Variance-sensitive Thompson sampling for generalised linear bandits, revisited

Tom Perneczky; Marc Abeille; David Janz

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arXiv · 2606.00431

Variance-sensitive Thompson sampling for generalised linear bandits, revisited

Tom Perneczky·Marc Abeille·David Janz

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Abstract

We prove a variance-sensitive regret bound for Thompson sampling in stochastic generalised linear bandits. The argument assumes a warm-up, after which the regret is controlled through using the Gaussian Poincar\'e inequality. This bypasses the point at which previous optimism-based analyses break down. Removing the warm-up while retaining the same variance-sensitive scaling remains open, and appears nontrivial.

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Tom Perneczky, Marc Abeille, David Janz. 2026-05-29. Variance-sensitive Thompson sampling for generalised linear bandits, revisited. https://arxiv.org/abs/2606.00431

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