SPSA

SPSA stands for Stochastic Parallel Search Algorithm. It is an optimization algorithm used to find the minimum or maximum of a function. SPSA is particularly well-suited for optimizing functions that are noisy or where the gradient is difficult to compute directly. It belongs to the class of simultaneous perturbation stochastic approximation algorithms.

The core idea behind SPSA is to estimate the gradient of the function using randomly perturbed function evaluations. Unlike traditional gradient descent methods that require calculating the gradient at a specific point, SPSA perturbs the parameters in all directions simultaneously and then uses the difference in function values to approximate the gradient. This makes it efficient when function evaluations are expensive or when dealing with complex, high-dimensional problems.

SPSA is often used in control systems, machine learning, and other fields where optimizing performance metrics is crucial. Its robustness to noise and ability to handle non-differentiable or black-box functions are key advantages. The algorithm iteratively updates the search parameters based on the estimated gradient and a decreasing step size. The randomness in the perturbation ensures exploration of the search space, helping to avoid local optima. The convergence properties of SPSA have been studied extensively, and it is known to converge to a local optimum under certain conditions.