The paper investigates Bayesian optimization using information geometry, deriving a local sensitivity tensor from the Fisher information metric that bounds the gradient of reparameterizable acquisition functions. This framework explains vanishing-gradient issues in high-dimensional settings and unifies heuristics like RAASP and dimension-scaled lengthscales. Leveraging this insight, the authors introduce FITR, a trust‑region BO method that replaces lengthscale scaling with local pullback‑Fisher weights, achieving competitive performance on GP benchmarks and extending naturally to non‑isotropic surrogates.
By Saksham Kiroriwal, Julius Pfrommer, J\"urgen Beyerer
arXiv:2606. 20469v1 Announce Type: new Abstract: A widely held intuition in deep learning is that stochastic gradient descent (SGD) implicitly favors flat minima and that flat minima generalize better, but standard Euclidean measures of flatness such as the trace or maximum eigenvalue of the loss Hessian are not invariant under reparametrizations that preserve the network function, which undermines the theoretical foundations of this narrative.
By Md Sakir Ahmed, Kumaresh Sarmah, Hemen Dutta
arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
By Vu Khac Ky
arXiv:2606. 07561v1 Announce Type: new Abstract: Gaussian processes with stationary kernels on bounded domains exhibit inflated posterior variance near the boundary.
By Maria B{\aa}nkestad, Sanna Jarl, Jens Sj\"olund
arXiv:2606. 08438v1 Announce Type: cross Abstract: Bayesian optimization (BO) is a widely used approach for black-box optimization that uses a Gaussian process (GP) as a surrogate and guides sequential evaluations via an acquisition function, with the ultimate goal of locating the global optimum $\mathbf{x}^{\star}$.
By Yilin Zheng, Haowei Wang, Szu Hui Ng, Enlu Zhou
arXiv:2607. 04977v1 Announce Type: new Abstract: Accurately estimating the unknown target label distribution is the critical first step for adapting to label shift.
By Alejandro Moreo, Pablo Gonz\'alez, Juan Jos\'e del Coz
arXiv:2605. 07565v2 Announce Type: replace-cross Abstract: We study Bayesian Optimisation (BO) in settings where the objective function is influenced by uncontrollable environmental contexts governed by an unknown probability distribution.
By Tigran Ramazyan, Denis Derkach
arXiv:2608. 02576v1 Announce Type: new Abstract: We consider optimization problems defined on product spaces of simplices.
By Shashwat Kumar, Arafat Rahman, Anuj Srivastava, P. -A. Absil
arXiv:2510. 21033v3 Announce Type: replace-cross Abstract: We develop a theory of iso-Riemannian optimization for problems constrained to learned data manifolds, a setting in which classical Riemannian optimization - and Riemannian gradient descent in particular - can be poorly suited.
By Willem Diepeveen, Melanie Weber
arXiv:2509. 21725v3 Announce Type: replace Abstract: A bilevel optimization problem consists of two optimization problems nested as an upper- and a lower-level problem, in which the optimality of the lower-level problem defines a constraint for the upper-level problem.
By Takuya Kanayama, Yuki Ito, Tomoyuki Tamura, Masayuki Karasuyama
arXiv:2609.09126v1 Announce Type: new
Abstract: Amari's contributions to information geometry and machine learning are well known. Here, we revisit Amari's work on Bayesian duality which has not rece...
By Mohammad Emtiyaz Khan, Thomas M\"ollenhoff
The paper introduces Finite-Library Input-Warped Bayesian Optimization (FLIWBO), a method that selects input warps from a finite library to adapt the geometry used by Gaussian‑process Bayesian optimization. FLIWBO maintains high‑probability convergence guarantees while improving sample efficiency on problems where raw coordinates poorly match the objective’s geometry, such as log‑scaled hyperparameters or localized peaks. Experiments on synthetic benchmarks, Fashion‑MNIST hyperparameter tuning, and a 20‑dimensional multi‑agent system design demonstrate that FLIWBO‑UCB outperforms raw‑coordinate GP‑UCB and other methods with regret guarantees, especially under misspecified geometry.
By Edvin Ketabati Augustinsson, Robert A. Bridges