On overfitting and asymptotic bias in batch reinforcement learning with partial observability

TL;DR

This paper analyzes the balance between asymptotic bias and overfitting in batch reinforcement learning with partial observability, highlighting how smaller state representations can reduce overfitting at the cost of increased bias.

Contribution

It provides a formal theoretical framework for understanding the bias-overfitting tradeoff in POMDPs and empirically demonstrates these effects on synthetic and real-world data.

Findings

Smaller state representations decrease overfitting risk.

Increasing asymptotic bias can be a consequence of reduced state complexity.

Function approximation and discount factor tuning can improve the bias-overfitting tradeoff.

Abstract

This paper provides an analysis of the tradeoff between asymptotic bias (suboptimality with unlimited data) and overfitting (additional suboptimality due to limited data) in the context of reinforcement learning with partial observability. Our theoretical analysis formally characterizes that while potentially increasing the asymptotic bias, a smaller state representation decreases the risk of overfitting. This analysis relies on expressing the quality of a state representation by bounding L1 error terms of the associated belief states. Theoretical results are empirically illustrated when the state representation is a truncated history of observations, both on synthetic POMDPs and on a large-scale POMDP in the context of smartgrids, with real-world data. Finally, similarly to known results in the fully observable setting, we also briefly discuss and empirically illustrate how using function approximators and adapting the discount factor may enhance the tradeoff between asymptotic bias and overfitting in the partially observable context.