Abstract Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2 m Θ(N) on the worst case number of iterations needed by both of these algorithms for providing non-trivial approximations to the value of a game with N non-terminal positions and m actions for each player in each position. In particular, both algorithms have doubly-exponential complexity. Even when the game given as input has only one non-terminal position, we prove an exponential lower bound on the worst case number of iterations needed to provide non-trivial approximations.
It was shown in REF that the standard algorithms for (approximately) solving these games, value iteration and policy iteration, can be extremely slow in the worst-case: they can take a doubly exponential number of iterations to obtain any nontrivial approximation, even when the value v * is 1.
The Complexity of Solving Reachability Games Using Value and Strategy Iteration
Theory of Computing Systems
Theory of Computing Systems
Computer Science Mathematics