  This paper investigates the problem of tracking solutions of stochastic
optimization problems with time-varying costs that depend on random variables
with decision-dependent distributions. In this context, we propose the use of
an online stochastic gradient descent method to solve the optimization, and we
provide explicit bounds in expectation and in high probability for the distance
between the optimizers and the points generated by the algorithm. In
particular, we show that when the gradient error due to sampling is modeled as
a sub-Weibull random variable, then the tracking error is ultimately bounded in
expectation and in high probability. The theoretical findings are validated via
numerical simulations in the context of charging optimization of a fleet of
electric vehicles.
