Related papers: Projection-Free Non-Smooth Convex Programming
We design differentially private algorithms for the bandit convex optimization problem in the projection-free setting. This setting is important whenever the decision set has a complex geometry, and access to it is done efficiently only…
We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…
This paper presents an algorithm for approximately minimizing a convex function in simple, not necessarily bounded convex domains, assuming only that function values and subgradients are available. No global information about the objective…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
Nonconvex and nonsmooth optimization problems are important and challenging for statistics and machine learning. In this paper, we propose Projected Proximal Gradient Descent (PPGD) which solves a class of nonconvex and nonsmooth…
We propose a novel Stochastic Frank-Wolfe (a.k.a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization…
We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients. Focusing on non-asymptotic bounds on convergence rates, we show that if pairs of…
This paper concerns a convex, stochastic zeroth-order optimization (S-ZOO) problem. The objective is to minimize the expectation of a cost function whose gradient is not directly accessible. For this problem, traditional optimization…
Frank--Wolfe methods avoid projections, but over curved feasible regions the full-space linear minimization oracle (LMO) can itself become the computational bottleneck. We introduce random-subspace Frank--Wolfe (RSFW), the first…
This paper is concerned with multi-agent optimization problem. A distributed randomized gradient-free mirror descent (DRGFMD) method is developed by introducing a randomized gradient-free oracle in the mirror descent scheme where the…
In this paper, we propose the first computationally efficient projection-free algorithm for bandit convex optimization (BCO). We show that our algorithm achieves a sublinear regret of $O(nT^{4/5})$ (where $T$ is the horizon and $n$ is the…
We consider the classical setting of optimizing a nonsmooth Lipschitz continuous convex function over a convex constraint set, when having access to a (stochastic) first-order oracle (FO) for the function and a projection oracle (PO) for…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…
This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are…
We study constrained stochastic programs where the decision vector at each time slot cannot be chosen freely but is tied to the realization of an underlying random state vector. The goal is to minimize a general objective function subject…
In this paper, we propose and analyze algorithms for zeroth-order optimization of non-convex composite objectives, focusing on reducing the complexity dependence on dimensionality. This is achieved by exploiting the low dimensional…
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…
Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…