Fixed-Confidence Multiple Change Point Identification under Bandit Feedback

TL;DR

This paper introduces a fixed-confidence bandit framework for efficiently detecting change points in piecewise constant functions through sequential noisy sampling, providing theoretical bounds and an asymptotically optimal method.

Contribution

It formulates a new fixed-confidence change point detection problem under bandit feedback, derives lower bounds, and proposes an asymptotically optimal, computationally efficient algorithm.

Findings

Lower bounds on change point identification complexity.

Optimal sampling focuses near change points, inversely proportional to change magnitude.

Experimental results demonstrate the method's efficiency in synthetic environments.

Abstract

Piecewise constant functions describe a variety of real-world phenomena in domains ranging from chemistry to manufacturing. In practice, it is often required to confidently identify the locations of the abrupt changes in these functions as quickly as possible. For this, we introduce a fixed-confidence piecewise constant bandit problem. Here, we sequentially query points in the domain and receive noisy evaluations of the function under bandit feedback. We provide instance-dependent lower bounds for the complexity of change point identification in this problem. These lower bounds illustrate that an optimal method should focus its sampling efforts adjacent to each of the change points, and the number of samples around each change point should be inversely proportional to the magnitude of the change. Building on this, we devise a simple and computationally efficient variant of Track-and-Stop and prove that it is asymptotically optimal in many regimes. We support our theoretical findings with experimental results in synthetic environments demonstrating the efficiency of our method.