Title: Stochastic Oracles and Where to Find Them

Abstract: Continuous optimization is a mature field, which has recently undergone major expansion and change. One of the key new directions is the development of methods that do not require exact information about the objective function. Nevertheless, the majority of these methods, from stochastic gradient descent to "zero-th order" methods use some kind of approximate first order information. We will introduce a general definition of a stochastic oracle and show how this definition applies in a variety of familiar settings, including simple stochastic gradient via sampling, traditional and randomized finite difference methods, but also more specialized settings, such as robust gradient estimation. We will also overview several stochastic methods and how the general definition extends to the oracles used by these methods.