The Complexity of All-Switches Strategy Improvement



Fearnley, J and Savani, R ORCID: 0000-0003-1262-7831
(2016) The Complexity of All-Switches Strategy Improvement. In: ACM-SIAM Symposium on Discrete Algorithms (SODA-16).

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Abstract

Strategy improvement is a widely-used and well-studied class of algorithms for solving graph-based infinite games. These algorithms are parametrized by a switching rule, and one of the most natural rules is “all switches” which switches as many edges as possible in each iteration. Continuing a recent line of work, we study all-switches strategy improvement from the perspective of computational complexity. We consider two natural decision problems, both of which have as input a game G, a starting strategy s, and an edge e. The problems are: 1. The edge switch problem, namely, is the edge e ever switched by all-switches strategy improvement when it is started from s on game G? 2. The optimal strategy problem, namely, is the edge e used in the final strategy that is found by strategy improvement when it is started from s on game G? We show PSPACE-completeness of the edge switch problem and optimal strategy problem for the following settings: Parity games with the discrete strategy improvement algorithm of Vöge and Jurdziński; mean-payoff games with the gain-bias algorithm [11, 33]; and discounted-payoff games and simple stochastic games with their standard strategy improvement algorithms. We also show PSPACE-completeness of an analogous problem to edge switch for the bottom-antipodal algorithm for Acyclic Unique Sink Orientations on Cubes.

Item Type: Conference or Workshop Item (Unspecified)
Depositing User: Symplectic Admin
Date Deposited: 19 Sep 2018 08:47
Last Modified: 19 Jan 2023 01:17
DOI: 10.1137/1.9781611974331.ch10
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3026474