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This paper investigates the problem of tracking solutions of stochasticoptimization problems with time-varying costs that depend on random variableswith decision-dependent distributions. In this context, we propose the use ofan online stochastic gradient descent method to solve the optimization, and weprovide explicit bounds in expectation and in high probability for the distancebetween the optimizers and the points generated by the algorithm. Inparticular, we show that when the gradient error due to sampling is modeled asa sub-Weibull random variable, then the tracking error is ultimately bounded inexpectation and in high probability. The theoretical findings are validated vianumerical simulations in the context of charging optimization of a fleet ofelectric vehicles.

Online Projected Gradient Descent for Stochastic Optimization with Decision-Dependent Distributions