相关论文: Optimizing over Multiple Distributions under Gener…
This paper explores the performance of a random Gaussian smoothing zeroth-order (ZO) scheme for minimising quasar-convex (QC) and strongly quasar-convex (SQC) functions in both unconstrained and constrained settings. For the unconstrained…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
This paper investigates a new class of non-convex optimization, which provides a unified framework for linear precoding in single/multi-user multiple-input multiple-output (MIMO) channels with arbitrary input distributions. The new…
Many optimization problems arising in high-dimensional statistics decompose naturally into a sum of several terms, where the individual terms are relatively simple but the composite objective function can only be optimized with iterative…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
Motivated by approximation Bayesian computation using mean-field variational approximation and the computation of equilibrium in multi-species systems with cross-interaction, this paper investigates the composite geodesically convex…
Quasar convexity is a condition that allows some first-order methods to efficiently minimize a function even when the optimization landscape is non-convex. Previous works develop near-optimal accelerated algorithms for minimizing this class…
We address the problem of distributed convex unconstrained optimization over networks characterized by asynchronous and possibly lossy communications. We analyze the case where the global cost function is the sum of locally coupled local…
This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…
We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been…
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…
We provide new insight into a {\em generalized conditional subgradient} algorithm and a {\em generalized mirror descent} algorithm for the convex minimization problem \[ \min_x \; \{f(Ax) + h(x)\}.\] As Bach showed in [{\em SIAM J. Optim.},…
Structured sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design. In this paper we investigate the…
In this thesis, I study the minimax oracle complexity of distributed stochastic optimization. First, I present the "graph oracle model", an extension of the classic oracle complexity framework that can be applied to study distributed…
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…
This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…
The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of…
Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to…
We develop and analyze the Generalized Multiplicative Gradient (GMG) method for solving a class of convex optimization problems over symmetric cones, where the objective function does not have Lipschitz gradient over the feasible region.…