Simultaneous Perturbation Stochastic Approximation (SPSA) Algorithm for Optimization
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Simultaneous Perturbation Stochastic Approximation (SPSA) is an optimization algorithm used for parameter estimation and function minimization. Unlike traditional gradient-based methods, SPSA does not require explicit gradient information, making it particularly useful for real-world problems where gradients are difficult to compute or systems are affected by noise. The algorithm employs a stochastic approach by simultaneously perturbing all parameters with a random vector, significantly reducing the number of function evaluations needed compared to finite-difference methods. This approach also helps mitigate the risk of converging to local minima, making SPSA widely applicable for nonlinear optimization problems. In implementation, SPSA typically involves two key steps per iteration: generating a random perturbation vector and evaluating the objective function at two symmetric points around the current parameter values to approximate the gradient direction.
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