PFN-TS: Thompson Sampling for Contextual Bandits via Prior-Data Fitted Networks

Thompson sampling is a widely used strategy for contextual bandits: at each round, it samples a reward function from a Bayesian posterior and acts greedily under that sample. Prior-data fitted networks (PFNs), such as TabPFN v2+ and TabICL v2, are attractive candidates for this purpose because they approximate Bayesian posterior predictive distributions in a single forward pass. However, PFNs predict noisy future rewards, while Thompson sampling requires uncertainty over the latent mean reward function. We propose PFN-TS, a Thompson sampling algorithm that converts PFN posterior predictives into mean-reward samples using a subsampled predictive central limit theorem. The method estimates posterior variance from a geometric grid of $O(\log n)$ dataset prefixes rather than the full $O(n)$ predictive sequence used in previous predictive-sequence approaches, and reuses TabICL's cached representations across rounds. We prove consistency of the subsampled variance estimator and give a Bayesian regret bound that decomposes PFN-TS regret into exact posterior-sampling regret under the PFN prior plus approximation terms. Empirically, PFN-TS achieves the best average rank across nonlinear synthetic and OpenML classification-to-bandit benchmarks, remains competitive on linear and BART-generated rewards, and attains the highest estimated policy value in an offline mobile-health evaluation. Code is available at https://anonymous.4open.science/r/PFN_TS-36ED/.

BFTS: Thompson Sampling with Bayesian Additive Regression Trees

Contextual bandits are a core technology for personalized mobile health interventions, where decision-making requires adapting to complex, non-linear user behaviors. While Thompson Sampling (TS) is a preferred strategy for these problems, its performance hinges on the quality of the underlying reward model. Standard linear models suffer from high bias, while neural network approaches are often brittle and difficult to tune in online settings. Conversely, tree ensembles dominate tabular data prediction but typically rely on heuristic uncertainty quantification, lacking a principled probabilistic basis for TS. We propose Bayesian Forest Thompson Sampling (BFTS), the first contextual bandit algorithm to integrate Bayesian Additive Regression Trees (BART), a fully probabilistic sum-of-trees model, directly into the exploration loop. We prove that BFTS is theoretically sound, deriving an information-theoretic Bayesian regret bound of $\tilde{O}(\sqrt{T})$. As a complementary result, we establish frequentist minimax optimality for a "feel-good" variant, confirming the structural suitability of BART priors for non-parametric bandits. Empirically, BFTS achieves state-of-the-art regret on tabular benchmarks with near-nominal uncertainty calibration. Furthermore, in an offline policy evaluation on the Drink Less micro-randomized trial, BFTS improves engagement rates by over 30% compared to the deployed policy, demonstrating its practical effectiveness for behavioral interventions.