Improved Regret Bounds for Tracking Experts with Memory

TL;DR

This paper introduces a linear-time algorithm for sequential prediction with expert advice in non-stationary environments, improving regret bounds by using a relative entropy projection step that offers advantages over previous methods.

Contribution

The paper presents a novel linear-time algorithm that enhances regret bounds for expert tracking with memory, incorporating an efficient relative entropy projection.

Findings

Improved regret bounds over previous algorithms

Linear-time computation of the projection step

Enhanced performance in non-stationary environments

Abstract

We address the problem of sequential prediction with expert advice in a non-stationary environment with long-term memory guarantees in the sense of Bousquet and Warmuth [4]. We give a linear-time algorithm that improves on the best known regret bounds [26]. This algorithm incorporates a relative entropy projection step. This projection is advantageous over previous weight-sharing approaches in that weight updates may come with implicit costs as in for example portfolio optimization. We give an algorithm to compute this projection step in linear time, which may be of independent interest.