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We consider an unconstrained problem of minimizing a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is…

We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed…

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the…

This paper studies efficient distributed optimization methods for multi-agent networks. Specifically, we consider a convex optimization problem with a globally coupled linear equality constraint and local polyhedra constraints, and develop…

This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…

We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…

During the past two decades, multi-agent optimization problems have drawn increased attention from the research community. When multiple objective functions are present among agents, many works optimize the sum of these objective functions.…

This paper studies a compressed momentum-based single-point zeroth-order algorithm for stochastic distributed nonconvex optimization, aiming to alleviate communication overhead and address the unavailability of explicit gradient…

This paper proposes a multi-scale method to design a continuous-time distributed algorithm for constrained convex optimization problems by using multi-agents with Markov switched network dynamics and noisy inter-agent communications. Unlike…

In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…

This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…

We consider the optimization problem of the form $\min_{x \in \mathbb{R}^d} f(x) \triangleq \mathbb{E}_{\xi} [F(x; \xi)]$, where the component $F(x;\xi)$ is $L$-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The recently…

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

Proximal gradient method has been playing an important role to solve many machine learning tasks, especially for the nonsmooth problems. However, in some machine learning problems such as the bandit model and the black-box learning problem,…

This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…

We consider a network of agents, each with its own private cost consisting of the sum of two possibly nonsmooth convex functions, one of which is composed with a linear operator. At every iteration each agent performs local calculations and…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

We consider minimizing the sum of three convex functions, where the first one F is smooth, the second one is nonsmooth and proximable and the third one is the composition of a nonsmooth proximable function with a linear operator L. This…

We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the…

In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed…