Online least-squares policy iteration for reinforcement learning control

Reinforcement learning is a promising paradigm for learning optimal control. We consider policy iteration (PI) algorithms for reinforcement learning, which iteratively evaluate and improve control policies. State-of-the-art, least-squares techniques for policy evaluation are sample-efficient and have relaxed convergence requirements. However, they are typically used in offline PI, whereas a central goal of reinforcement learning is to develop online algorithms. Therefore, we propose an online PI algorithm that evaluates policies with the so-called least-squares temporal difference for Q-functions (LSTD-Q). The crucial difference between this online least-squares policy iteration (LSPI) algorithm and its offline counterpart is that, in the online case, policy improvements must be performed once every few state transitions, using only an incomplete evaluation of the current policy. In an extensive experimental evaluation, online LSPI is found to work well for a wide range of its parameters, and to learn successfully in a real-time example. Online LSPI also compares favorably with offline LSPI and with a different flavor of online PI, which instead of LSTD-Q employs another least-squares method for policy evaluation.