19 accepted papers
The auto-regressive decoding of Large Language Models (LLMs) results in significant overheads in their hardware performance. While recent research has explored various speculative decoding techniques for multi-token generation, these methods introduce high memory costs from the additional weights an
In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local curvature information of smooth functions. We propose adaptive v…
We consider the problem of estimating the learning rate in adaptive methods, such as AdaGrad and Adam. We propose Prodigy, an algorithm that provably estimates the distance to the solution $D$, which is needed to set the learning rate optimally. At its core, Prodigy is a modification of the D-Adapta…
Existing learning rate schedules that do not require specification of the optimization stopping step $T$ are greatly out-performed by learning rate schedules that depend on $T$. We propose an approach that avoids the need for this stopping time by eschewing the use of schedules entirely, while exhib…
This paper proposes a new easy-to-implement parameter-free gradient-based optimizer: DoWG (Distance over Weighted Gradients). We prove that DoWG is efficient---matching the convergence rate of optimally tuned gradient descent in convex optimization up to a logarithmic factor without tuning any param…
The speed of gradient descent for convex Lipschitz functions is highly dependent on the choice of learning rate. Setting the learning rate to achieve the optimal convergence rate requires knowing the distance D from the initial point to the solution set. In this work, we describe a single-loop metho…
We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal-point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the dif…
The existing analysis of asynchronous stochastic gradient descent (SGD) degrades dramatically when any delay is large, giving the impression that performance depends primarily on the delay. On the contrary, we prove much better guarantees for the same asynchronous SGD algorithm regardless of the del…
We propose a family of adaptive integer compression operators for distributed Stochastic Gradient Descent (SGD) that do not communicate a single float. This is achieved by multiplying floating-point vectors with a number known to every device and then rounding to integers. In contrast to the prior w…
We introduce ProxSkip—a surprisingly simple and provably efficient method for minimizing the sum of a smooth ($f$) and an expensive nonsmooth proximable ($\psi$) function. The canonical approach to solving such problems is via the proximal gradient descent (ProxGD) algorithm, which is based on the e…
Random Reshuffling (RR), also known as Stochastic Gradient Descent (SGD) without replacement, is a popular and theoretically grounded method for finite-sum minimization. We propose two new algorithms: Proximal and Federated Random Reshuffling (ProxRR and FedRR). The first algorithm, ProxRR, solves c…
In this paper we discuss sparsification of worker-to-server communication in large distributed systems. We improve upon algorithms that fit the following template: a local gradient estimate is computed independently by each worker, then communicated to a master, which subsequently performs averaging…
We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the function except for the gradients. By following…
In this paper, we consider distributed algorithms for solving the empirical risk minimization problem under the master/worker communication model. We develop a distributed asynchronous quasi-Newton algorithm that can achieve superlinear convergence. To our knowledge, this is the first distributed as…
Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is usually faster in practice and enjoys significant popularity in…
We fix a fundamental issue in the stochastic extragradient method by providing a new sampling strategy that is motivated by approximating implicit updates. Since the existing stochastic extragradient algorithm, called Mirror-Prox, of (Juditsky, 2011) diverges on a simple bilinear problem when the do…
We provide a new analysis of local SGD, removing unnecessary assumptions and elaborating on the difference between two data regimes: identical and heterogeneous. In both cases, we improve the existing theory and provide values of the optimal stepsize and optimal number of local iterations. Our bound…
Distributed learning aims at computing high-quality models by training over scattered data. This covers a diversity of scenarios, including computer clusters or mobile agents. One of the main challenges is then to deal with heterogeneous machines and unreliable communications. In this setting, we pr…
We propose a novel randomized first order optimization method---SEGA (SkEtched GrAdient method)---which progressively throughout its iterations builds a variance-reduced estimate of the gradient from random linear measurements (sketches) of the gradient provided at each iteration by an oracle. In e…