Papers › Thompson Sampling for Linearly Constrained Bandits

Thompson Sampling for Linearly Constrained Bandits

20 Apr 2020arXiv:2004.09258archive 2025-07-28

Vidit Saxena, Joseph E. Gonzalez, Joakim Jaldén

We address multi-armed bandits (MAB) where the objective is to maximize the cumulative reward under a probabilistic linear constraint. For a few real-world instances of this problem, constrained extensions of the well-known Thompson Sampling (TS) heuristic have recently been proposed. However, finite-time analysis of constrained TS is challenging; as a result, only O(\sqrt{T}) bounds on the cumulative reward loss (i.e., the regret) are available. In this paper, we describe LinConTS, a TS-based algorithm for bandits that place a linear constraint on the probability of earning a reward in every round. We show that for LinConTS, the regret as well as the cumulative constraint violations are upper bounded by O(\log T) for the suboptimal arms. We develop a proof technique that relies on careful analysis of the dual problem and combine it with recent theoretical work on unconstrained TS. Through numerical experiments on two real-world datasets, we demonstrate that LinConTS outperforms an asymptotically optimal upper confidence bound (UCB) scheme in terms of simultaneously minimizing the regret and the violation.

PaperPDFCode

Code

vidits-kth/LinConTS officialmentioned in paper report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Tasks

Multi-Armed BanditsThompson Sampling

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Methods

TS

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections