A note on continuous-time online learning

TL;DR

This paper extends discrete-time online learning algorithms to continuous-time models across various problems, providing concise proofs of optimal regret bounds in the process.

Contribution

It introduces continuous-time versions of algorithms for online linear optimization and adversarial bandits, with simplified proofs of their optimal regret bounds.

Findings

Extended algorithms to continuous-time setting

Provided concise proofs of optimal regret bounds

Unified treatment across multiple online learning problems

Abstract

In online learning, the data is provided in a sequential order, and the goal of the learner is to make online decisions to minimize overall regrets. This note is concerned with continuous-time models and algorithms for several online learning problems: online linear optimization, adversarial bandit, and adversarial linear bandit. For each problem, we extend the discrete-time algorithm to the continuous-time setting and provide a concise proof of the optimal regret bound.