Journal ArticleDOI
Markovian Decision Processes with Uncertain Transition Probabilities
Jay K. Satia,Roy E. Lave +1 more
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In this article, the authors consider Markovian decision processes in which the transition probabilities corresponding to alternative decisions are not known with certainty, and they consider both a game-theoretic and a Bayesian formulation.Abstract:
This paper examines Markovian decision processes in which the transition probabilities corresponding to alternative decisions are not known with certainty. The processes are assumed to be finite-state, discrete-time, and stationary. The rewards axe time discounted. Both a game-theoretic and the Bayesian formulation are considered. In the game-theoretic formulation, variants of a policy-iteration algorithm are provided for both the max-min and the max-max cases. An implicit enumeration algorithm is discussed for the Bayesian formulation where upper and lower bounds on the total expected discounted return are provided by the max-max and max-min optimal policies. Finally, the paper discusses asymptotically Bayes-optimal policies.read more
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Robust Control of Markov Decision Processes with Uncertain Transition Matrices
Arnab Nilim,Laurent El Ghaoui +1 more
TL;DR: This work considers a robust control problem for a finite-state, finite-action Markov decision process, where uncertainty on the transition matrices is described in terms of possibly nonconvex sets, and shows that perfect duality holds for this problem, and that it can be solved with a variant of the classical dynamic programming algorithm, the "robust dynamic programming" algorithm.
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A survey of maintenance models: The control and surveillance of deteriorating systems
TL;DR: The literature on maintenance models is surveyed and includes models which involve an optimal decision to procure, inspect, and repair and/or replace a unit subject to deterioration in service.
Journal ArticleDOI
Robust Dynamic Programming
TL;DR: It is proved that when this set of measures has a certain "rectangularity" property, all of the main results for finite and infinite horizon DP extend to natural robust counterparts.
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Robust Markov Decision Processes
TL;DR: This work considers robust MDPs that offer probabilistic guarantees in view of the unknown parameters to counter the detrimental effects of estimation errors and determines a policy that attains the highest worst-case performance over this confidence region.
References
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Book
Dynamic Programming
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
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Stochastic Games
TL;DR: In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players, and the expected total gain or loss is bounded by M, which depends on N 2 + N matrices.
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Applied Statistical Decision Theory
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Branch-and-Bound Methods: A Survey
Eugene L. Lawler,D. E. Wood +1 more
TL;DR: The essential features of the branch-and-bound approach to constrained optimization are described, and several specific applications are reviewed, including integer linear programming Land-Doig and Balas methods, nonlinear programming minimization of nonconvex objective functions, and the quadratic assignment problem Gilmore and Lawler methods.