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rom the 1950s to today: How amazing is the evolution of stochastic gradient descent
Stochastic gradient descent (SGD) is an iterative method for optimizing an objective function that has undergone a phenomenal evolution since the 1950s, especially in the context of machine learning. This method was first proposed by Herbert Robbins and Sutton Monod in 1951. The core idea is to approximate the actual gradient of a data set by estimating it on a randomly selected subset of the data. This strategy allows SGD to reduce the computational burden and achieve faster iterations when dealing with high-dimensional optimization problems.
"Stochastic gradient descent provides an efficient way to solve optimization problems on large datasets."
Background
In statistical estimation and machine learning, narrowing down the minimization problem of the objective function is considered of utmost importance. These problems can often be expressed as a sum where each term is associated with an observation in the dataset. In statistics, such minimization problems arise in the least squares method and maximum likelihood estimation. With the rapid rise of deep learning today, stochastic gradient descent has become an important tool in optimization algorithms.
Iterative Methods
The main feature of stochastic gradient descent is that it uses only one sample to compute the gradient at each update. This makes the computational cost of performing each iteration significantly lower when the dataset is very large. To further improve efficiency, later research introduced the concept of mini-batch gradient descent, which uses multiple samples in each update, thereby taking advantage of vectorized libraries to speed up computation.
“Mini-batch methods combine the efficiency of stochastic gradient descent with the stability of batch methods.”
Linear Regression
Take linear regression as an example, the optimal model parameters can be obtained by minimizing the difference between the predicted value and the true value. This can be achieved using stochastic gradient descent, where the parameters are updated one data point at a time. This not only makes it feasible to process large amounts of data, but also increases the speed at which models can be updated.
Historical evolution
Since the initial work of Robbins and Monod, stochastic gradient descent has undergone several major changes. In 1956, Jack Keefer and Jacob Wolfowitz published an optimization algorithm very similar to stochastic gradient descent, and Frank Rosenblatt used this method to optimize his perceptron in the same year. Model. With the first description of the back-propagation algorithm, SGD has been widely used for parameter optimization of multi-layer neural networks.
In the 2010s, variants of stochastic gradient descent emerged one after another, especially techniques for automatically adjusting the learning rate, such as AdaGrad, RMSprop, and Adam. These methods made SGD more effective in handling complex learning tasks. Today, most mainstream machine learning libraries such as TensorFlow and PyTorch include Adam-based optimizers, which have become the cornerstone of modern machine learning.
Significant Applications
To date, the application of stochastic gradient descent has spread to many fields, including computer vision, speech recognition, and natural language processing. In these fields, SGD is widely used due to its high efficiency and flexibility, becoming an essential tool for training deep learning models. From the past to the present, stochastic gradient descent has not only changed the way we deal with big data, but also paved the way for the development of artificial intelligence.
"Stochastic gradient descent is not only a technological advancement, but also an important driving force for realizing an intelligent world."
From the initial experiments in the 1950s to the widespread application today, stochastic gradient descent has demonstrated its strong vitality and adaptability. How will it affect new technological advances in the future?
