Theoretical and Practical Advances on Smoothing for ExtensiveForm Games
Abstract
Sparse iterative methods, in particular firstorder methods, are known to be among the most effective in solving largescale twoplayer zerosum extensiveform games. The convergence rates of these methods depend heavily on the properties of the distancegenerating function that they are based on. We investigate the acceleration of firstorder methods for solving extensiveform games through better design of the dilated entropy functiona class of distancegenerating functions related to the domains associated with the extensiveform games. By introducing a new weighting scheme for the dilated entropy function, we develop the first distancegenerating function for the strategy spaces of sequential games that has no dependence on the branching factor of the player. This result improves the convergence rate of several firstorder methods by a factor of $\Omega(b^dd)$, where $b$ is the branching factor of the player, and $d$ is the depth of the game tree. Thus far, counterfactual regret minimization methods have been faster in practice, and more popular, than firstorder methods despite their theoretically inferior convergence rates. Using our new weighting scheme and practical tuning we show that, for the first time, the excessive gap technique can be made faster than the fastest counterfactual regret minimization algorithm, CFR+, in practice.
 Publication:

arXiv eprints
 Pub Date:
 February 2017
 arXiv:
 arXiv:1702.04849
 Bibcode:
 2017arXiv170204849K
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Artificial Intelligence