Related papers: Open Problem: Anytime Convergence Rate of Gradient…
Much recent attention has been devoted to gradient descent algorithms where the steepest descent step size is replaced by a similar one from a previous iteration or gets updated only once every second step, thus forming a {\em faster…
This work introduces a two-step stepsize schedule for stochastic gradient methods minimizing smooth strongly convex functions. We consider the setting where only stochastic gradient approximations, which are unbiased, of bounded variance,…
In this work, we study the iteration complexity of gradient methods for minimizing convex quadratic functions regularized by powers of Euclidean norms. We show that, due to the uniform convexity of the objective, gradient methods have…
We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a…
In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal…
By analyzing accelerated proximal gradient methods under a local quadratic growth condition, we show that restarting these algorithms at any frequency gives a globally linearly convergent algorithm. This result was previously known only for…
We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by…
In this paper, we present a new complexity result for the gradient descent method with an appropriately fixed stepsize for minimizing a strongly convex function with locally $\alpha$-H{\"o}lder continuous gradients ($0 < \alpha \leq 1$).…
In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate $O\left(\frac{1}{\varepsilon^2}\right)$ improving over the…
This article derives lower bounds on the convergence rate of continuous-time gradient-based optimization algorithms. The algorithms are subjected to a time-normalization constraint that avoids a reparametrization of time in order to make…
We study the gradient method under the assumption that an additively inexact gradient is available for, generally speaking, non-convex problems. The non-convexity of the objective function, as well as the use of an inexactness specified…
Algorithms with fast convergence, small number of data access, and low per-iteration complexity are particularly favorable in the big data era, due to the demand for obtaining \emph{highly accurate solutions} to problems with \emph{a large…
In this note, we present a new averaging technique for the projected stochastic subgradient method. By using a weighted average with a weight of t+1 for each iterate w_t at iteration t, we obtain the convergence rate of O(1/t) with both an…
We consider stochastic gradient descent algorithms for minimizing a non-smooth, strongly-convex function. Several forms of this algorithm, including suffix averaging, are known to achieve the optimal $O(1/T)$ convergence rate in…
An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…
In this work, based on the continuous time approach, we propose an accelerated gradient method with adaptive residual restart for convex multiobjective optimization problems. For the first, we derive rigorously the continuous limit of the…
This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast…
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…
In this paper, we investigate accelerated first-order methods for smooth convex optimization problems under inexact information on the gradient of the objective. The noise in the gradient is considered to be additive with two possibilities:…