Optimal Comparator Adaptive Online Learning with Switching Cost

TL;DR

This paper introduces a new comparator adaptive online learning algorithm that effectively handles switching costs, achieving optimal regret bounds and demonstrating practical benefits in sequential investment tasks.

Contribution

The paper develops a novel dual space scaling strategy for comparator adaptive algorithms with switching costs, improving regret bounds to the optimal rate.

Findings

Achieves optimal comparator adaptive regret bounds with switching costs.

Extends benefits to the expert setting.

Demonstrates practicality through a sequential investment task.

Abstract

Practical online learning tasks are often naturally defined on unconstrained domains, where optimal algorithms for general convex losses are characterized by the notion of comparator adaptivity. In this paper, we design such algorithms in the presence of switching cost - the latter penalizes the typical optimism in adaptive algorithms, leading to a delicate design trade-off. Based on a novel dual space scaling strategy discovered by a continuous-time analysis, we propose a simple algorithm that improves the existing comparator adaptive regret bound [ZCP22a] to the optimal rate. The obtained benefits are further extended to the expert setting, and the practicality of the proposed algorithm is demonstrated through a sequential investment task.