# A Near-Optimal Change-Detection Based Algorithm for Piecewise-Stationary Combinatorial Semi-Bandits

arXiv: https://arxiv.org/abs/1908.10402 · HTML: https://mlsanity.com/paper/1908.10402/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2019.

## Built on by (most cited first, 5 of 5)

- [Matroid Semi-Bandits in Sublinear Time](https://mlsanity.com/paper/2405.17968/) (2024)
- [Distributed Consensus Algorithm for Decision-Making in Multi-agent Multi-armed Bandit](https://mlsanity.com/paper/2306.05998/) (2023)
- [Piecewise-Stationary Combinatorial Semi-Bandit with Causally Related Rewards](https://mlsanity.com/paper/2307.14138/) (2023)
- [DAL: A Practical Prior-Free Black-Box Framework for Piecewise Stationary Bandits](https://mlsanity.com/paper/2501.19401/) (2025)
- [MAB-Based Channel Scheduling for Asynchronous Federated Learning in Non-Stationary Environments](https://mlsanity.com/paper/2503.01324/) (2025)

## Abstract (arXiv)

We investigate the piecewise-stationary combinatorial semi-bandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-stationary manner at unknown time steps. We propose an algorithm, textttGLR-CUCB, which incorporates an efficient combinatorial semi-bandit algorithm, textttCUCB, with an almost parameter-free change-point detector, the Generalized Likelihood Ratio Test (GLRT). Our analysis shows that the regret of textttGLR-CUCB is upper bounded by O(√NKTlogT), where N is the number of piecewise-stationary segments, K is the number of base arms, and T is the number of time steps. As a complement, we also derive a nearly matching regret lower bound on the order of Omega(√NKT), for both piecewise-stationary multi-armed bandits and combinatorial semi-bandits, using information-theoretic techniques and judiciously constructed piecewise-stationary bandit instances. Our lower bound is tighter than the best available regret lower bound, which is Omega(√T). Numerical experiments on both synthetic and real-world datasets demonstrate the superiority of textttGLR-CUCB compared to other state-of-the-art algorithms.