Related papers: New Results on the Polyak Stepsize: Tight Converge…
We provide a general convergence theorem of an idealized stochastic Polyak step size called SPS$^*$. Besides convexity, we only assume a local expected gradient bound, that includes locally smooth and locally Lipschitz losses as special…
We propose an adaptive step-size rule for decentralized optimization. Choosing a step-size that balances convergence and stability is challenging. This is amplified in the decentralized setting as agents observe only local (possibly…
We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates…
We perform the first tight convergence analysis of the gradient method with varying step sizes when applied to smooth hypoconvex (weakly convex) functions. Hypoconvex functions are smooth nonconvex functions whose curvature is bounded and…
In this paper, we propose a proximal stochasitc gradient algorithm (PSGA) for solving composite optimization problems by incorporating variance reduction techniques and an adaptive step-size strategy. In the PSGA method, the objective…
A prevalent belief among optimization specialists is that linear convergence of gradient descent is contingent on the function growing quadratically away from its minimizers. In this work, we argue that this belief is inaccurate. We show…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
We propose two Polyak-type step sizes for mirror descent and prove their convergences for minimizing convex locally Lipschitz functions. Both step sizes, unlike the original Polyak step size, do not need the optimal value of the objective…
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:…
In this paper, we consider gradient-type methods for convex positively homogeneous optimization problems with relative accuracy. An analogue of the accelerated universal gradient-type method for positively homogeneous optimization problems…
We study stochastic gradient descent (SGD) for composite optimization problems with $N$ sequential operators subject to perturbations in both the forward and backward passes. Unlike classical analyses that treat gradient noise as additive…
Recently, the stochastic Polyak step size (SPS) has emerged as a competitive adaptive step size scheme for stochastic gradient descent. Here we develop ProxSPS, a proximal variant of SPS that can handle regularization terms. Developing a…
We consider the classical gradient descent algorithm with constant stepsizes, where some error is introduced in the computation of each gradient. More specifically, we assume some relative bound on the inexactness, in the sense that the…
In this paper, we study the convergence properties of the Stochastic Gradient Descent (SGD) method for finding a stationary point of a given objective function $J(\cdot)$. The objective function is not required to be convex. Rather, our…
The purpose of this manuscript is to derive new convergence results for several subgradient methods applied to minimizing nonsmooth convex functions with H\"olderian growth. The growth condition is satisfied in many applications and…
We develop a high-dimensional scaling limit for Stochastic Gradient Descent with Polyak Momentum (SGD-M) and adaptive step-sizes. This provides a framework to rigourously compare online SGD with some of its popular variants. We show that…
We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…
Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…
Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for…
We study stochastic gradient descent (SGD) with gradient clipping on convex functions under a generalized smoothness assumption called $(L_0,L_1)$-smoothness. Using gradient clipping, we establish a high probability convergence rate that…