Keisuke Morita

Keisuke Morita, Yoshihiko Nishikawa, Masayuki Ohzeki

Model-based sequential approaches to discrete "black-box" optimization, including Bayesian optimization techniques, often access the same points multiple times for a given objective function in interest, resulting in many steps to find the global optimum. Here, we numerically study the effect of a postprocessing method on Bayesian optimization that strictly prohibits duplicated samples in the dataset. We find the postprocessing method significantly reduces the number of sequential steps to find the global optimum, especially when the acquisition function is of maximum a posterior estimation. Our results provide a simple but general strategy to solve the slow convergence of Bayesian optimization for high-dimensional problems.

Keisuke Morita, Federico Ricci-Tersenghi, Masayuki Ohzeki

In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching the Bayes-optimal reconstruction limit. Nonconvex alternatives, such as the log-sum penalty, have been proposed to promote stronger sparsity. However, maintaining their algorithmic stability is challenging. To address this challenge, we introduce an adaptive smoothing strategy within an approximate message passing framework to mitigate algorithmic instability. Furthermore, we evaluate the typical exact-recovery threshold for Gaussian measurement matrices using the replica method and state evolution. The results indicate that the adaptive method achieves exact recovery over a broader region than $\ell_1$ norm minimization, although metastable states hinder reaching the information-theoretic limit.

Keisuke Morita, Masayuki Ohzeki

We study sparse signal recovery from noisy linear observations using nonconvex log-sum regularization. The log-sum penalty reduces the shrinkage bias of $\ell_1$ regularization and more closely approximates the $\ell_0$ regularization, but its nonconvexity can make reconstruction algorithms unstable. To mitigate this instability, we use an adaptive smoothing strategy that determines the smoothing parameter so that the scalar proximal operator remains continuous. Using this proximal operator, we formulate the approximate message passing (AMP) algorithm and derive the corresponding state evolution (SE) recursion. The fixed point of the SE recursion predicts the final mean squared error (MSE) and, in the noiseless limit, the exact-recovery phase transition. To further investigate finite-dimensional reconstruction behavior, we implement an alternating direction method of multipliers (ADMM) algorithm. In the noiseless setting, we find that the empirical success boundary of ADMM closely agrees with the SE-predicted phase transition. In the noisy setting, we observe that AMP closely follows the SE prediction, whereas ADMM qualitatively reproduces the SE-predicted dependence of the final MSE on the regularization parameter. A comparison with $\ell_1$ regularization shows that log-sum regularization is beneficial in low-density or high-measurement-rate regimes, whereas $\ell_1$ regularization remains preferable at higher densities and lower measurement rates.

Makoto Otsuka, Kento Kodama, Keisuke Morita et al.

This study proposes an approach for removing mislabeled instances from contaminated training datasets by combining surrogate model-based black-box optimization (BBO) with postprocessing and quantum annealing. Mislabeled training instances, a common issue in real-world datasets, often degrade model generalization, necessitating robust and efficient noise-removal strategies. The proposed method evaluates filtered training subsets based on validation loss, iteratively refines loss estimates through surrogate model-based BBO with postprocessing, and leverages quantum annealing to efficiently sample diverse training subsets with low validation error. Experiments on a noisy majority bit task demonstrate the method's ability to prioritize the removal of high-risk mislabeled instances. Integrating D-Wave's clique sampler running on a physical quantum annealer achieves faster optimization and higher-quality training subsets compared to OpenJij's simulated quantum annealing sampler or Neal's simulated annealing sampler, offering a scalable framework for enhancing dataset quality. This work highlights the effectiveness of the proposed method for supervised learning tasks, with future directions including its application to unsupervised learning, real-world datasets, and large-scale implementations.