EN FR
EN FR


Project Team Sierra


Overall Objectives
Application Domains
Bibliography


Project Team Sierra


Overall Objectives
Application Domains
Bibliography


Section: New Results

Minimax Policies for Combinatorial Prediction Games

Participant : Jean-Yves Audibert.

Collaboration with: Sébastien Bubeck (Centre de Recerca Matematica of Barcelona) and Gabor Lugosi (ICREA and Pompeu Fabra University)

In [8] , we address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the problem under three different assumptions for the feedback: full information, and the partial information models of the so-called "semi-bandit", and "bandit" problems. We consider both L -, and L 2 -type of restrictions for the losses assigned by the adversary. We formulate a general strategy using Bregman projections on top of a potential-based gradient descent, which generalizes the ones studied in numerous recent works. We provide simple proofs that recover most of the previous results. We propose new upper bounds for the semi-bandit game. Moreover we derive lower bounds for all three feedback assumptions. With the only exception of the bandit game, the upper and lower bounds are tight, up to a constant factor. Finally, we answer an open question raised by W. M. Koolen, M. K. Warmuth, and J. Kivinen by showing that the exponentially weighted average forecaster is suboptimal against L adversaries.