arXiv research

We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from $τ$ rounds ago. First, we show that without stochastic noise, delays strongly affect the attainable optimization error: In fact, the error…

We propose a novel robust aggregation rule for distributed synchronous Stochastic Gradient Descent~(SGD) under a general Byzantine failure model. The attackers can arbitrarily manipulate the data transferred between the servers and the workers in the parameter server~(PS) architecture. We prove the Byzantine resilience…

We introduce a new, high-throughput, synchronous, distributed, data-parallel, stochastic-gradient-descent learning algorithm. This algorithm uses amortized inference in a compute-cluster-specific, deep, generative, dynamical model to perform joint posterior predictive inference of the mini-batch gradient computation ti…

Despite their popularity, the practical performance of asynchronous stochastic gradient descent methods (ASGD) for solving large scale machine learning problems are not as good as theoretical results indicate. We adopt and analyze a synchronous K-step averaging stochastic gradient descent algorithm which we call K-AVG.…

Proposes DC-S3GD for efficient large-scale decentralized neural network training.

Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset)…

GA method reduces gradient staleness in cloud computing.

DORE reduces communication costs in distributed learning by 95%.

FedAc accelerates Federated Averaging for distributed optimization.

Nonlinear conjugate gradient (NLCG) based optimizers have shown superior loss convergence properties compared to gradient descent based optimizers for traditional optimization problems. However, in Deep Neural Network (DNN) training, the dominant optimization algorithm of choice is still Stochastic Gradient Descent (SG…

CSER improves SGD efficiency by resetting errors and partial synchronization.

In this paper, we focus on approaches to parallelizing stochastic gradient descent (SGD) wherein data is farmed out to a set of workers, the results of which, after a number of updates, are then combined at a central master node. Although such synchronized SGD approaches parallelize well in idealized computing environm…

With the increase in the amount of data and the expansion of model scale, distributed parallel training becomes an important and successful technique to address the optimization challenges. Nevertheless, although distributed stochastic gradient descent (SGD) algorithms can achieve a linear iteration speedup, they are l…

This paper presents Rudra, a parameter server based distributed computing framework tuned for training large-scale deep neural networks. Using variants of the asynchronous stochastic gradient descent algorithm we study the impact of synchronization protocol, stale gradient updates, minibatch size, learning rates, and n…

We propose three new robust aggregation rules for distributed synchronous Stochastic Gradient Descent~(SGD) under a general Byzantine failure model. The attackers can arbitrarily manipulate the data transferred between the servers and the workers in the parameter server~(PS) architecture. We prove the Byzantine resilie…

A new method reduces data movement in neural network training.

Stochastic Gradient Descent (SGD) is the most popular algorithm for training deep neural networks (DNNs). As larger networks and datasets cause longer training times, training on distributed systems is common and distributed SGD variants, mainly asynchronous and synchronous SGD, are widely used. Asynchronous SGD is com…

Asynchronous SGD can speed up training with a trade-off of gradient staleness.

Most commonly used distributed machine learning systems are either synchronous or centralized asynchronous. Synchronous algorithms like AllReduce-SGD perform poorly in a heterogeneous environment, while asynchronous algorithms using a parameter server suffer from 1) communication bottleneck at parameter servers when wo…

We propose a novel coding theoretic framework for mitigating stragglers in distributed learning. We show how carefully replicating data blocks and coding across gradients can provide tolerance to failures and stragglers for Synchronous Gradient Descent. We implement our schemes in python (using MPI) to run on Amazon EC…

We study a distributed framework for stochastic optimization which is inspired by models of collective motion found in nature (e.g., swarming) with mild communication requirements. Specifically, we analyze a scheme in which each one of $N > 1$ independent threads, implements in a distributed and unsynchronized fashion,…

Stochastic gradient descent on manifolds improves low-rank approximation.

Distributed Stochastic Gradient Descent (SGD) when run in a synchronous manner, suffers from delays in waiting for the slowest learners (stragglers). Asynchronous methods can alleviate stragglers, but cause gradient staleness that can adversely affect convergence. In this work we present a novel theoretical characteriz…

New method reduces communication in deep learning training.

A new method improves stochastic gradient descent for faster and more efficient estimation.

New adaptive step-size method for convex optimization without tuning.

Can health entities collaboratively train deep learning models without sharing sensitive raw data? This paper proposes several configurations of a distributed deep learning method called SplitNN to facilitate such collaborations. SplitNN does not share raw data or model details with collaborating institutions. The prop…

SGD and stochastic gradient descent converge at optimal rates for certain non-convex functions.

The paper studies stochastic gradient descent with infinite variance gradients.

Proof given for SGD convergence in a concise manner.

SGD reduces test error by decorrelating updates.

NHGD solves bilevel optimization problems with reduced computational time.

New dynamics for SGD in small learning rate regime.

Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires careful tuning of key parameters. Here, we introduce implicit stochastic gradien…

We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for a broad family of loss functions, with proper random weight initialization, both…

Gradient descent variants improve phase retrieval accuracy.

SAGD uses Langevin algorithm for efficient gradient descent.

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 projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan an…

Deep learning has led to tremendous advancements in the field of Artificial Intelligence. One caveat however is the substantial amount of compute needed to train these deep learning models. Training a benchmark dataset like ImageNet on a single machine with a modern GPU can take upto a week, distributing training on mu…

Langevin algorithms enhance training of deep neural networks for stochastic control problems.

Stochastic gradient methods converge for training wide PINNs.

Asynchronous SGD generalizes well with enough data, improving stability and reducing error.

The paper analyzes stability and generalization of decentralized SGD.

Gradient descent stagnates in low-precision, but unbiased rounding schemes improve convergence.

Stochastic gradient descent approximates Gaussian process posteriors efficiently.

Riemannian stochastic gradient descent approximates a diffusion process called Riemannian stochastic modified flow.

Stochastic gradient descent improves Gaussian process regression.

Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive gradient) methods are the two main techniques to improve the slow convergence of \text…