ℓ 1-penalized projected Bellman residual

Abstract

We consider the task of feature selection for value function approximation in reinforcement learning. A promising approach consists in combining the Least-Squares Temporal Difference (LSTD) algorithm with ℓ 1- regularization, which has proven to be effective in the supervised learning community. This has been done recently whit the LARS-TD algorithm, which replaces the projection operator of LSTD with an ℓ 1-penalized projection and solves the corresponding fixed-point problem. However, this approach is not guaranteed to be correct in the general off-policy setting. We take a different route by adding an ℓ 1-penalty term to the projected Bellman residual, which requires weaker assumptions while offering a comparable performance. However, this comes at the cost of a higher computational complexity if only a part of the regularization path is computed. Nevertheless, our approach ends up to a supervised learning problem, which let envision easy extensions to other penalties. © 2012 Springer-Verlag.