Universal Online Optimization in Dynamic Environments via Uniclass Prediction

TL;DR

This paper introduces a universal online optimization framework for dynamic environments that reduces the problem to uniclass prediction, enabling better dynamic regret bounds without relying on expert sets.

Contribution

It presents a novel approach that transforms dynamic online convex optimization into a uniclass prediction problem, achieving state-of-the-art dynamic regret guarantees.

Findings

Achieves improved dynamic regret bounds for convex functions.

Does not rely on expert sets or meta-algorithms.

First universal method with such guarantees for general convex costs.

Abstract

Recently, several universal methods have been proposed for online convex optimization which can handle convex, strongly convex and exponentially concave cost functions simultaneously. However, most of these algorithms have been designed with static regret minimization in mind, but this notion of regret may not be suitable for changing environments. To address this shortcoming, we propose a novel and intuitive framework for universal online optimization in dynamic environments. Unlike existing universal algorithms, our strategy does not rely on the construction of a set of experts and an accompanying meta-algorithm. Instead, we show that the problem of dynamic online optimization can be reduced to a uniclass prediction problem. By leaving the choice of uniclass loss function in the user's hands, they are able to control and optimize dynamic regret bounds, which in turn carry over into the original problem. To the best of our knowledge, this is the first paper proposing a universal approach with state-of-the-art dynamic regret guarantees even for general convex cost functions.