MS&E 336 Lecture 11: The multiplicative weights algorithm
نویسنده
چکیده
This lecture is based on the corresponding paper of Freund and Schapire [2], though with some differences in notation and analysis. We introduce and study the multiplicative weights (MW) algorithm, which is an external regret minimizing (i.e., Hannan consistent) algorithm for playing a game. The same algorithm has been analyzed in various forms, particularly in the study of online learning; see the references in [2]. Indeed, as we will observe in the subsequent lecture, the multiplicative weights algorithm is in fact a special case of stochastic fictitious play. Our focus in this lecture is on establishing Hannan consistency of the algorithm. Throughout the lecture we use the same notation as in Lecture 10, but restrict attention to twoplayer games. (Note that by grouping all players other than player 1 into “player 2”, any game can be viewed as a two player game for the purposes of establishing Hannan consistency of the multiplicative weights algorithm.)
منابع مشابه
CS261: A Second Course in Algorithms Lecture #12: Applications of Multiplicative Weights to Games and Linear Programs∗
1 Extensions of the Multiplicative Weights Guarantee Last lecture we introduced the multiplicative weights algorithm for online decision-making. You don't need to remember the algorithm details for this lecture, but you should remember that it's a simple and natural algorithm (just one simple update per action per time step). You should also remember its regret guarantee, which we proved last l...
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