Online (Non-)Convex Learning via Tempered Optimism

TL;DR

This paper introduces the optimistically tempered (OT) framework for online learning, improving performance with imperfect experts in non-convex and convex settings, and demonstrates its effectiveness on real datasets.

Contribution

It proposes the OT framework for online learning, modifies existing algorithms for non-convex and convex losses, and evaluates practical benefits on real data.

Findings

Tempered optimism enhances online learning with imperfect experts.

Modified algorithms perform well in non-convex and convex scenarios.

Empirical results show practical efficiency of the OT approach.

Abstract

Optimistic Online Learning aims to exploit experts conveying reliable information to predict the future. However, such implicit optimism may be challenged when it comes to practical crafting of such experts. A fundamental example consists in approximating a minimiser of the current problem and use it as expert. In the context of dynamic environments, such an expert only conveys partially relevant information as it may lead to overfitting. To tackle this issue, we introduce in this work the \emph{optimistically tempered} (OT) online learning framework designed to handle such imperfect experts. As a first contribution, we show that tempered optimism is a fruitful paradigm for Online Non-Convex Learning by proposing simple, yet powerful modification of Online Gradient and Mirror Descent. Second, we derive a second OT algorithm for convex losses and third, evaluate the practical efficiency of tempered optimism on real-life datasets and a toy experiment.