PG-TS: Improved Thompson Sampling for Logistic Contextual Bandits
This work addresses the problem of efficient decision-making in sequential actions with binary rewards for learners in contextual bandits, representing an incremental improvement over existing methods.
The paper tackles regret minimization in logistic contextual bandits by proposing PG-TS, an improved Thompson Sampling method using Polya-Gamma augmentation, which achieves state-of-the-art performance on simulated and real data with low regret.
We address the problem of regret minimization in logistic contextual bandits, where a learner decides among sequential actions or arms given their respective contexts to maximize binary rewards. Using a fast inference procedure with Polya-Gamma distributed augmentation variables, we propose an improved version of Thompson Sampling, a Bayesian formulation of contextual bandits with near-optimal performance. Our approach, Polya-Gamma augmented Thompson Sampling (PG-TS), achieves state-of-the-art performance on simulated and real data. PG-TS explores the action space efficiently and exploits high-reward arms, quickly converging to solutions of low regret. Its explicit estimation of the posterior distribution of the context feature covariance leads to substantial empirical gains over approximate approaches. PG-TS is the first approach to demonstrate the benefits of Polya-Gamma augmentation in bandits and to propose an efficient Gibbs sampler for approximating the analytically unsolvable integral of logistic contextual bandits.