Autonomy Talks - Nicolas Lanzetti: Dynamic Programming in Probability Spaces via Optimal Transport

Autonomy Talks - 03/21/23

Speaker: Nicolas Lanzetti, ETH Zürich

Abstract: In this talk, we present dynamic programming in probability spaces and explain why it is relevant for the control of multi-agent systems, such as fleets of identical robots. To start, we show that many problems in the context of multi-agent systems, both in discrete (with finitely many agents) and continuous (with infinitely many agents) settings, can be cast as optimal control problems in probability spaces, whereby the state of the system is a prob- ability measure. Thereafter, we demonstrate that the solution of dynamic programming in probability spaces results from two ingredients: (i) the solution of dynamic program- ming in the ”ground space” (i.e., the space on which the probability measures live) and (ii) the solution of an optimal transport problem. From a multi-agent control perspective, a separation principle holds: The ”low-level control of the agents of the fleet” (how to reach the destination?) and ”fleet-level control” (who goes where?) are decoupled. In other words, our results predicate that it is optimal to first devise control strategies for individual agents (“forgetting” about the fleet) and, subsequently, to determine fleet-level dispatching strategies. This is joint work with Antonio Terpin and Florian Do ̈rfler.

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