Related papers: Quantile Optimization via Multiple Timescale Local…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…
Algorithms for bandit convex optimization and online learning often rely on constructing noisy gradient estimates, which are then used in appropriately adjusted first-order algorithms, replacing actual gradients. Depending on the properties…
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number of training examples. The time complexity of our…
We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide…
This paper develops negative curvature methods for continuous nonlinear unconstrained optimization in stochastic settings, in which function, gradient, and Hessian information is available only through probabilistic oracles, i.e., oracles…
Standard techniques for differentially private estimation, such as Laplace or Gaussian noise addition, require guaranteed bounds on the sensitivity of the estimator in question. But such sensitivity bounds are often large or simply unknown.…
Local algorithms are common tools for estimating intrinsic volumes from black-and-white digital images. However, these algorithms are typically biased in the design based setting, even when the resolution tends to infinity. Moreover, images…
This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient…
Although a large number of optimization algorithms have been proposed for black box optimization problems, the no free lunch theorems inform us that no algorithm can beat others on all types of problems. Different types of optimization…
In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in…
The prevalence of variational methods in near-term quantum computing makes optimizer choice critical, yet selection is frequently intuition-based. We therefore present a systematic benchmark of eight classical optimization algorithms for…
This work studies minimization problems with zero-order noisy oracle information under the assumption that the objective function is highly smooth and possibly satisfies additional properties. We consider two kinds of zero-order projected…
We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…
We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
We propose two distributed iterative algorithms that can be used to solve, in finite time, the distributed optimization problem over quadratic local cost functions in large-scale networks. The first algorithm exhibits synchronous operation…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1}^n, we show a lower bound of Omega(2^{n/4}/n) on…
In this paper we propose a new parallel algorithm for solving global optimization (GO) multidimensional problems. The method unifies two powerful approaches for accelerating the search: parallel computations and local tuning on the behavior…