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

Killian Wood, Gianluca Bianchin, Emiliano Dall'Anese

This paper investigates the problem of tracking solutions of stochastic optimization problems with time-varying costs and decision-dependent distributions. In this context, the paper focuses on the online stochastic gradient descent method, and establishes its convergence to the sequence of optimizers (within a bounded error) in expectation and in high probability. In particular, high-probability convergence results are derived by modeling the gradient error as a sub-Weibull random variable. The theoretical findings are validated via numerical simulations in the context of charging optimization of a fleet of electric vehicles.

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