Related papers: Conformal Symplectic and Relativistic Optimization

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…

Treating optimization methods as dynamical systems can be traced back centuries ago in order to comprehend the notions and behaviors of optimization methods. Lately, this mind set has become the driving force to design new optimization…

We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution. This result is proven both for an a…

First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…

In this paper, we study a bilinear saddle point problem of the form $\min_{x}\max_{y} F(x) + \langle Ax, y \rangle - G(y)$, where $F$ and $G$ are $\mu_F$- and $\mu_G$-strongly convex functions, respectively. By incorporating Nesterov…

Heavy ball momentum is crucial in accelerating (stochastic) gradient-based optimization algorithms for machine learning. Existing heavy ball momentum is usually weighted by a uniform hyperparameter, which relies on excessive tuning.…

In this paper, we adapt the control theoretic concept of dissipativity theory to provide a natural understanding of Nesterov's accelerated method. Our theory ties rigorous convergence rate analysis to the physically intuitive notion of…

Distributed optimization algorithms have emerged as a superior approaches for solving machine learning problems. To accommodate the diverse ways in which data can be stored across devices, these methods must be adaptable to a wide range of…

In a Hilbert space setting, for convex optimization, we analyze the convergence rate of a class of first-order algorithms involving inertial features. They can be interpreted as discrete time versions of inertial dynamics involving both…

We study the convergence behavior of the stochastic heavy-ball method with a small stepsize. Under a change of time scale, we approximate the discrete method by a stochastic differential equation that models small random perturbations of a…

We study nonsmooth convex minimization through a continuous-time dynamical system that can be seen as a high-resolution ODE of Nesterov Accelerated Gradient (NAG) adapted to the nonsmooth case. We apply a time-varying Moreau envelope…

Nesterov's momentum trick is famously known for accelerating gradient descent, and has been proven useful in building fast iterative algorithms. However, in the stochastic setting, counterexamples exist and prevent Nesterov's momentum from…

This paper addresses smooth convexly constrained optimization problems where the Euclidean projection onto the feasible set is computationally tractable. Although momentum techniques like Polyak's heavy-ball are known for accelerating…

The cubic regularized Newton method of Nesterov and Polyak has become increasingly popular for non-convex optimization because of its capability of finding an approximate local solution with second-order guarantee. Several recent works…

Asynchronous optimization algorithms often require delay bounds to prove their convergence, though these bounds can be difficult to obtain in practice. Existing algorithms that do not require delay bounds often converge slowly. Therefore,…

The proximal point method (PPM) is a fundamental method in optimization that is often used as a building block for designing optimization algorithms. In this work, we use the PPM method to provide conceptually simple derivations along with…

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

The adaptive stochastic gradient descent (SGD) with momentum has been widely adopted in deep learning as well as convex optimization. In practice, the last iterate is commonly used as the final solution to make decisions. However, the…

The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…