Adaptive Selective Sampling for Online Prediction with Experts

TL;DR

This paper introduces label-efficient online prediction algorithms that selectively sample labels to reduce labeling costs while maintaining optimal regret, and demonstrates their effectiveness both theoretically and empirically.

Contribution

It proposes novel label-efficient algorithms for online prediction with experts that adaptively reduce label complexity without sacrificing regret guarantees.

Findings

Label complexity scales as the square root of the number of rounds in certain scenarios.

Algorithms match minimax rates in pool-based active learning.

Numerical experiments confirm asymptotic optimality of the proposed methods.

Abstract

We consider online prediction of a binary sequence with expert advice. For this setting, we devise label-efficient forecasting algorithms, which use a selective sampling scheme that enables collecting much fewer labels than standard procedures, while still retaining optimal worst-case regret guarantees. These algorithms are based on exponentially weighted forecasters, suitable for settings with and without a perfect expert. For a scenario where one expert is strictly better than the others in expectation, we show that the label complexity of the label-efficient forecaster scales roughly as the square root of the number of rounds. Finally, we present numerical experiments empirically showing that the normalized regret of the label-efficient forecaster can asymptotically match known minimax rates for pool-based active learning, suggesting it can optimally adapt to benign settings.