Approximate discounting-free policy evaluation from transient and recurrent states

In order to distinguish policies that prescribe good from bad actions in transient states, we need to evaluate the so-called bias of a policy from transient states. However, we observe that most (if not all) works in approximate discounting-free policy evaluation thus far are developed for estimating the bias solely from recurrent states. We therefore propose a system of approximators for the bias (specifically, its relative value) from transient and recurrent states. Its key ingredient is a seminorm LSTD (least-squares temporal difference), for which we derive its minimizer expression that enables approximation by sampling required in model-free reinforcement learning. This seminorm LSTD also facilitates the formulation of a general unifying procedure for LSTD-based policy value approximators. Experimental results validate the effectiveness of our proposed method.