Online Learning also known as Online Convex Opimization has famous algorithms like Follow-the-Leader and Online Gradient Descent (See OCO Book)
Now stoastic programming has algorithms like Sample Average Approximation and Stoastic Approximation. (See SSA Paper)
So what is the relathionsship between these two frameworks? To me it seems in online learning you assume that the sequence of sample comes over time and is abitrary. In stoastic programming you either see it as a offline problem or as an online problem, where the samples arrive in an i.i.d fashion.
So if you assume you take a look at the online problem, is then the only difference the assumption that the samples come from i.i.d, but the algorithms are same, i.e. Follow-the-Leader = Sample Average Approximation and Online Gradient Descent = Stoastic Approximation?