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Register a new userDisordered high-dimensional optimal control
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Added by
Pierfrancesco Urbani
Publication date
2021
fields
Physics
and research's language is
English
Authors
Pierfrancesco Urbani
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Mean field optimal control problems are a class of optimization problems that arise from optimal control when applied to the many body setting. In the noisy case one has a set of controllable stochastic processes and a cost function that is a functional of their trajectories. The goal of the optimization is to minimize this cost over the control variables. Here we consider the case in which we have $N$ stochastic processes, or agents, with the associated control variables, which interact in a disordered way so that the resulting cost function is random. The goal is to find the average minimal cost for $Nto infty$, when a typical realization of the quenched random interactions is considered. We introduce a simple model and show how to perform a dimensional reduction from the infinite dimensional case to a set of one dimensional stochastic partial differential equations of the Hamilton-Jacobi-Bellman and Fokker-Planck type. The statistical properties of the corresponding stochastic terms must be computed self-consistently, as we show explicitly.
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