The Cost of Learning under Multiple Change Points

TL;DR

This paper introduces a new online learning algorithm, ATC, designed for environments with multiple change points, overcoming limitations of classical methods by balancing detection sensitivity and robustness, and achieving near-optimal regret bounds.

Contribution

The paper proposes the Anytime Tracking CUSUM (ATC), a horizon-free algorithm for multiple change point detection that is nearly minimax-optimal and addresses endogenous confounding issues.

Findings

ATC outperforms classical methods in multiple change point scenarios.

Theoretical regret bounds closely match the information-theoretic lower bound.

Experimental results validate the effectiveness of ATC on synthetic and real data.

Abstract

We consider an online learning problem in environments with multiple change points. In contrast to the single change point problem that is widely studied using classical "high confidence" detection schemes, the multiple change point environment presents new learning-theoretic and algorithmic challenges. Specifically, we show that classical methods may exhibit catastrophic failure (high regret) due to a phenomenon we refer to as endogenous confounding. To overcome this, we propose a new class of learning algorithms dubbed Anytime Tracking CUSUM (ATC). These are horizon-free online algorithms that implement a selective detection principle, balancing the need to ignore "small" (hard-to-detect) shifts, while reacting "quickly" to significant ones. We prove that the performance of a properly tuned ATC algorithm is nearly minimax-optimal; its regret is guaranteed to closely match a novel information-theoretic lower bound on the achievable performance of any learning algorithm in the multiple change point problem. Experiments on synthetic as well as real-world data validate the aforementioned theoretical findings.