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This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
In the General Position Subset Selection (GPSS) problem, the goal is to find the largest possible subset of a set of points such that no three of its members are collinear. If $s_{\mathrm{GPSS}}$ is the size of the optimal solution,…
When predicting observations across space and time, the spatial layout of errors impacts a model's real-world utility. For instance, in bike sharing demand prediction, error patterns translate to relocation costs. However, commonly used…
The study of optimal decision trees has gained increasing attention in recent years; however, despite substantial progress, it still suffers from two major challenges: First, trees constructed by existing optimal decision tree (ODT)…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
Under interpolation-type assumptions such as the strong growth condition, stochastic optimization methods can attain convergence rates comparable to full-batch methods, but their performance, particularly for SGD, remains highly sensitive…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
We study a spatiotemporal service matching problem in which demand, heterogeneous in location and time sensitivity/preference, is to be assigned to service stations. The planner seeks to maximize social welfare, defined as total service…
We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…
We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic…
The random grid search (RGS) is a simple, but efficient, stochastic algorithm to find optimal cuts that was developed in the context of the search for the top quark at Fermilab in the mid-1990s. The algorithm, and associated code, have been…
This paper investigates the problem of optimal predictor design for distributed parameter systems using neural networks and shape optimization. Sensors with various shapes are placed on the domain of the distributed parameter system. Data…
We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…
Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…
This research considers the ranking and selection (R&S) problem of selecting the optimal subset from a finite set of alternative designs. Given the total simulation budget constraint, we aim to maximize the probability of correctly…
Fine-tuning large language models (LLMs) for specialized domains often necessitates a trade-off between acquiring domain expertise and retaining general reasoning capabilities, a phenomenon known as catastrophic forgetting. Existing…
Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…
Large tensor learning algorithms are typically computationally expensive and require storing a vast amount of data. In this paper, we propose a unified online Riemannian gradient descent (oRGrad) algorithm for tensor learning, which is…
Accurate spatial-temporal prediction of network-based travelers' requests is crucial for the effective policy design of ridesharing platforms. Having knowledge of the total demand between various locations in the upcoming time slots enables…