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# Scalable Bilinear Pi Learning Using State and Action Features

*Proceedings of the 35th International Conference on Machine Learning*, PMLR 80:834-843, 2018.

#### 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 linear and bilinear models to represent the high-dimensional value function and state-action distributions, respectively, 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.