Temporal Difference Learning with Neural Networks - Study of the Leakage Propagation Problem

TL;DR

This paper investigates the leakage propagation problem in temporal difference learning with neural networks, providing empirical and analytical insights into how approximation errors affect convergence and proposing potential mitigation strategies.

Contribution

It offers the first detailed analysis of leakage propagation in TD learning with neural networks, including empirical evidence, analytical proofs, and exploration of mitigation methods.

Findings

Leakage propagation occurs when approximation errors are present in sharp discontinuities.

Analytical proof shows leakage must happen in simple Markov chains with errors.

Better state representations can help mitigate the problem.

Abstract

Temporal-Difference learning (TD) [Sutton, 1988] with function approximation can converge to solutions that are worse than those obtained by Monte-Carlo regression, even in the simple case of on-policy evaluation. To increase our understanding of the problem, we investigate the issue of approximation errors in areas of sharp discontinuities of the value function being further propagated by bootstrap updates. We show empirical evidence of this leakage propagation, and show analytically that it must occur, in a simple Markov chain, when function approximation errors are present. For reversible policies, the result can be interpreted as the tension between two terms of the loss function that TD minimises, as recently described by [Ollivier, 2018]. We show that the upper bounds from [Tsitsiklis and Van Roy, 1997] hold, but they do not imply that leakage propagation occurs and under what conditions. Finally, we test whether the problem could be mitigated with a better state representation, and whether it can be learned in an unsupervised manner, without rewards or privileged information.