Stochastic First Order Oracle for Sampled Gradients

A stochastic first order oracle that returns a sampled gradient given A, S exists. This type of oracle is crucial for optimization algorithms involving large datasets or complex models. It allows for efficient computation of gradients by sampling a subset of the data, reducing the computational burden and enabling the use of stochastic gradient descent (SGD) methods. The oracle's existence and properties are key to understanding and developing advanced optimization techniques in machine learning.