On Regression-Based Stopping Times

We study approaches that fit a linear combination of basis functions to the continuation value function of an optimal stopping problem and then employ a greedy policy based on the resulting approximation. We argue that computing weights to maximize expected payoff of the greedy policy or to minimize expected squared-error with respect to an invariant measure is intractable. On the other hand, certain versions of approximate value iteration lead to policies competitive with those that would result from optimizing the latter objective.