Related papers: Fairness with Continuous Optimal Transport
Optimal Transport (OT) distances such as Wasserstein have been used in several areas such as GANs and domain adaptation. OT, however, is very sensitive to outliers (samples with large noise) in the data since in its objective function,…
We study dynamical optimal transport of discrete time systems (dDOT) with Lagrangian cost. The problem is approached by combining optimal control and Kantorovich duality theory. Based on the derived solution, a first order splitting…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
Stochastic distributed optimization methods that solve an optimization problem over a multi-agent network have played an important role in a variety of large-scale signal processing and machine leaning applications. Among the existing…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
This paper addresses two fundamental challenges in distributed online convex optimization: communication efficiency and optimization under limited feedback. We propose a unified framework named Online Compressed Gradient Tracking (OCGT),…
The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…
In recent years, two prominent paradigms have shaped distributionally robust optimization (DRO), modeling distributional ambiguity through $\phi$-divergences and Wasserstein distances, respectively. While the former focuses on ambiguity in…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…
Zero-order (ZO) optimization is a powerful tool for dealing with realistic constraints. On the other hand, the gradient-tracking (GT) technique proved to be an efficient method for distributed optimization aiming to achieve consensus.…
Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbol{\mu}, \boldsymbol{\nu})$ are coupled to covariates, a challenging conditional distribution learning setting arises.…
We propose Mirror Descent Optimal Transport (MDOT), a novel method for solving discrete optimal transport (OT) problems with high precision, by unifying temperature annealing in entropic-regularized OT (EOT) with mirror descent techniques.…
Human lives are increasingly being affected by the outcomes of automated decision-making systems and it is essential for the latter to be, not only accurate, but also fair. The literature of algorithmic fairness has grown considerably over…
We consider the problem of learning a counterfactually fair regressor. We adopt a causal uncertainty view in which counterfactual fairness is defined with resampled noise. We focus on obtaining theoretical fairness guarantees for a new…
We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…
Missing data is a crucial issue when applying machine learning algorithms to real-world datasets. Starting from the simple assumption that two batches extracted randomly from the same dataset should share the same distribution, we leverage…
The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…
With the advent of large datasets, offline reinforcement learning (RL) is a promising framework for learning good decision-making policies without the need to interact with the real environment. However, offline RL requires the dataset to…