Everything about Stochastic Optimization totally explained
Stochastic optimization (SO) methods are
optimization algorithms which incorporate
probabilistic (random) elements, either in the problem data (the
objective function, the constraints, etc.), or in the algorithm itself (through random parameter values, random choices, etc.), or in both .
The concept contrasts with the
deterministic optimization methods, where the values of the objective function are assumed to be exact, and the computation is completely determined by the values sampled so far.
Methods for stochastic functions
Partly-random input data arise in such areas as real-time estimation and control, simulation-based optimization where
Monte Carlo simulations are run as estimates of an actual system,
and problems where there's experimental (random) error in the measurements of the criterion. In such cases, knowledge that the function values are contaminated by random "noise" leads naturally to algorithms that use
statistical inference tools to estimate the "true" values of the function and/or make statistically optimal decisions about the next steps. Methods of this class include
Randomized search methods
On the other hand, even when the data is exact, it's sometimes beneficial to deliberately introduce randomness into the search process as a means of speeding convergence and making the algorithm less sensitive to modeling errors. Further, the injected randomness may provide the necessary impetus to move away from a local solution when searching for a global optimum. Indeed, this
randomization principle is known to be a simple and effective way to obtain algorithms with
almost certain good performance uniformly across all data sets, for all sorts of problems. Stochastic optimization method of this kind include:
simulated annealing by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi (1983)
evolutionary algorithms
Cross-entropy method by Rubinstein and Kroese (2004)
random search by Zhigljavsky (1991) Further Information
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