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Using Randomization to Break the Curse of Dimensionality
 Econometrica
, 1997
"... Abstract: This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the “curse of dimensionality ” fo ..."
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Cited by 86 (0 self)
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Abstract: This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the “curse of dimensionality ” for a subclass of MDPs known as discrete decision processes (DDPs). 1
The Policy Iteration Algorithm for Average Reward Markov Decision Processes with General State Space
 IEEE Trans. Automat. Control
, 1997
"... The average cost optimal control problem is addressed for Markov decision processes with unbounded cost. It is found that the policy iteration algorithm generates a sequence of policies which are cregular (a strong stability condition) , where c is the cost function under consideration. This result ..."
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Cited by 22 (9 self)
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The average cost optimal control problem is addressed for Markov decision processes with unbounded cost. It is found that the policy iteration algorithm generates a sequence of policies which are cregular (a strong stability condition) , where c is the cost function under consideration. This result only requires the existence of an initial cregular policy, and an irreducibility condition on the state space. Furthermore, under these conditions the sequence of relative value functions generated by the algorithm is bounded from below, and "nearly" decreasing, from which it follows that the algorithm is always convergent. Under further conditions, it is shown that the algorithm does compute a solution to the optimality equations, and hence an optimal average cost policy. These results provide elementary criteria for the existence of optimal policies for Markov decision processes with unbounded cost, and recover known results for the standard LQG problem. When these results are specialize...
FiniteState Average Cost Stochastic Games With Compact Constraint Sets And A Recurrence Condition
 SIAM Journal on Control and Optimization
, 1998
"... . We characterize and establish the existence of stationary equilibrium solutions for a class of finitestate average cost games. We assume that two players choose actions at each stage from compact constraint sets, enforcing some relatively mild assumptions on the transition probability and cost fu ..."
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Cited by 1 (1 self)
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. We characterize and establish the existence of stationary equilibrium solutions for a class of finitestate average cost games. We assume that two players choose actions at each stage from compact constraint sets, enforcing some relatively mild assumptions on the transition probability and cost functions. We also assume that there is a distinguished state which is recurrent under each pair of stationary policies and that the corresponding Markov chains have a single recurrent class. In the second half of the paper, we establish the convergence of several dynamic programming algorithms. Key words. game theory, average cost stochastic games, optimization, dynamic programming, stochastic shortest paths AMS subject classifications. 90D15, 93E05, 49L20 1. Introduction. In this paper, we consider two player Markov decision processes where one player seeks to minimize average cost in controlling a finite state system and the other player seeks to maximize cost. The players choose actions...