Bayesian Optimization with Fisher Information Geometry: Gradient Bounds and Trust-Region Methods
We study Bayesian optimization (BO) through the lens of information geometry. Pulling back the Fisher information metric through the surrogate posterior map yields a local sensitivity tensor on the input space, which leads to an upper bound on the gradient of reparameterizable acquisition functions. This view explains vanishing-gradient behavior in high-dimensional BO and provides a common interpretation of heuristics such as RAASP and dimension-scaled lengthscales. Building on this analysis, we propose FITR, a trust-region-based BO method that replaces lengthscale-based scaling by local pullback-Fisher weights. FITR is not restricted to GP kernels with explicit lengthscales. On GP benchm...
| Authors | Saksham Kiroriwal, Julius Pfrommer, Jürgen Beyerer |
|---|---|
| Primary category | cs.LG |
| Published | 25 September 2026 |
| Last updated at source | 25 September 2026 |
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