We Still Don't Understand High-Dimensional Bayesian Optimization

A new framework called min-max Functional Bayesian Optimization (MM-FBO) has been proposed to optimize functional responses under min-max criteria, addressing limitations of traditional Bayesian optimization methods that focus on scalar responses. This approach minimizes the maximum error across the functional domain, utilizing functional principal component analysis and Gaussian process surrogates for improved performance.

A new method for the direct transfer of optimized controllers to similar systems using dimensionless model predictive control (MPC) has been proposed, allowing for automatic tuning of closed-loop performance. This approach enhances the applicability of scaled model experiments in engineering by facilitating the transfer of controller behavior from scaled models to full-scale systems without the need for extensive retuning.

The methodology known as gp2Scale has been introduced, enabling the scaling of exact Gaussian processes to over 10 million data points without relying on traditional approximations. This advancement addresses the persistent trade-off between computational speed and accuracy in Gaussian process methodologies, which have been limited by various approximations in the past.

A recent study has provided a unified characterization of the scaling of parameter norms in overparameterized linear regression and diagonal linear networks under $l_p$ bias. This work addresses the unresolved question of how the family of $l_r$ norms behaves with varying sample sizes, revealing a competition between signal spikes and null coordinates in the data.

The Agent Capability Problem (ACP) framework has been introduced to predict whether autonomous agents can solve tasks under resource constraints by framing problem-solving as information acquisition. The framework calculates an effective cost based on the total bits needed to identify a solution and the bits gained per action, providing both lower and upper bounds for expected costs. Experimental validation shows that ACP closely aligns with actual agent performance, enhancing efficiency over traditional strategies.

The introduction of K-DAREK, a novel learning algorithm for Kurkova Kolmogorov Networks (KKANs), enhances function approximation and uncertainty quantification in neural networks. This advancement builds on the existing framework of Kolmogorov-Arnold networks, which utilize spline layers for efficient modeling of complex functions. K-DAREK aims to improve the stability and robustness of these architectures by incorporating distance-aware error metrics.