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Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
Motivated by machine learning applications in networks of sensors, internet-of-things (IoT) devices, and autonomous agents, we propose techniques for distributed stochastic convex learning from high-rate data streams. The setup involves a…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
In this paper, we consider a distributed constrained optimization problem with delayed subgradient information over the time-varying communication network, where each agent can only communicate with its neighbors and the communication…
This article studies and solves the problem of optimal portfolio allocation with CV@R penalty when dealing with imperfectly simulated financial assets. We use a Stochastic biased Mirror Descent to find optimal resource allocation for a…
The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for…
This paper seeks to address how to solve non-smooth convex and strongly convex optimization problems with functional constraints. The introduced Mirror Descent (MD) method with adaptive stepsizes is shown to have a better convergence rate…
Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
This paper introduces a general framework for iterative optimization algorithms and establishes under general assumptions that their convergence is asymptotically geometric. We also prove that under appropriate assumptions, the rate of…
This paper presents an optimization-based receding horizon trajectory planning algorithm for dynamical systems operating in unstructured and cluttered environments. The proposed approach is a two-step procedure that uses a motion planning…
We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL)…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
This paper considers distributed optimization problems, where each agent cooperatively minimizes the sum of local objective functions through the communication with its neighbors. The widely adopted distributed gradient method in solving…
The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
Wasserstein gradient flows are continuous time dynamics that define curves of steepest descent to minimize an objective function over the space of probability measures (i.e., the Wasserstein space). This objective is typically a divergence…