Cyclic stochastic optimization via arbitrary selection procedures for updating parameters

Many of the algorithms that exist to tackle optimization problems (either stochastic or deterministic) are iterative in nature. Methods where only a subset of the parameter vector is updated each time have been frequently used in practice. While some of these methods update different sets of parameters according to some predetermined pattern, others select the parameters to update according to a random variable. Much work exists on the convergence of such procedures in the case of deterministic optimization. However, very little is known about their convergence when applied to general stochastic optimization problems; this is the setting this work focuses on. We describe the generalized cyclic seesaw algorithm-a general method for selecting which parameters to update during each iteration-and give sufficient conditions for its convergence.