Technology

We study the non-stationary kernelized bandit problem, in which the reward function changes over time. In this study, we derive the first algorithm-independent regret lower bounds for squared exponential and Matérn kernels, and design an algorithm with near-optimal performance. To address the high computational cost of existing methods, we propose a new algorithm, R-PERP (Restarting Phased Elimination with Random Permutation). By using a simple random permutation of candidate points, this method derives a new confidence bound suited to non-stationary problems and achieves both computational efficiency and theoretical optimality.

This study investigates the milling process of AISI 4340 steel with the aim of improving tool life and surface quality. Using a cutting fluid containing TiO₂ nanoparticles, the study optimised spindle speed, depth of cut, and feed rate. By combining Response Surface Methodology (RSM) and Bayesian optimisation, it derived machining conditions that jointly improve tool wear, surface roughness, and spindle load. Experimental results confirmed extended tool life, improved machining quality, and reduced energy consumption. miHub® was used in this study.

Genetic algorithms are widely used optimisation methods, but they can suffer from premature convergence to local optima. In this study, we propose an adaptive multi-restart method that maintains diversity in the search space and continues exploration when necessary. The method statistically analyses the best solutions obtained from multiple parallel searches and determines whether to continue exploration or converge. Experiments confirmed substantial improvements over conventional genetic algorithms in the ability to escape local optima, as well as in accuracy and robustness.

This study improves regret analysis for Gaussian process bandit problems in the setting where the reward function belongs to a reproducing kernel Hilbert space (RKHS). We establish a new upper bound on the maximum posterior variance and, based on this result, improve the MVR (Maximum Variance Reduction) and PE (Phased Elimination) algorithms. As a result, we obtain a near-optimal regret bound in the noiseless setting and an optimal regret bound with respect to the RKHS norm. We further analyse a setting with time-varying noise variance and show that the resulting performance matches the theoretical lower bound.