Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
A polynomial-time algorithm for a class of linear complementary problems
Mathematical Programming: Series A and B
Linear programming, complexity theory and elementary functional analysis
Mathematical Programming: Series A and B
A primal-dual interior point method whose running time depends only on the constraint matrix
Mathematical Programming: Series A and B
Complexity and real computation
Complexity and real computation
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
A modified layered-step interior-point algorithm for linear programming
Mathematical Programming: Series A and B
A Variant of the Vavasis-Ye Layered-Step Interior-Point Algorithm for Linear Programming
SIAM Journal on Optimization
Learning and value function approximation in complex decision processes
Learning and value function approximation in complex decision processes
A New Iteration-Complexity Bound for the MTY Predictor-Corrector Algorithm
SIAM Journal on Optimization
On the complexity of policy iteration
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
On the complexity of solving Markov decision problems
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Discounted deterministic Markov decision processes and discounted all-pairs shortest paths
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Strongly Polynomial Algorithm for Controlled Queues
Mathematics of Operations Research
Discounted deterministic Markov decision processes and discounted all-pairs shortest paths
ACM Transactions on Algorithms (TALG)
Mathematics of Operations Research
Robust Markov Decision Processes
Mathematics of Operations Research
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We present a new complexity result on solving the Markov decision problem (MDP) with n states and a number of actions for each state, a special class of real-number linear programs with the Leontief matrix structure. We prove that when the discount factor Î赂 is strictly less than 1, the problem can be solved in at most O(n1.5(log 1/(1 - Î赂)+log n)) classical interior-point method iterations and O(n4(log 1/(1 - Î赂)+log n)) arithmetic operations. Our method is a combinatorial interior-point method related to the work of Ye (1990. A "build-down" scheme for linear programming. Math. Programming46 61-72) and Vavasis and Ye (1996. A primal-dual interior-point method whose running time depends only on the constraint matrix. Math. Programming74 79-120). To our knowledge, this is the first strongly polynomial-time algorithm for solving the MDP when the discount factor is a constant less than 1.