Fixed-Confidence Multiple Change Point Identification under Bandit Feedback

2025-07-11

AI Summary

This paper addresses the problem of efficiently identifying multiple change points in a piecewise-constant function under noisy bandit feedback, with a fixed confidence guarantee. Existing methods suffer from high sampling complexity and lack theoretical optimality guarantees. To address this, we first derive an instance-dependent lower bound on sample complexity, revealing that optimal sampling concentrates near change points and scales inversely with jump magnitudes. Building upon this insight, we propose a Track-and-Stop-based asymptotically optimal algorithm that integrates a piecewise-constant bandwidth model with an adaptive sequential sampling scheme. We establish a theoretical guarantee that the algorithm achieves the information-theoretic lower bound under general conditions. Empirical evaluation on synthetic benchmarks demonstrates that our method significantly reduces sample complexity compared to state-of-the-art baselines.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Topic discovery and tracking
• Security and Privacy: Tracking, profiling, and countermeasures against them

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.

Problem

• Identify abrupt change points in piecewise constant functions efficiently
• Optimize sampling near change points for faster detection
• Develop asymptotically optimal method for change point identification

Innovation

• Fixed-confidence piecewise constant bandit problem
• Instance-dependent lower bounds for complexity
• Asymptotically optimal Track-and-Stop variant