Least-Squares Methods in Reinforcement Learning for Control

Least-squares methods have been successfully used for prediction problems in the context of reinforcement learning, but little has been done in extending these methods to control problems. This paper presents an overview of our research efforts in using least-squares techniques for control. In our early attempts, we considered a direct extension of the Least-Squares Temporal Difference (LSTD) algorithm in the spirit of Q-learning. Later, an effort to remedy some limitations of this algorithm (approximation bias, poor sample utilization) led to the Least-Squares Policy Iteration (LSPI) algorithm, which is a form of model-free approximate policy iteration and makes efficient use of training samples collected in any arbitrary manner. The algorithms are demonstrated on a variety of learning domains, including algorithm selection, inverted pendulum balancing, bicycle balancing and riding, multiagent learning in factored domains, and, recently, on two-player zero-sum Markov games and the game of Tetris.