Related papers: Parameter-free Stochastic Optimization of Variatio…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
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…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
This paper proposes the first-ever algorithmic framework for tuning hyper-parameters of stochastic optimization algorithm based on reinforcement learning. Hyper-parameters impose significant influences on the performance of stochastic…
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
In multistage decision problems, it is often the case that an initial strategic decision (such as investment) is followed by many operational ones (operating the investment). Such initial strategic decision can be seen as a parameter…
A parametrized convex function depends on a variable and a parameter, and is convex in the variable for any valid value of the parameter. Such functions can be used to specify parametrized convex optimization problems, i.e., a convex…
Stochastic optimization is an important task in many optimization problems where the tasks are not expressible as convex optimization problems. In the case of non-convex optimization problems, various different stochastic algorithms like…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…
We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…
Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…
We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has…
This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…