Related papers: Min-Max Grassmannian Optimization for Online Subsp…
This paper proposes a random subspace trust-region algorithm for general convex-constrained derivative-free optimization (DFO) problems. Similar to previous random subspace DFO methods, the convergence of our algorithm requires a certain…
Gradient descent with momentum has been widely applied in various signal processing and machine learning tasks, demonstrating a notable empirical advantage over standard gradient descent. However, momentum-based distributed Riemannian…
Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…
We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and…
Wasserstein distributionally robust optimization (WDRO) attempts to learn a model that minimizes the local worst-case risk in the vicinity of the empirical data distribution defined by Wasserstein ball. While WDRO has received attention as…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
In this paper, we consider the problem of unsupervised video object segmentation via background subtraction. Specifically, we pose the nonsemantic extraction of a video's moving objects as a nonconvex optimization problem via a sum of…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
We study optimal transport (OT) problem for probability measures supported on a tree metric space. It is known that such OT problem (i.e., tree-Wasserstein (TW)) admits a closed-form expression, but depends fundamentally on the underlying…
To ensure safety in confined environments such as mines or subway tunnels, a (wireless) sensor network can be deployed to monitor various environmental conditions. One of its most important applications is to track personnel, mobile…
We study distributionally robust online learning, where a risk-averse learner updates decisions sequentially to guard against worst-case distributions drawn from a Wasserstein ambiguity set centered at past observations. While this paradigm…
The Gromov-Wasserstein (GW) distance is an effective measure of alignment between distributions supported on distinct ambient spaces. Calculating essentially the mutual departure from isometry, it has found vast usage in domain translation…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this…
We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification. Our study focuses on robustness, a measure of how much deviation from the assumed linear…
This paper presents a novel distributed formulation of the min-max optimization problem. Such a formulation enables enhanced flexibility among agents when optimizing their maximization variables. To address the problem, we propose two…
This paper deals with a network of computing agents aiming to solve an online optimization problem in a distributed fashion, i.e., by means of local computation and communication, without any central coordinator. We propose the gradient…
Robust optimization is one of the fundamental approaches to deal with uncertainty in combinatorial optimization. This paper considers the robust spanning tree problem with interval data, which arises in a variety of telecommunication…
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this…
For linear systems, many data-driven control methods rely on the behavioral framework, using historical data of the system to predict the future trajectories. However, measurement noise introduces errors in predictions. When the noise is…