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

Adaptive Temporal-Difference Learning for Policy Evaluation with Per-State Uncertainty Estimates

“…The errors, however, behave differently for the two methods: while the errors of Monte Carlo are localized to the regions with discontinuities due to directly fitting the data, TD bootstraps values from this problematic region, and thus propagates the errors even further. We refer to such errors arising due to discontinuities as leakage [16].…”