8 papers
Scalable Dynamic Optimal Transport via Distributed Linearized ADMM
Hari Dahal, Rongjie Lai, Yangyang Xu
In this paper, we address two fundamental challenges in the numerical solution of dynamic opti- mal transport (OT) problems. The first challenge arises when the initial and/or term…
LoDAdaC: a unified local training-based decentralized framework with adaptive gradients and compressed communication
Wei Liu, Anweshit Panda, Ujwal Pandey +5
In the decentralized distributed learning, achieving fast convergence and low communication cost is essential for scalability and high efficiency. Adaptive gradient methods, such a…
Compressed Decentralized Momentum Stochastic Gradient Methods for Nonconvex Optimization
Wei Liu, Anweshit Panda, Ujwal Pandey +6
In this paper, we design two compressed decentralized algorithms for solving nonconvex stochastic optimization under two different scenarios. Both algorithms adopt a momentum techn…
A Near-optimal Method for Linearly Constrained Composite Non-convex Non-smooth Problems
Wei Liu, Qihang Lin, Yangyang Xu
We study first-order methods (FOMs) for solving \emph{composite nonconvex nonsmooth} optimization with linear constraints. Recently, the lower complexity bounds of FOMs on finding…
Inexact Moreau Envelope Lagrangian Method for Non-Convex Constrained Optimization under Local Error Bound Conditions on Constraint Functions
Yankun Huang, Qihang Lin, Yangyang Xu
In this paper, we investigate how structural properties of the constraint system impact the oracle complexity of smooth non-convex optimization problems with convex inequality cons…
Lower Complexity Bounds of First-order Methods for Affinely Constrained Composite Non-convex Problems
Wei Liu, Qihang Lin, Yangyang Xu
Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-ca…
A stochastic smoothing framework for nonconvex-nonconcave minEmax problems with applications to Wasserstein distributionally robust optimization
Wei Liu, Muhammad Khan, Gabriel Mancino-Ball +1
We study a class of stochastic nonsmooth optimization problems in which an outer variable minimizes the expectation of a pointwise maximum. This minimization--expectation--maximiza…
A single-loop SPIDER-type stochastic subgradient method for expectation-constrained nonconvex nonsmooth optimization
Wei Liu, Yangyang Xu
Many real-world problems, such as those with fairness constraints, involve complex expectation constraints and large datasets, necessitating the design of efficient stochastic meth…