《2016 On Boundedness of Q-Learning Iterates for Stochastic Shortest Path Problems》.pdf

《2016 On Boundedness of Q-Learning Iterates for Stochastic Shortest Path Problems》.pdf

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MATHEMATICS OF OPERATIONS RESEARCH Vol. 38, No. 2, May 2013, pp. 209–227 ISSN 0364-765X (print) ISSN 1526-5471 (online) /10.1287/moor.1120.0562 © 2013 INFORMS On Boundedness of Q-Learning Iterates for Stochastic Shortest Path Problems . . Huizhen Yu ) / s g Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, ( r r o. Cambridge, Massachusetts 02139, janey_yu@ o h s t m u Dimitri P. Bertsekas a r o f Laboratory for Information and Decision Systems and Department of EECS, Massachusetts Institute of Technology, e n h i. Cambridge, Massachusetts 02139, dimitrib@ t s l o a We consider a totally asynchronous stochastic approximation algorithm, Q-learning, for solving finite space stochastic shortest t n r y u path (SSP) problems, which are undiscounted, total cost Markov decision processes with an absorbing and cost-free state. For s o j the most commonly used SSP models, existing convergence proofs assume that the sequence of Q-learning iterates is bounded e / t / r : with probability one, or some other condition that guarantees boundedness. We prove that the sequence of iterates is naturally u p t o t bounded with probability one, thus furnishing the boundedness condition in the convergence

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