相关论文: Parameter-free Clipped Gradient Descent Meets Poly…

In this paper, we propose a new inexact version of the projected subgradient method to solve nondifferentiable constrained convex optimization problems. The method combine $\epsilon$-subgradient method with a procedure to obtain a feasible…

It has been observed in a variety of contexts that gradient descent methods have great success in solving low-rank matrix factorization problems, despite the relevant problem formulation being non-convex. We tackle a particular instance of…

Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…

In this paper, we consider two variants of the concept of sharp minimum for mathematical programming problems with quasiconvex objective function and inequality constraints. It investigated the problem of describing a variant of a simple…

In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…

The performance of stochastic gradient descent (SGD) depends critically on how learning rates are tuned and decreased over time. We propose a method to automatically adjust multiple learning rates so as to minimize the expected error at any…

Machine learning training methods depend plentifully and intricately on hyperparameters, motivating automated strategies for their optimisation. Many existing algorithms restart training for each new hyperparameter choice, at considerable…

Recent efforts to accelerate first-order methods have focused on convex optimization problems that satisfy a geometric property known as error-bound condition, which covers a broad class of problems, including piece-wise linear programs and…

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…

We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings:…

The Polyak stepsize has been proven to be a fundamental stepsize in convex optimization, giving near optimal gradient descent rates across a wide range of assumptions. The universality of the Polyak stepsize has also inspired many…

We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a…

Hyperparameter tuning, particularly the selection of an appropriate learning rate in adaptive gradient training methods, remains a challenge. To tackle this challenge, in this paper, we propose a novel parameter-free optimizer,…

The learning rate in stochastic gradient methods is a critical hyperparameter that is notoriously costly to tune via standard grid search, especially for training modern large-scale models with billions of parameters. We identify a…

We study the statistical and computational complexities of the Polyak step size gradient descent algorithm under generalized smoothness and Lojasiewicz conditions of the population loss function, namely, the limit of the empirical loss…

The stochastic proximal gradient method is a powerful generalization of the widely used stochastic gradient descent (SGD) method and has found numerous applications in Machine Learning. However, it is notoriously known that this method…

We introduce a novel dynamic learning-rate scheduling scheme grounded in theory with the goal of simplifying the manual and time-consuming tuning of schedules in practice. Our approach is based on estimating the locally-optimal stepsize,…

This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c >0$. It is widely used for example for stabilizing the training of deep learning…

In this paper, we propose a simple, fast and easy to implement algorithm LOSSGRAD (locally optimal step-size in gradient descent), which automatically modifies the step-size in gradient descent during neural networks training. Given a…