Posterior Tempering Explains Variance Inflation in Linear and Generalized Linear Thompson Sampling
We study a variant of the Thompson Sampling (TS) algorithm, called $α$-TS, for solving stochastic generalized linear bandit problems. Existing analyses of TS require inflating the posterior variance to derive near-optimal regret guarantees. We formalize the idea of variance inflation by introducing $α$-TS that uses a fractional or $α$-posterior instead of the standard posterior. Our main contribution is to identify general regularity conditions on the prior and reward distributions that enable a regret analysis of $α$-TS without assuming any tractable approximation of the posterior distribution, unlike previous works. For a specific choice of $α\propto d^{-1}$, our general regret bound yi...
| Authors | Prateek Jaiswal, Debdeep Pati, Anirban Bhattacharya et al. |
|---|---|
| Primary category | stat.ML |
| Published | 2 September 2026 |
| Last updated at source | 2 September 2026 |
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