Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. Recent works suggest that these estimators are more statistically efficient than plug-in (linear programming-based) OT estimators when comparing probability measures in high-dimensions~\citep{Vacher-2021-Dimension}. Unfortunately, that statistical benefit comes at a very steep computational price: because their computation relies on the short-step interior-point method (SSIPM), which comes with a large iteration count in practice, these estimators quickly become intractable w.r.t. sample size $n$. To scale these estimators to larger $n$, we propose a nonsmooth fixed-point model for the kernel-based OT problem, and show that it can be efficiently solved via a specialized semismooth Newton (SSN) method: We show, exploring the problem's structure, that the per-iteration cost of performing one SSN step can be significantly reduced in practice. We prove that our SSN method achieves a global convergence rate of $O(1/\sqrt{k})$, and a local quadratic convergence rate under standard regularity conditions. We show substantial speedups over SSIPM on both synthetic and real datasets.

We introduce new algorithms rooted in scattered data approximation that rely on a random exploration step to ensure that the fill-distance of query points decays at a near-optimal rate. Our algorithms retain the ease of implementation of the classical GP-UCB algorithm and satisfy cumulative regret bounds that nearly match those conjectured in [Vak22], hence solving a COLT open problem. Furthermore, the new algorithms outperform GP-UCB and other popular Bayesian optimization strategies in several examples.

We propose a novel algorithm for online resource allocation with non-stationary customer arrivals and unknown click-through rates. We assume multiple types of customers arrive in a nonstationary stochastic fashion, with unknown arrival rates in each period, and that customers' click-through rates are unknown and can only be learned online. By leveraging results from the stochastic contextual bandit with knapsack and online matching with adversarial arrivals, we develop an online scheme to allocate the resources to nonstationary customers. We prove that under mild conditions, our scheme achieves a ``best-of-both-world'' result: the scheme has a sublinear regret when the customer arrivals are near-stationary, and enjoys an optimal competitive ratio under general (non-stationary) customer arrival distributions. Finally, we conduct extensive numerical experiments to show our approach generates near-optimal revenues for all different customer scenarios.

This paper uses topological data analysis (TDA) tools and introduces a data-driven clustering-based stock selection strategy tailored for sparse portfolio construction. Our asset selection strategy exploits the topological features of stock price movements to select a subset of topologically similar (different) assets for a sparse index tracking (Markowitz) portfolio. We introduce new distance measures, which serve as an input to the clustering algorithm, on the space of persistence diagrams and landscapes that consider the time component of a time series. We conduct an empirical analysis on the S\&P index from 2009 to 2020, including a study on the COVID-19 data to validate the robustness of our methodology. Our strategy to integrate TDA with the clustering algorithm significantly enhanced the performance of sparse portfolios across various performance measures in diverse market scenarios.

The transformation model is an essential component of any deformable image registration approach. It provides a representation of physical deformations between images, thereby defining the range and realism of registrations that can be found. Two types of transformation models have emerged as popular choices: B-spline models and mesh models. Although both models have been investigated in detail, a direct comparison has not yet been made, since the models are optimized using very different optimization methods in practice. B-spline models are predominantly optimized using gradient-descent methods, while mesh models are typically optimized using finite-element method solvers or evolutionary algorithms. Multi-objective optimization methods, which aim to find a diverse set of high-quality trade-off registrations, are increasingly acknowledged to be important in deformable image registration. Since these methods search for a diverse set of registrations, they can provide a more complete picture of the capabilities of different transformation models, making them suitable for a comparison of models. In this work, we conduct the first direct comparison between B-spline and mesh transformation models, by optimizing both models with the same state-of-the-art multi-objective optimization method, the Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA). The combination with B-spline transformation models, moreover, is novel. We experimentally compare both models on two different registration problems that are both based on pelvic CT scans of cervical cancer patients, featuring large deformations. Our results, on three cervical cancer patients, indicate that the choice of transformation model can have a profound impact on the diversity and quality of achieved registration outcomes.

Congestion pricing, while adopted by many cities to alleviate traffic congestion, raises concerns about widening socioeconomic disparities due to its disproportionate impact on low-income travelers. In this study, we address this concern by proposing a new class of congestion pricing schemes that not only minimize congestion levels but also incorporate an equity objective to reduce cost disparities among travelers with different willingness-to-pay. Our analysis builds on a congestion game model with heterogeneous traveler populations. We present four pricing schemes that account for practical considerations, such as the ability to charge differentiated tolls to various traveler populations and the option to toll all or only a subset of edges in the network. We evaluate our pricing schemes in the calibrated freeway network of the San Francisco Bay Area. We demonstrate that the proposed congestion pricing schemes improve both efficiency (in terms of reduced average travel time) and equity (the disparities of travel costs experienced by different populations) compared to the current pricing scheme. Moreover, our pricing schemes also generate a total revenue comparable to the current pricing scheme. Our results further show that pricing schemes charging differentiated prices to traveler populations with varying willingness-to-pay lead to a more equitable distribution of travel costs compared to those that charge a homogeneous price to all.

Robotic arms are highly common in various automation processes such as manufacturing lines. However, these highly capable robots are usually degraded to simple repetitive tasks such as pick-and-place. On the other hand, designing an optimal robot for one specific task consumes large resources of engineering time and costs. In this paper, we propose a novel concept for optimizing the fitness of a robotic arm to perform a specific task based on human demonstration. Fitness of a robot arm is a measure of its ability to follow recorded human arm and hand paths. The optimization is conducted using a modified variant of the Particle Swarm Optimization for the robot design problem. In the proposed approach, we generate an optimal robot design along with the required path to complete the task. The approach could reduce the time-to-market of robotic arms and enable the standardization of modular robotic parts. Novice users could easily apply a minimal robot arm to various tasks. Two test cases of common manufacturing tasks are presented yielding optimal designs and reduced computational effort by up to 92%.

Optimization of expensive, noisy, black-box functions commonly occurs in designing sustainable process systems; we review some motivating applications in Section 2 below. In principle, one can apply any type of derivativefree optimization (DFO) method [2] to tackle such problems; however, these methods may require a large number of evaluations to converge. When evaluations of f are expensive, we desire an intelligent sample selection strategy that accounts for all available information to select future samples. The BO framework provides a systematic and versatile way to identify highly informative design candidates using minimal function evaluations. This article reviews recent advances in BO methods and highlights their relevance to design of next-generation sustainable energy and process systems. We also offer some perspectives on future research directions and associated challenges.

Large language models are becoming increasingly practical for translating code across programming languages, a process known as $transpiling$. Even though automated transpilation significantly boosts developer productivity, a key concern is whether the generated code is correct. Existing work initially used manually crafted test suites to test the translations of a small corpus of programs; these test suites were later automated. In contrast, we devise the first approach for automated, functional, property-based testing of code translation models. Our general, user-provided specifications about the transpiled code capture a range of properties, from purely syntactic to purely semantic ones. As shown by our experiments, this approach is very effective in detecting property violations in popular code translation models, and therefore, in evaluating model quality with respect to given properties. We also go a step further and explore the usage scenario where a user simply aims to obtain a correct translation of some code with respect to certain properties without necessarily being concerned about the overall quality of the model. To this purpose, we develop the first property-guided search procedure for code translation models, where a model is repeatedly queried with slightly different parameters to produce alternative and potentially more correct translations. Our results show that this search procedure helps to obtain significantly better code translations.

We consider the optimization of complex performance metrics in multi-label classification under the population utility framework. We mainly focus on metrics linearly decomposable into a sum of binary classification utilities applied separately to each label with an additional requirement of exactly $k$ labels predicted for each instance. These "macro-at-$k$" metrics possess desired properties for extreme classification problems with long tail labels. Unfortunately, the at-$k$ constraint couples the otherwise independent binary classification tasks, leading to a much more challenging optimization problem than standard macro-averages. We provide a statistical framework to study this problem, prove the existence and the form of the optimal classifier, and propose a statistically consistent and practical learning algorithm based on the Frank-Wolfe method. Interestingly, our main results concern even more general metrics being non-linear functions of label-wise confusion matrices. Empirical results provide evidence for the competitive performance of the proposed approach.