Online Convex Optimization Using Predictions

TL;DR

This paper explores how to effectively utilize noisy, correlated predictions in online convex optimization, demonstrating that with stochastic models, algorithms can achieve near-optimal performance using only limited prediction windows.

Contribution

It introduces a stochastic prediction error model and shows that AFHC can achieve sublinear regret and constant competitive ratio with a constant prediction window under this model.

Findings

AFHC achieves sublinear regret in stochastic prediction models.

Constant prediction window suffices for near-optimal performance.

Performance of AFHC is tightly concentrated around its mean.

Abstract

Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error model that generalizes prior models in the learning and stochastic control communities, incorporates correlation among prediction errors, and captures the fact that predictions improve as time passes. We prove that achieving sublinear regret and constant competitive ratio for online algorithms requires the use of an unbounded prediction window in adversarial settings, but that under more realistic stochastic prediction error models it is possible to use Averaging Fixed Horizon Control (AFHC) to simultaneously achieve sublinear regret and constant competitive ratio in expectation using only a constant-sized prediction window. Furthermore, we show that the performance of AFHC is tightly concentrated around its mean.