A Comparative Analysis of Expected and Distributional Reinforcement Learning

TL;DR

This paper investigates why distributional reinforcement learning often outperforms expected RL by analyzing theoretical differences in various settings and empirically testing their effects in control tasks.

Contribution

It provides the first theoretical analysis of distributional RL's behavior in different approximation settings and compares it empirically to expected RL in non-linear control tasks.

Findings

Distributional RL behaves like expected RL in many tabular and linear cases.

In some cases, distributional RL can harm performance if behaviors differ.

Empirical results suggest specific scenarios where distributional RL offers advantages.

Abstract

Since their introduction a year ago, distributional approaches to reinforcement learning (distributional RL) have produced strong results relative to the standard approach which models expected values (expected RL). However, aside from convergence guarantees, there have been few theoretical results investigating the reasons behind the improvements distributional RL provides. In this paper we begin the investigation into this fundamental question by analyzing the differences in the tabular, linear approximation, and non-linear approximation settings. We prove that in many realizations of the tabular and linear approximation settings, distributional RL behaves exactly the same as expected RL. In cases where the two methods behave differently, distributional RL can in fact hurt performance when it does not induce identical behaviour. We then continue with an empirical analysis comparing distributional and expected RL methods in control settings with non-linear approximators to tease apart where the improvements from distributional RL methods are coming from.