Related papers: Robust and efficient algorithms for high-dimension…
We study the Hamiltonian flow for optimization (HF-opt), which simulates the Hamiltonian dynamics for some integration time and resets the velocity to $0$ to decrease the objective function; this is the optimization analogue of the…
Stochastic Gradient Descent (SGD) and its variants are the most used algorithms in machine learning applications. In particular, SGD with adaptive learning rates and momentum is the industry standard to train deep networks. Despite the…
Adversarial examples, crafted by adding imperceptible perturbations to natural inputs, can easily fool deep neural networks (DNNs). One of the most successful methods for training adversarially robust DNNs is solving a nonconvex-nonconcave…
Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
We present a new accelerated gradient-based method for solving smooth unconstrained optimization problems. The goal is to embed a heavy-ball type of momentum into the Fast Gradient Method (FGM). For this purpose, we devise a generalization…
We develop a general method for incentive-based programming of hybrid quantum-classical computing systems using reinforcement learning, and apply this to solve combinatorial optimization problems on both simulated and real gate-based…
The simulation of quantum dynamics on a digital quantum computer with parameterized circuits has widespread applications in fundamental and applied physics and chemistry. In this context, using the hybrid quantum-classical algorithm,…
We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
The local gradient points to the direction of the steepest slope in an infinitesimal neighborhood. An optimizer guided by the local gradient is often trapped in local optima when the loss landscape is multi-modal. A directional Gaussian…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
Hybrid Quantum Classical (HQC) algorithms constitute one of the most effective paradigms for exploiting the computational advantages of quantum systems in large-scale numerical tasks. By operating in high-dimensional Hilbert spaces, quantum…
We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…
Motivated by recent efforts to develop quantum computing for practical, industrial-scale challenges, we demonstrate the effectiveness of state-of-the-art hybrid (not necessarily quantum) solvers in addressing the business-centric…
Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources by useful control schemes. In this paper, we develop an HQC algorithm using an efficient variational…
Decentralized learning recently has received increasing attention in machine learning due to its advantages in implementation simplicity and system robustness, data privacy. Meanwhile, the adaptive gradient methods show superior…
Much of the existing theory on first-order non-smooth optimization is built on a restrictive assumption that the gradients of the objective function are uniformly bounded. We introduce a much more realistic class of generalized Lipschitz…
When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…
Solving for adversarial examples with projected gradient descent has been demonstrated to be highly effective in fooling the neural network based classifiers. However, in the black-box setting, the attacker is limited only to the query…