Making Deep Q-learning methods robust to time discretization

TL;DR

This paper addresses the sensitivity of Deep Q-learning methods to time discretization in near continuous-time environments, proposing a new approach that maintains performance across various time steps.

Contribution

It identifies time discretization as a critical sensitivity in DRL and introduces a robust off-policy algorithm that performs well over different time discretizations.

Findings

Q-learning collapses with small time steps

Q-learning does not exist in continuous time

Proposed method achieves robustness across time discretizations

Abstract

Despite remarkable successes, Deep Reinforcement Learning (DRL) is not robust to hyperparameterization, implementation details, or small environment changes (Henderson et al. 2017, Zhang et al. 2018). Overcoming such sensitivity is key to making DRL applicable to real world problems. In this paper, we identify sensitivity to time discretization in near continuous-time environments as a critical factor; this covers, e.g., changing the number of frames per second, or the action frequency of the controller. Empirically, we find that Q-learning-based approaches such as Deep Q- learning (Mnih et al., 2015) and Deep Deterministic Policy Gradient (Lillicrap et al., 2015) collapse with small time steps. Formally, we prove that Q-learning does not exist in continuous time. We detail a principled way to build an off-policy RL algorithm that yields similar performances over a wide range of time discretizations, and confirm this robustness empirically.