This paper discusses the use of stochastic gradient descent (SGD) for large-scale machine learning. The computational complexity of learning algorithms becomes the critical limiting factor when dealing with very large datasets. The paper advocates for stochastic gradient algorithms due to their efficiency in handling large-scale problems. It describes the stochastic gradient algorithm, analyzes why it is attractive for large datasets, discusses the asymptotic efficiency of estimates obtained after a single pass over the training set, and presents empirical evidence. The paper begins by introducing the concept of gradient descent, which is used to minimize the empirical risk. It then describes stochastic gradient descent, which is a simplified version of gradient descent that uses a single randomly selected example per iteration. The paper discusses the convergence of SGD, noting that its convergence speed is limited by the noisy approximation of the true gradient. It also introduces second-order stochastic gradient descent (2SGD), which uses a positive definite matrix to approximate the inverse of the Hessian, but this does not significantly improve the variance of the parameter estimates. The paper then discusses the trade-offs of large-scale learning, decomposing the excess error into approximation, estimation, and optimization errors. It shows that the optimal solution to the trade-off problem involves balancing these three errors. The paper also presents an asymptotic analysis of the excess error, showing that the computational effort required to make a term decrease faster would be wasted. It concludes that SGD and 2SGD, despite being the worst optimization algorithms, achieve the fastest convergence speed on the expected risk. The paper also discusses efficient learning methods, including the use of averaged stochastic gradient descent (ASGD), which performs the normal stochastic gradient update and recursively computes the average of the weights. The paper presents experimental results showing that SGD performs well on various linear systems, including linear SVMs and CRFs. The results show that SGD is faster than other algorithms and achieves near-optimal results on certain tasks. The paper concludes that stochastic gradient descent is an effective method for large-scale machine learning.This paper discusses the use of stochastic gradient descent (SGD) for large-scale machine learning. The computational complexity of learning algorithms becomes the critical limiting factor when dealing with very large datasets. The paper advocates for stochastic gradient algorithms due to their efficiency in handling large-scale problems. It describes the stochastic gradient algorithm, analyzes why it is attractive for large datasets, discusses the asymptotic efficiency of estimates obtained after a single pass over the training set, and presents empirical evidence. The paper begins by introducing the concept of gradient descent, which is used to minimize the empirical risk. It then describes stochastic gradient descent, which is a simplified version of gradient descent that uses a single randomly selected example per iteration. The paper discusses the convergence of SGD, noting that its convergence speed is limited by the noisy approximation of the true gradient. It also introduces second-order stochastic gradient descent (2SGD), which uses a positive definite matrix to approximate the inverse of the Hessian, but this does not significantly improve the variance of the parameter estimates. The paper then discusses the trade-offs of large-scale learning, decomposing the excess error into approximation, estimation, and optimization errors. It shows that the optimal solution to the trade-off problem involves balancing these three errors. The paper also presents an asymptotic analysis of the excess error, showing that the computational effort required to make a term decrease faster would be wasted. It concludes that SGD and 2SGD, despite being the worst optimization algorithms, achieve the fastest convergence speed on the expected risk. The paper also discusses efficient learning methods, including the use of averaged stochastic gradient descent (ASGD), which performs the normal stochastic gradient update and recursively computes the average of the weights. The paper presents experimental results showing that SGD performs well on various linear systems, including linear SVMs and CRFs. The results show that SGD is faster than other algorithms and achieves near-optimal results on certain tasks. The paper concludes that stochastic gradient descent is an effective method for large-scale machine learning.