The paper "Large-Scale Machine Learning with Stochastic Gradient Descent" by Léon Bottou discusses the challenges and solutions for large-scale machine learning problems, where the computational complexity of algorithms becomes a critical limiting factor. The author highlights the efficiency of stochastic gradient descent (SGD) and second-order stochastic gradient descent (2SGD) in handling large datasets. These algorithms are particularly attractive because they can process examples in a deployed system without needing to remember previously visited examples. The paper also analyzes the trade-offs between approximation error, estimation error, and optimization error in large-scale learning problems, showing that SGD and 2SGD achieve faster convergence to the expected risk compared to other optimization algorithms. Empirical results from various machine learning tasks, such as linear SVMs and CRFs, demonstrate the superior performance of SGD and 2SGD in terms of both speed and accuracy. The paper concludes that in large-scale settings, where computing time is the primary constraint, stochastic learning algorithms perform asymptotically better.The paper "Large-Scale Machine Learning with Stochastic Gradient Descent" by Léon Bottou discusses the challenges and solutions for large-scale machine learning problems, where the computational complexity of algorithms becomes a critical limiting factor. The author highlights the efficiency of stochastic gradient descent (SGD) and second-order stochastic gradient descent (2SGD) in handling large datasets. These algorithms are particularly attractive because they can process examples in a deployed system without needing to remember previously visited examples. The paper also analyzes the trade-offs between approximation error, estimation error, and optimization error in large-scale learning problems, showing that SGD and 2SGD achieve faster convergence to the expected risk compared to other optimization algorithms. Empirical results from various machine learning tasks, such as linear SVMs and CRFs, demonstrate the superior performance of SGD and 2SGD in terms of both speed and accuracy. The paper concludes that in large-scale settings, where computing time is the primary constraint, stochastic learning algorithms perform asymptotically better.