aiqbench analysis
This paper presents a theoretical framework for achieving logarithmic regret in control systems that undergo piecewise-stationary changes, leveraging passive change detection rather than active exploration. By utilizing the energy signature of system outputs to distinguish between noise and structural shifts, the proposed method ensures stability while adapting to unknown dynamics without requiring explicit reward signals. The work bridges classical control theory with modern learning guarantees, offering a robust approach for autonomous systems operating in non-stationary environments.
Logarithmic Regret via Passive Change Detection in Piecewise-Stationary Self-Tuning Regulation
arXiv:2610.10250v1 Announce Type: new Abstract: We study minimum-variance control of an unknown autoregressive system with exogenous inputs and coefficients that change at unknown times. Under bounded independent disturbances, fixed detection gaps, stability and feasibility conditions, and sufficient time between changes, we prove \(O((C+1)\log((T+1)/\delta))\) regret with probability at least \(1-\delta\), where \(T\) is the horizon and \(C\) the number of changes. Unlike switching bandits, where unselected arms can change unobserved, admissible plant changes provide information during exploitation: the correct feasible controller leaves only the disturbance in the output, whereas a detectable change raises output energy under the old controller. PIECE-CD explores initially and after alarms, then uses gated recursive least squares for control. Its energy test compares windowed output power with a threshold above the noise floor; the extension to unstable controller mismatches also monitors the reference controller's input proposal. We control false alarms across the horizon and prove logarithmic detection delay. Inputs are clipped to prescribed bounds. Logarithmic regret also holds under an explicit condition ensuring that clipping becomes inactive after a finite burn-in. Under the stated feasibility conditions, the extended detector covers destabilizing changes with detectable excess energy over a fixed window.
Abstract:We study minimum-variance control of an unknown autoregressive system with exogenous inputs and coefficients that change at unknown times. Under bounded independent disturbances, fixed detection gaps, stability and feasibility conditions, and sufficient time between changes, we prove \(O((C+1)\log((T+1)/\delta))\) regret with probability at least \(1-\delta\), where \(T\) is the horizon and \(C\) the number of changes. Unlike switching bandits, where unselected arms can change unobserved, admissible plant changes provide information during exploitation: the correct feasible controller leaves only the disturbance in the output, whereas a detectable change raises output energy under the old controller. PIECE-CD explores initially and after alarms, then uses gated recursive least squares for control. Its energy test compares windowed output power with a threshold above the noise floor; the extension to unstable controller mismatches also monitors the reference controller's input proposal. We control false alarms across the horizon and prove logarithmic detection delay. Inputs are clipped to prescribed bounds. Logarithmic regret also holds under an explicit condition ensuring that clipping becomes inactive after a finite burn-in. Under the stated feasibility conditions, the extended detector covers destabilizing changes with detectable excess energy over a fixed window.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.10250 [cs.LG]
(or arXiv:2610.10250v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.10250 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 285 words
Related coverage
On Non-Stationary Dynamic Pricing: Adaptivity and Optimality
arXiv · Jul 28, 2026
Trivium: Temporal Regret as a First-Class Objective for Causal-Memory Controllers
arXiv · Aug 6, 2026
Fooling Algorithms in Non-Stationary Bandits using Belief Inertia
arXiv · Sep 30, 2026
Trivium: Temporal Regret as a First-Class Objective for Causal-Memory Controllers
arXiv · Jun 9, 2026