Abstract
Stochastic computer simulations enable users to gain new insights into complex physical systems. Optimization is a common problem in this context: users seek to find model inputs that maximize the expected value of an objective function. The objective function, however, is time-intensive to evaluate, and cannot be directly measured. Instead, the stochastic nature of the model means that individual realizations are corrupted by noise. More formally, we consider the problem of optimizing the expected value of an expensive black-box function with continuously-differentiable mean, from which observations are corrupted by Gaussian noise. We present parallel simultaneous perturbation optimization (PSPO), which extends a well-known stochastic optimization algorithm, simultaneous perturbation stochastic approximation, in several important ways. Our modifications allow the algorithm to fully take advantage of parallel computing resources, like high-performance cloud computing. The resulting PSPO algorithm takes fewer time-consuming iterations to converge, automatically chooses the step size, and can vary the error tolerance by step. Theoretical results are supported by a numerical example.
Highlights
Stochastic optimization is of core practical importance in many fields of science and engineering
We introduce parallel simultaneous perturbation optimization (PSPO), an algorithm for optimization of stochastic objective functions
We demonstrate that PSPO works well in practice and compares favorably to the conventional simultaneous perturbation stochastic approximation (SPSA)
Summary
Stochastic optimization is of core practical importance in many fields of science and engineering. In many cases the gradient of the loss function is not available This is a common occurrence, for example, in complex systems, such as the optimization problems given in Tsilifis et al (2017) and Alaeddini and Klein (2017), the exact functional relationship between the loss function value and the parameters is not known, and the loss function is evaluated by measurements on the system or by running simulation. The SPSA algorithm is used extensively in many different areas, e.g., signal timing for traffic control (Ma et al, 2013), and some large scale machine learning problems (Byrd et al, 2011) The convergence of this algorithm to the optimal value in the stochastic almost sure sense makes it suitable in many applications.
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