Continuous Prediction with Experts' Advice
Abstract
Prediction with experts' advice is one of the most fundamental problems in online learning and captures many of its technical challenges. A recent line of work has looked at online learning through the lens of differential equations and continuous-time analysis. This viewpoint has yielded optimal results for several problems in online learning. In this paper, we employ continuous-time stochastic calculus in order to study the discrete-time experts' problem. We use these tools to design a continuous-time, parameter-free algorithm with improved guarantees for the quantile regret. We then develop an analogous discrete-time algorithm with a very similar analysis and identical quantile regret bounds. Finally, we design an anytime continuous-time algorithm with regret matching the optimal fixed-time rate when the gains are independent Brownian Motions; in many settings, this is the most difficult case. This gives some evidence that, even with adversarial gains, the optimal anytime and fixed-time regrets may coincide.
Cite
@article{arxiv.2206.00236,
title = {Continuous Prediction with Experts' Advice},
author = {Victor Sanches Portella and Christopher Liaw and Nicholas J. A. Harvey},
journal= {arXiv preprint arXiv:2206.00236},
year = {2022}
}
Comments
30 pages, 1 figure. Version 2 diff: minor edits, reorganization for a journal submission, correct statement of Lemma 5.1 and a better formatted proof of the same lemma