Quoc-Anh Hoang Nguyen | Search arXiv

arXiv2026

In-Context Batch Black-box Optimization via Flow Matching

Batch black-box optimization is important for expensive systems where many candidates can be evaluated in parallel, yet only a few rounds of evaluation are affordable. In this regime, effective batch construction must identify multiple promising regions while avoiding redundant evaluations, and conventional Bayesian optimization can require increasingly difficult batch-selection procedures as the batch size grows. We introduce Flow Matching for Thompson-Sampling Refinement (FMTR), an amortized approach that learns offline a continuous, history-conditioned proposal distribution from which variable-size batches can be sampled. FMTR is trained offline by conditional flow matching on Thompson-sampling argmaxes refined toward high-value regions via a horizon-dependent Langevin pushforward map, adapting the exploration-exploitation tradeoff over the optimization horizon. At test time, the model parameters remain fixed and batch generation requires neither task-specific surrogate refitting nor numerical acquisition optimization. FMTR achieves strong performance against batch BO and in-context baselines on synthetic and real-world benchmarks, while substantially reducing the computational cost of batch selection.

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arXiv2024

High-Dimensional Bayesian Optimization via Random Projection of Manifold Subspaces

Bayesian Optimization (BO) is a popular approach to optimizing expensive-to-evaluate black-box functions. Despite the success of BO, its performance may decrease exponentially as the dimensionality increases. A common framework to tackle this problem is to assume that the objective function depends on a limited set of features that lie on a low-dimensional manifold embedded in the high-dimensional ambient space. The latent space can be linear or more generally nonlinear. To learn feature mapping, existing works usually use an encode-decoder framework which is either computationally expensive or susceptible to overfittting when the labeled data is limited. This paper proposes a new approach for BO in high dimensions by exploiting a new representation of the objective function. Our approach combines a random linear projection to reduce the dimensionality, with a representation learning of the nonlinear manifold. When the geometry of the latent manifold is available, a solution to exploit this geometry is proposed for representation learning. In contrast, we use a neural network. To mitigate overfitting by using the neural network, we train the feature mapping in a geometry-aware semi-supervised manner. Our approach enables efficient optimizing of BO's acquisition function in the low-dimensional space, with the advantage of projecting back to the original high-dimensional space compared to existing works in the same setting. Finally, we show empirically that our algorithm outperforms other high-dimensional BO baselines in various synthetic functions and real applications.

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