Isotropic Gaussian Processes Improve Vanilla Bayesian Optimization in High Dimensions
High-dimensional Bayesian optimization (BO) often fits Gaussian process (GP) surrogates from far fewer observations than input dimensions. Modern Vanilla BO can perform well in this regime with dimension-aware priors, initialization, and acquisition optimization, but it typically retains automatic relevance determination (ARD), fitting one lengthscale per input coordinate. We study this modeling choice and propose Iso-BO, a controlled modification that replaces the ARD GP with an isotropic GP using one shared lengthscale while keeping the surrounding BO pipeline matched. For radial kernels, we show that the marginal log likelihood (MLL) depends on the inverse-squared ARD lengthscales only...
| Authors | Wei-Ting Tang, Madhav Muthyala, Joel A. Paulson |
|---|---|
| Primary category | stat.ML |
| Published | 5 October 2026 |
| Last updated at source | 5 October 2026 |
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