5,239 research outputs found

    On Monte-Carlo tree search for deterministic games with alternate moves and complete information

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    We consider a deterministic game with alternate moves and complete information, of which the issue is always the victory of one of the two opponents. We assume that this game is the realization of a random model enjoying some independence properties. We consider algorithms in the spirit of Monte-Carlo Tree Search, to estimate at best the minimax value of a given position: it consists in simulating, successively, nn well-chosen matches, starting from this position. We build an algorithm, which is optimal, step by step, in some sense: once the nn first matches are simulated, the algorithm decides from the statistics furnished by the nn first matches (and the a priori we have on the game) how to simulate the (n+1)(n+1)-th match in such a way that the increase of information concerning the minimax value of the position under study is maximal. This algorithm is remarkably quick. We prove that our step by step optimal algorithm is not globally optimal and that it always converges in a finite number of steps, even if the a priori we have on the game is completely irrelevant. We finally test our algorithm, against MCTS, on Pearl's game and, with a very simple and universal a priori, on the games Connect Four and some variants. The numerical results are rather disappointing. We however exhibit some situations in which our algorithm seems efficient

    Graph Oracle Models, Lower Bounds, and Gaps for Parallel Stochastic Optimization

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    We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed updates and parallel processing with intermittent communication. We highlight gaps between lower and upper bounds on the oracle complexity, and cases where the "natural" algorithms are not known to be optimal
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