Scalable Bilinear $\pi$ Learning Using State and Action Features

TL;DR

This paper introduces a scalable, model-free bilinear $ ext{ extpi}$ learning algorithm for large MDPs that efficiently uses features, operates online with minimal memory, and is proven to be sample-efficient.

Contribution

It develops a novel bilinear $ ext{ extpi}$ learning algorithm that leverages features for scalable, online, and sample-efficient reinforcement learning in large MDPs.

Findings

Algorithm has runtime depending on feature count, not MDP size

Operates fully online with minimal memory usage

Proven to be sample-efficient with linear complexity in parameter dimension

Abstract

Approximate linear programming (ALP) represents one of the major algorithmic families to solve large-scale Markov decision processes (MDP). In this work, we study a primal-dual formulation of the ALP, and develop a scalable, model-free algorithm called bilinear $\pi$ learning for reinforcement learning when a sampling oracle is provided. This algorithm enjoys a number of advantages. First, it adopts (bi)linear models to represent the high-dimensional value function and state-action distributions, using given state and action features. Its run-time complexity depends on the number of features, not the size of the underlying MDPs. Second, it operates in a fully online fashion without having to store any sample, thus having minimal memory footprint. Third, we prove that it is sample-efficient, solving for the optimal policy to high precision with a sample complexity linear in the dimension of the parameter space.