Direct Regret Optimization in Bayesian Optimization

• URL: http://arxiv.org/abs/2507.06529v1
• Date: Wed, 09 Jul 2025 04:09:58 GMT
• Title: Direct Regret Optimization in Bayesian Optimization
• Authors: Fengxue Zhang, Yuxin Chen,
• Abstract summary: We propose a novel direct regret optimization approach that jointly learns the optimal model and non-myopic acquisition.<n>We show that our method consistently outperforms BO baselines, achieving lower simple regret and demonstrating more robust exploration.
• Score: 10.705151736050967
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Bayesian optimization (BO) is a powerful paradigm for optimizing expensive black-box functions. Traditional BO methods typically rely on separate hand-crafted acquisition functions and surrogate models for the underlying function, and often operate in a myopic manner. In this paper, we propose a novel direct regret optimization approach that jointly learns the optimal model and non-myopic acquisition by distilling from a set of candidate models and acquisitions, and explicitly targets minimizing the multi-step regret. Our framework leverages an ensemble of Gaussian Processes (GPs) with varying hyperparameters to generate simulated BO trajectories, each guided by an acquisition function chosen from a pool of conventional choices, until a Bayesian early stop criterion is met. These simulated trajectories, capturing multi-step exploration strategies, are used to train an end-to-end decision transformer that directly learns to select next query points aimed at improving the ultimate objective. We further adopt a dense training--sparse learning paradigm: The decision transformer is trained offline with abundant simulated data sampled from ensemble GPs and acquisitions, while a limited number of real evaluations refine the GPs online. Experimental results on synthetic and real-world benchmarks suggest that our method consistently outperforms BO baselines, achieving lower simple regret and demonstrating more robust exploration in high-dimensional or noisy settings.

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