Aligning beamlines at synchrotron light sources is a high-dimensional, expensive-to-sample optimization problem, as beams are focused using a series of dynamic optical components. Bayesian Optimization is an efficient machine learning approach to finding global optima of beam quality, but the model can easily be impaired by faulty data points caused by the beam going off the edge of the sensor or by background noise. This study, conducted at the National Synchrotron Light Source II (NSLS-II) facility at Brookhaven National Laboratory (BNL), is an investigation of methods to identify untrustworthy readings of beam quality and discourage the optimization model from seeking out points likely to yield low-fidelity beams. The approaches explored include dynamic pruning using loss analysis of size and position models and a lengthscale-based genetic algorithm to determine which points to include in the model for optimal fit. Each method successfully classified high and low fidelity points. This research advances BNL's mission to tackle our nation's energy challenges by providing scientists at all beamlines with access to higher quality beams, and faster convergence to these optima for their experiments.

Ensemble learning is a method that leverages weak learners to produce a strong learner. However, obtaining a large number of base learners requires substantial time and computational resources. Therefore, it is meaningful to study how to achieve the performance typically obtained with many base learners using only a few. We argue that to achieve this, it is essential to enhance both classification performance and generalization ability during the ensemble process. To increase model accuracy, each weak base learner needs to be more efficiently integrated. It is observed that different base learners exhibit varying levels of accuracy in predicting different classes. To capitalize on this, we introduce confidence tensors $\tilde{\mathbf{\Theta}}$ and $\tilde{\mathbf{\Theta}}_{rst}$ signifies the degree of confidence that the $t$-th base classifier assigns the sample to class $r$ while it actually belongs to class $s$. To the best of our knowledge, this is the first time an evaluation of the performance of base classifiers across different classes has been proposed. The proposed confidence tensor compensates for the strengths and weaknesses of each base classifier in different classes, enabling the method to achieve superior results with a smaller number of base learners. To enhance generalization performance, we design a smooth and convex objective function that leverages the concept of margin, making the strong learner more discriminative. Furthermore, it is proved that in gradient matrix of the loss function, the sum of each column's elements is zero, allowing us to solve a constrained optimization problem using gradient-based methods. We then compare our algorithm with random forests of ten times the size and other classical methods across numerous datasets, demonstrating the superiority of our approach.

We study the dynamics of two local optimization algorithms, online stochastic gradient descent (SGD) and gradient flow, within the framework of the multi-spiked tensor model in the high-dimensional regime. This multi-index model arises from the tensor principal component analysis (PCA) problem, which aims to infer $r$ unknown, orthogonal signal vectors within the $N$-dimensional unit sphere through maximum likelihood estimation from noisy observations of an order-$p$ tensor. We determine the number of samples and the conditions on the signal-to-noise ratios (SNRs) required to efficiently recover the unknown spikes from natural initializations. Specifically, we distinguish between three types of recovery: exact recovery of each spike, recovery of a permutation of all spikes, and recovery of the correct subspace spanned by the signal vectors. We show that with online SGD, it is possible to recover all spikes provided a number of sample scaling as $N^{p-2}$, aligning with the computational threshold identified in the rank-one tensor PCA problem [Ben Arous, Gheissari, Jagannath 2020, 2021]. For gradient flow, we show that the algorithmic threshold to efficiently recover the first spike is also of order $N^{p-2}$. However, recovering the subsequent directions requires the number of samples to scale as $N^{p-1}$. Our results are obtained through a detailed analysis of a low-dimensional system that describes the evolution of the correlations between the estimators and the spikes. In particular, the hidden vectors are recovered one by one according to a sequential elimination phenomenon: as one correlation exceeds a critical threshold, all correlations sharing a row or column index decrease and become negligible, allowing the subsequent correlation to grow and become macroscopic. The sequence in which correlations become macroscopic depends on their initial values and on the associated SNRs.

Recovering natural language prompts for image generation models, solely based on the generated images is a difficult discrete optimization problem. In this work, we present the first head-to-head comparison of recent discrete optimization techniques for the problem of prompt inversion. We evaluate Greedy Coordinate Gradients (GCG), PEZ , Random Search, AutoDAN and BLIP2's image captioner across various evaluation metrics related to the quality of inverted prompts and the quality of the images generated by the inverted prompts. We find that focusing on the CLIP similarity between the inverted prompts and the ground truth image acts as a poor proxy for the similarity between ground truth image and the image generated by the inverted prompts. While the discrete optimizers effectively minimize their objectives, simply using responses from a well-trained captioner often leads to generated images that more closely resemble those produced by the original prompts.

This paper examines the application of the Kernel Sum of Squares (KSOS) method for enhancing kernel learning from data, particularly in the context of dynamical systems. Traditional kernel-based methods, despite their theoretical soundness and numerical efficiency, frequently struggle with selecting optimal base kernels and parameter tuning, especially with gradient-based methods prone to local optima. KSOS mitigates these issues by leveraging a global optimization framework with kernel-based surrogate functions, thereby achieving more reliable and precise learning of dynamical systems. Through comprehensive numerical experiments on the Logistic Map, Henon Map, and Lorentz System, KSOS is shown to consistently outperform gradient descent in minimizing the relative-$\rho$ metric and improving kernel accuracy. These results highlight KSOS's effectiveness in predicting the behavior of chaotic dynamical systems, demonstrating its capability to adapt kernels to underlying dynamics and enhance the robustness and predictive power of kernel-based approaches, making it a valuable asset for time series analysis in various scientific fields.

This article describes a novel game structure for autonomously optimizing decentralized manufacturing systems with multi-objective optimization challenges, namely Distributed Stackelberg Strategies in State-Based Potential Games (DS2-SbPG). DS2-SbPG integrates potential games and Stackelberg games, which improves the cooperative trade-off capabilities of potential games and the multi-objective optimization handling by Stackelberg games. Notably, all training procedures remain conducted in a fully distributed manner. DS2-SbPG offers a promising solution to finding optimal trade-offs between objectives by eliminating the complexities of setting up combined objective optimization functions for individual players in self-learning domains, particularly in real-world industrial settings with diverse and numerous objectives between the sub-systems. We further prove that DS2-SbPG constitutes a dynamic potential game that results in corresponding converge guarantees. Experimental validation conducted on a laboratory-scale testbed highlights the efficacy of DS2-SbPG and its two variants, such as DS2-SbPG for single-leader-follower and Stack DS2-SbPG for multi-leader-follower. The results show significant reductions in power consumption and improvements in overall performance, which signals the potential of DS2-SbPG in real-world applications.

We present the Learned Ranking Function (LRF), a system that takes short-term user-item behavior predictions as input and outputs a slate of recommendations that directly optimizes for long-term user satisfaction. Most previous work is based on optimizing the hyperparameters of a heuristic function. We propose to model the problem directly as a slate optimization problem with the objective of maximizing long-term user satisfaction. We also develop a novel constraint optimization algorithm that stabilizes objective trade-offs for multi-objective optimization. We evaluate our approach with live experiments and describe its deployment on YouTube.

Pareto set learning (PSL) is an emerging approach for acquiring the complete Pareto set of a multi-objective optimization problem. Existing methods primarily rely on the mapping of preference vectors in the objective space to Pareto optimal solutions in the decision space. However, the sampling of preference vectors theoretically requires prior knowledge of the Pareto front shape to ensure high performance of the PSL methods. Designing a sampling strategy of preference vectors is difficult since the Pareto front shape cannot be known in advance. To make Pareto set learning work effectively in any Pareto front shape, we propose a Pareto front shape-agnostic Pareto Set Learning (GPSL) that does not require the prior information about the Pareto front. The fundamental concept behind GPSL is to treat the learning of the Pareto set as a distribution transformation problem. Specifically, GPSL can transform an arbitrary distribution into the Pareto set distribution. We demonstrate that training a neural network by maximizing hypervolume enables the process of distribution transformation. Our proposed method can handle any shape of the Pareto front and learn the Pareto set without requiring prior knowledge. Experimental results show the high performance of our proposed method on diverse test problems compared with recent Pareto set learning algorithms.

Determining the John ellipsoid - the largest volume ellipsoid contained within a convex polytope - is a fundamental problem with applications in machine learning, optimization, and data analytics. Recent work has developed fast algorithms for approximating the John ellipsoid using sketching and leverage score sampling techniques. However, these algorithms do not provide privacy guarantees for sensitive input data. In this paper, we present the first differentially private algorithm for fast John ellipsoid computation. Our method integrates noise perturbation with sketching and leverage score sampling to achieve both efficiency and privacy. We prove that (1) our algorithm provides $(\epsilon,\delta)$-differential privacy, and the privacy guarantee holds for neighboring datasets that are $\epsilon_0$-close, allowing flexibility in the privacy definition; (2) our algorithm still converges to a $(1+\xi)$-approximation of the optimal John ellipsoid in $O(\xi^{-2}(\log(n/\delta_0) + (L\epsilon_0)^{-2}))$ iterations where $n$ is the number of data point, $L$ is the Lipschitz constant, $\delta_0$ is the failure probability, and $\epsilon_0$ is the closeness of neighboring input datasets. Our theoretical analysis demonstrates the algorithm's convergence and privacy properties, providing a robust approach for balancing utility and privacy in John ellipsoid computation. This is the first differentially private algorithm for fast John ellipsoid computation, opening avenues for future research in privacy-preserving optimization techniques.

Multiview learning (MVL) seeks to leverage the benefits of diverse perspectives to complement each other, effectively extracting and utilizing the latent information within the dataset. Several twin support vector machine-based MVL (MvTSVM) models have been introduced and demonstrated outstanding performance in various learning tasks. However, MvTSVM-based models face significant challenges in the form of computational complexity due to four matrix inversions, the need to reformulate optimization problems in order to employ kernel-generated surfaces for handling non-linear cases, and the constraint of uniform noise assumption in the training data. Particularly in cases where the data possesses a heteroscedastic error structure, these challenges become even more pronounced. In view of the aforementioned challenges, we propose multiview twin parametric margin support vector machine (MvTPMSVM). MvTPMSVM constructs parametric margin hyperplanes corresponding to both classes, aiming to regulate and manage the impact of the heteroscedastic noise structure existing within the data. The proposed MvTPMSVM model avoids the explicit computation of matrix inversions in the dual formulation, leading to enhanced computational efficiency. We perform an extensive assessment of the MvTPMSVM model using benchmark datasets such as UCI, KEEL, synthetic, and Animals with Attributes (AwA). Our experimental results, coupled with rigorous statistical analyses, confirm the superior generalization capabilities of the proposed MvTPMSVM model compared to the baseline models. The source code of the proposed MvTPMSVM model is available at \url{https://github.com/mtanveer1/MvTPMSVM}.