The Complexity of All-Switches Strategy Improvement

Fearnley, JS and Savani, RSJ ORCID: 0000-0003-1262-7831 (2018) The Complexity of All-Switches Strategy Improvement. Logical Methods in Computer Science, 14 (4). pp. 1-57.

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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 parameterized 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 Jurdzi\'nski; mean-payoff games with the gain-bias algorithm [14,37]; 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 finding the sink of an Acyclic Unique Sink Orientation on a cube.

Item Type:	Article
Uncontrolled Keywords:	Computer Science, Data Structures and Algorithms,Computer Science, Computational Complexity,Computer Science, Computer Science and Game Theory,Computer Science, Logic in Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	12 Jan 2021 08:27
Last Modified:	18 Jan 2023 23:03
DOI:	10.23638/LMCS-14(4:9)2018
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3113288

Available Versions of this Item

• The complexity of all-switches strategy improvement. (deposited 01 Feb 2017 11:31)
  • The Complexity of All-Switches Strategy Improvement. (deposited 12 Jan 2021 08:27) [Currently Displayed]