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We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are…
Finite-sum Coupled Compositional Optimization (FCCO), characterized by its coupled compositional objective structure, emerges as an important optimization paradigm for addressing a wide range of machine learning problems. In this paper, we…
In this article, we consider the problem of unconstrained time-varying convex optimization, where the cost function changes with time. We provide an in-depth technical analysis of the problem and argue why freezing the cost at each time…
Classical analysis of convex and non-convex optimization methods often requires the Lipshitzness of the gradient, which limits the analysis to functions bounded by quadratics. Recent work relaxed this requirement to a non-uniform smoothness…
This paper is devoted to the study (common in many applications) of the black-box optimization problem, where the black-box represents a gradient-free oracle $\tilde{f} = f(x) + \xi$ providing the objective function value with some…
Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular…
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…
In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient…
We revisit the standard ``telescoping sum'' argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of…
This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…
Rank-based zeroth-order (ZO) optimization -- which relies only on the ordering of function evaluations -- offers strong robustness to noise and monotone transformations, and underlies many successful algorithms such as CMA-ES, natural…
In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a DC (Difference of Convex functions) function, where the differentiable function is not restricted to the global Lipschitz gradient…
In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
In this paper, we consider non-smooth convex optimization with a zeroth-order oracle corrupted by symmetric stochastic noise. Unlike the existing high-probability results requiring the noise to have bounded $\kappa$-th moment with $\kappa…
This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank-Wolfe algorithm and its variants already avoid…
In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately…
We characterize the query complexity of finding stationary points of one-dimensional non-convex but smooth functions. We consider four settings, based on whether the algorithms under consideration are deterministic or randomized, and…