An Exponential Lower Bound for the Latest Deterministic Strategy Iteration Algorithms

Oliver Friedmann

doi:10.2168/LMCS-7(3:23)2011

Oliver Friedmann - An Exponential Lower Bound for the Latest Deterministic Strategy Iteration Algorithms

lmcs:1026 - Logical Methods in Computer Science, October 3, 2011, Volume 7, Issue 3 - https://doi.org/10.2168/LMCS-7(3:23)2011

An Exponential Lower Bound for the Latest Deterministic Strategy Iteration AlgorithmsArticle

Authors: Oliver Friedmann

This paper presents a new exponential lower bound for the two most popular deterministic variants of the strategy improvement algorithms for solving parity, mean payoff, discounted payoff and simple stochastic games. The first variant improves every node in each step maximizing the current valuation locally, whereas the second variant computes the globally optimal improvement in each step. We outline families of games on which both variants require exponentially many strategy iterations.

https://doi.org/10.2168/LMCS-7(3:23)2011

Source: arXiv.org:1106.0778

Volume: Volume 7, Issue 3

Published on: October 3, 2011

Imported on: November 5, 2010

Keywords: Computer Science - Computer Science and Game Theory,F.2.2

Licence: arXiv.org - Non-exclusive license to distribute

Bibliographic References

19 Documents citing this article

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David Avis;Oliver Friedmann, 2016, An exponential lower bound for Cunningham’s rule, arXiv (Cornell University), 161, 1-2, pp. 271-305, 10.1007/s10107-016-1008-4, https://arxiv.org/abs/1305.3944.

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John Fearnley;Rahul Savani, arXiv (Cornell University), The Complexity of the Simplex Method, 2015, Portland Oregon USA, 10.1145/2746539.2746558.

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Oliver Friedmann, 2013, A superpolynomial lower bound for strategy iteration based on snare memorization, Discrete Applied Mathematics, 161, 10-11, pp. 1317-1337, 10.1016/j.dam.2013.02.007, https://doi.org/10.1016/j.dam.2013.02.007.

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Oliver Friedmann, Lecture Notes in Computer Science, A Subexponential Lower Bound for Zadeh’s Pivoting Rule for Solving Linear Programs and Games, pp. 192-206, 2011, 10.1007/978-3-642-20807-2_16.

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