Prediction with Expert Advice in Games with Unbounded One-Step Gains

TL;DR

This paper extends algorithms for prediction with expert advice to scenarios with unbounded one-step gains, providing bounds and a universal algorithm that performs optimally even with large gains.

Contribution

It introduces modifications to existing algorithms for unbounded gains, establishes lower bounds, and constructs a universal algorithm with optimal performance.

Findings

Universal algorithm achieves optimal performance with unbounded gains.

Performance close to the best expert under limited deviation conditions.

Provides lower bounds for cumulative gain in the general case.

Abstract

The games of prediction with expert advice are considered in this paper. We present some modification of Kalai and Vempala algorithm of following the perturbed leader for the case of unrestrictedly large one-step gains. We show that in general case the cumulative gain of any probabilistic prediction algorithm can be much worse than the gain of some expert of the pool. Nevertheless, we give the lower bound for this cumulative gain in general case and construct a universal algorithm which has the optimal performance; we also prove that in case when one-step gains of experts of the pool have ``limited deviations'' the performance of our algorithm is close to the performance of the best expert.