Feature Selection Using Regularization in Approximate Linear Programs for Markov Decision Processes

TL;DR

This paper introduces an $L_1$ regularization technique for approximate linear programming in Markov Decision Processes, enabling automatic feature selection and preventing overfitting with large feature sets.

Contribution

It proposes a novel regularization-based method with a homotopy algorithm for feature selection in approximate linear programs for MDPs, improving robustness and scalability.

Findings

Performs well on simple MDPs

Effective on standard benchmark problems

Maintains performance with increasing feature sets

Abstract

Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing algorithms to overfit because of a limited number of samples. We address this shortcoming using $L_1$ regularization in approximate linear programming. Because the proposed method can automatically select the appropriate richness of features, its performance does not degrade with an increasing number of features. These results rely on new and stronger sampling bounds for regularized approximate linear programs. We also propose a computationally efficient homotopy method. The empirical evaluation of the approach shows that the proposed method performs well on simple MDPs and standard benchmark problems.