Asymptotic normality and efficiency analysis of the cyclic seesaw stochastic optimization algorithm

In many real-world optimization problems, the loss function to minimize is unknown and only observable in the presence of noise. In other words, it is possible to obtain a noisy measurement of the loss function at a given input parameter. Here, stochastic optimization algorithms (which are often iterative in nature) can be used for optimization. Cyclic stochastic optimization is a type of stochastic optimization where only a subset of the parameter vector is updated at a time. While cyclic algorithms are commonly used in practice, most of the results on the asymptotic behavior of the iterates are restricted to the deterministic optimization setting (where the loss function is known). In this paper, we derive asymptotic normality results for the iterates produced by cyclic stochastic optimization algorithms. We also define and investigate the relative efficiency between a stochastic optimization algorithm and its cyclic formulation.

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