Near-Linear Time Algorithm with Near-Logarithmic Regret Per Switch for Mixable/Exp-Concave Losses

TL;DR

This paper introduces a near-linear time online learning algorithm for mixable and exp-concave losses that achieves near-logarithmic regret per switch in dynamic environments, improving computational efficiency.

Contribution

It presents the first near-logarithmic regret per switch algorithm with sub-polynomial complexity, advancing online learning in dynamic settings.

Findings

Achieves near-logarithmic regret per switch with sub-polynomial complexity.

Provides deterministic guarantees in individual sequence settings.

Extends the online mixture framework for dynamic environments.

Abstract

We investigate the problem of online learning, which has gained significant attention in recent years due to its applicability in a wide range of fields from machine learning to game theory. Specifically, we study the online optimization of mixable loss functions with logarithmic static regret in a dynamic environment. The best dynamic estimation sequence that we compete against is selected in hindsight with full observation of the loss functions and is allowed to select different optimal estimations in different time intervals (segments). We propose an online mixture framework that uses these static solvers as the base algorithm. We show that with the suitable selection of hyper-expert creations and weighting strategies, we can achieve logarithmic and squared logarithmic regret per switch in quadratic and linearithmic computational complexity, respectively. For the first time in literature, we show that it is also possible to achieve near-logarithmic regret per switch with sub-polynomial complexity per time. Our results are guaranteed to hold in a strong deterministic sense in an individual sequence manner.