bellman operator with the Sinkhorn distance, which is then parameterized with deep neural networks. This approach allows us to modify the Deep Q-Network algorithm to optimise for the worst case state transition. We illustrate the tractability and effectiveness of our approach through several applications, including a portfolio optimisation task based on S\&{P}~500 data.