On Local Regret

TL;DR

This paper introduces local regret, a new measure for online learning that focuses on near hypotheses, along with algorithms that leverage locality graphs to improve learning speed across various problems.

Contribution

It proposes the concept of local regret and provides algorithms that utilize locality graphs to enhance online learning efficiency.

Findings

Algorithms successfully minimize local regret in diverse online problems.

Exploiting graph structure significantly speeds up learning.

Applicable to online disjunct learning, Max-SAT, and decision trees.

Abstract

Online learning aims to perform nearly as well as the best hypothesis in hindsight. For some hypothesis classes, though, even finding the best hypothesis offline is challenging. In such offline cases, local search techniques are often employed and only local optimality guaranteed. For online decision-making with such hypothesis classes, we introduce local regret, a generalization of regret that aims to perform nearly as well as only nearby hypotheses. We then present a general algorithm to minimize local regret with arbitrary locality graphs. We also show how the graph structure can be exploited to drastically speed learning. These algorithms are then demonstrated on a diverse set of online problems: online disjunct learning, online Max-SAT, and online decision tree learning.