New Analysis and Algorithm for Learning with Drifting Distributions

TL;DR

This paper introduces a new theoretical framework and algorithm for learning in environments where data distributions change over time, providing tighter bounds and practical algorithms with promising experimental results.

Contribution

It offers a novel analysis using discrepancy measures, tighter learning bounds, a generalized online-to-batch conversion, and a new algorithm formulated as a quadratic program.

Findings

Tighter learning bounds based on discrepancy and Rademacher complexity.

A new algorithm formulated as a quadratic program demonstrating practical benefits.

Preliminary experiments show improved performance in drifting distribution scenarios.

Abstract

We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of distributions both for a drifting PAC scenario and a tracking scenario. Our bounds are always tighter and in some cases substantially improve upon previous ones based on the $L_1$ distance. We also present a generalization of the standard on-line to batch conversion to the drifting scenario in terms of the discrepancy and arbitrary convex combinations of hypotheses. We introduce a new algorithm exploiting these learning guarantees, which we show can be formulated as a simple QP. Finally, we report the results of preliminary experiments demonstrating the benefits of this algorithm.