Large-scale problems in data science are often modeled with optimization, and the optimization model is usually solved with first-order methods that may converge at a sublinear rate. Therefore, it is of interest to terminate the optimization algorithm as soon as the underlying data science task is accomplished. We consider FISTA for solving two binary classification … Read more
In large-scale AI training, Sparse Mixture-of-Experts (s-MoE) layers enable scaling by activating only a small subset of experts per token. An operational challenge in this design is load balancing: routing tokens to minimize the number of idle experts, which is important for the efficient utilization of (costly) GPUs. We provide a theoretical framework for analyzing … Read more
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution, and collaborative filtering. The subgradient method achieves local linear convergence when the composite loss is well-conditioned. However, if the smooth map is, in a … Read more
This survey proposes a unifying conceptual framework and taxonomy that systematically integrates Machine Learning (ML) and Reinforcement Learning (RL) with classical paradigms for Constraint Satisfaction and Boolean Satisfiability solving. Unlike prior reviews that focus on individual applications, we organize the literature around solver architecture, linking each major phase—constraint propagation, heuristic decision-making, conflict analysis, and meta-level … Read more
Combinatorial decision problems lie at the intersection of Operations Research (OR) and Artificial Intelligence (AI), encompassing structured optimization tasks such as submodular selection, dynamic programming, planning, and scheduling. These problems exhibit exponential growth in decision complexity, driven by interdependent choices coupled through logical, temporal, and resource constraints. Classical optimization frameworks—including integer programming, submodular optimization, and … Read more
The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite support — a regime that frequently arises in machine learning and operations research. The discrete Wasserstein barycenter problem is known to … Read more
This study explores the integration of market structure learning into pricing strategies to maximize revenue in e-commerce and retail environments. We consider the problem of determining the revenue maximizing price of a single product in a market of heterogeneous consumers segmented by their product valuations; and analyze the pricing strategies for varying levels of prior … Read more
Selecting an effective step-size is a fundamental challenge in first-order optimization, especially for problems with non-Euclidean geometries. This paper presents a novel adaptive step-size strategy for optimization algorithms that rely on linear minimization oracles, as used in the Conditional Gradient or non-Euclidean Normalized Steepest Descent algorithms. Using a simple heuristic to estimate a local Lipschitz … Read more
Abstract: Crowdshipping has gained attention as an emerging delivery model thanks to advantages such as flexibility and an asset-light structure. Yet, it chronically suffers from a lackof mechanisms to create and exploit consolidation opportunities, limiting its efficiency and scalability. This work contributes to the literature in two ways: first, by introducing a novel consolidation concept … Read more