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Online Linear Regression in Dynamic Environments via Discounting
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:21083-21120, 2024.
Abstract
We develop algorithms for online linear regression which achieve optimal static and dynamic regret guarantees even in the complete absence of prior knowledge. We present a novel analysis showing that a discounted variant of the Vovk-Azoury-Warmuth forecaster achieves dynamic regret of the form RT(→u)≤O(dlog(T)∨√dPγT(→u)T), where PγT(→u) is a measure of variability of the comparator sequence, and show that the discount factor achieving this result can be learned on-the-fly. We show that this result is optimal by providing a matching lower bound. We also extend our results to strongly-adaptive guarantees which hold over every sub-interval [a,b]⊆[1,T] simultaneously.