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In the presence of non-admissible heuristics, A* and other best-firstalgorithms can be converted into anytime optimal algorithms over OR graphs, bysimply continuing the search after the first solution is found. The same trick,however, does not work for best-first algorithms over AND/OR graphs, that mustbe able to expand leaf nodes of the explicit graph that are not necessarilypart of the best partial solution. Anytime optimal variants of AO* must thusaddress an exploration-exploitation tradeoff: they cannot just "exploit", theymust keep exploring as well. In this work, we develop one such variant of AO*and apply it to finite-horizon MDPs. This Anytime AO* algorithm eventuallydelivers an optimal policy while using non-admissible random heuristics thatcan be sampled, as when the heuristic is the cost of a base policy that can besampled with rollouts. We then test Anytime AO* for action selection over largeinfinite-horizon MDPs that cannot be solved with existing off-line heuristicsearch and dynamic programming algorithms, and compare it with UCT.

Action Selection for MDPs: Anytime AO* vs. UCT