Differential Games of Mixed Strategies in a Variational Inference Framework: An Application to the Perimeter Defense Problem
Author(s)
Kilanga, Dan Monga
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Abstract
This dissertation formulates a differential game of mixed strategies as an
adversarial Variational Inference (VI) problem so that it can be solved through
the lenses of inference. To achieve the aforementioned goal, the dissertation
extends two existing tools for solving non-adversarial VI problems to the adver-
sarial setting where they are used to solve a non-cooperative differential game
of mixed strategies.
The contributions of this thesis are as follows: a task variable that relates the
likelihood of the success variable conditioned on state and control variables of a
stochastic control problem to the objective function is a general tool that links
control to Bayesian inference; however, to the best of our knowledge, nowhere
in the literature can be found a situation in which it was used such that it
is dependent on states and controls that are adversarial. By formulating the
problem such that the task variable is conditioned on adversarial state and
control variables, we are able to extend results that apply in non-adversarial
settings to adversarial settings: we extends Stein Variational Model Predictive
Control (SV-MPC) to a Min-Max SV-MPC on one hand while we extends the
Cross-Entropy optimization method to a Min-Max Cross-Entropy optimization
method.
Moreover, we demonstrate the approach using robots as players in the perime-
ter defense problem in which multiple defenders are tasked to protect a high-
value target from a team of intruders.
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Date
2024-09-09
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Dissertation (PhD)