The 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 adversarial 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 dependant 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 perimeter defense problem in which multiple defenders are tasked to protect a high-value target from a team of intruders.