Acquisition Function-Guided Generation for Bayesian Optimization over Discrete Spaces

Tommaso Ancilli, Thomas Wedenig, Henry Moss, Robert Peharz

Bayesian optimization (BO) over discrete spaces is challenging due to missing gradients and the sparsity of valid solutions. Latent-space BO sidesteps both issues by fitting a surrogate in the latent space of a generative model, which however substantially complicates the direct incorporation of domain knowledge that is naturally expressed in the original discrete space. In this work, we instead combine a pretrained generative model with a surrogate defined directly in data space, where inductive biases such as domain-specific kernels can be readily incorporated. Rather than maximizing the acquisition function over the discrete design space, our method samples candidates from the generative model under a distribution tilted by the acquisition function. To recover useful gradients for sampling, we embed this tilted distribution into a diffusion bridge that yields a smooth, posterior-averaged acquisition function. This leads to \emph{acquisition function guided generation} (AFGG), which we instantiate with a categorical diffusion model and an autoregressive normalizing flow. Across a broad suite of molecular benchmarks, the diffusion model variant performs on par with leading BO…