Stochastic Generators

Abstract

The previous chapter formalized iterative stochastic optimization methods using generators and trajectors on the assumption that the search and value spaces were finite and that the stochasticity of these methods was finitely representable. From an analytic perspective, this latter requirement in particular is somewhat artificial and unnatural in that it imposed gaps between neighboring optimizers in terms of the distance metric. These gaps occurred as a consequence of underflow in floating point operations, and they can be removed by lifting the analysis into a continuous space.