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Unbalanced Optimal Transport (UOT) has emerged as a robust relaxation of standard Optimal Transport, particularly effective for handling outliers and mass variations. However, scalable algorithms for UOT, specifically those based on…
Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route,…
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…
We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O(log…
With the growing focus on semantic searches and interpretations, an increasing number of standardized vocabularies and ontologies are being designed and used to describe data. We investigate the querying of objects described by a…
We study the classic NP-Hard problem of finding the maximum $k$-set coverage in the data stream model: given a set system of $m$ sets that are subsets of a universe $\{1,\ldots,n \}$, find the $k$ sets that cover the most number of distinct…
We develop and analyze stochastic approximation algorithms for solving nested compositional bi-level optimization problems. These problems involve a nested composition of $T$ potentially non-convex smooth functions in the upper-level, and a…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets. In this context, given two large point clouds of sizes $n$ and $m$ in $\mathbb{R}^d$, entropic OT (EOT)…
During training, supervised object detection tries to correctly match the predicted bounding boxes and associated classification scores to the ground truth. This is essential to determine which predictions are to be pushed towards which…
Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise…
Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…
In this note, we consider the complexity of optimizing a highly smooth (Lipschitz $k$-th order derivative) and strongly convex function, via calls to a $k$-th order oracle which returns the value and first $k$ derivatives of the function at…
The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of partial and noisy observations. This paper presents a…
The stochastic three points (STP) algorithm is a derivative-free optimization technique designed for unconstrained optimization problems in $\mathbb{R}^d$. In this paper, we analyze this algorithm for three classes of functions: smooth…
Unbalanced optimal transport (UOT) extends optimal transport (OT) to take into account mass variations to compare distributions. This is crucial to make OT successful in ML applications, making it robust to data normalization and outliers.…
With the widespread application of optimal transport (OT), its calculation becomes essential, and various algorithms have emerged. However, the existing methods either have low efficiency or cannot represent discontinuous maps. A novel…
This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…
This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair…
Decision Trees (DTs) are widely used in safety-critical domains such as medical diagnosis, valued for their interpretability and effectiveness on tabular data. However, training accurate oblique DTs is challenging due to complex…