$\alpha$-PFN: Fast Entropy Search via In-Context Learning

Abstract: Information-theoretic acquisition functions such as Entropy Search (ES) offer a principled exploration-exploitation framework for Bayesian optimization (BO). However, their practical implementation relies on complicated and slow approximations, i.e., a Monte Carlo estimation of the information gain. This complexity can introduce numerical errors and requires specialized, hand-crafted implementations. We propose a two-stage amortization strategy that learns to approximate entropy search-based acquisition functions using Prior-data Fitted Networks (PFNs) in a single forward pass. A first PFN is trained to be conditioned on information about the optima; second, the $\alpha$-PFN is trained to predict the expected information gain by training on information gains measured with the first PFN. The $\alpha$-PFN offers a flexible learned approximation, which replaces the complex heuristic approximations with a single forward pass per candidate, enabling rapid and extensible acquisition evaluation. Empirically, our approach is competitive with state-of-the-art entropy search implementations on synthetic and real-world benchmarks, while accelerating the different entropy search variants across all our experiments, with speed ups over 50x. Source code: this https URL.

Machine Learning (cs.LG)

arXiv:2606.07134 [cs.LG]

(or arXiv:2606.07134v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.07134 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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