An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games

  • Sven Schewe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5213)


This paper presents a novel strategy improvement algorithm for parity and payoff games, which is guaranteed to select, in each improvement step, an optimal combination of local strategy modifications. Current strategy improvement methods stepwise improve the strategy of one player with respect to some ranking function, using an algorithm with two distinct phases: They first choose a modification to the strategy of one player from a list of locally profitable changes, and subsequently evaluate the modified strategy. This separation is unfortunate, because current strategy improvement algorithms have no effective means to predict the global effect of the individual local modifications beyond classifying them as profitable, adversarial, or stale. Furthermore, they are completely blind towards the cross effect of different modifications: Applying one profitable modification may render all other profitable modifications adversarial. Our new construction overcomes the traditional separation between choosing and evaluating the modification to the strategy. It thus improves over current strategy improvement algorithms by providing the optimal improvement in every step, selecting the best combination of local updates from a superset of all profitable and stale changes.


Ranking Function Tree Automaton Local Update Winning Region Improvement Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sven Schewe
    • 1
  1. 1.Universität des Saarlandes and University of Liverpool 

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