Probability Functional Descent: Unifying Generative Models, Inference, and Control through von Mises Calculus

The Fragmentation of Modern Machine Learning

Deep learning research has increasingly stratified into distinct communities, each developing specialized tools for what appear to be fundamentally different problems. Generative adversarial networks occupy the generative modeling literature with their adversarial training dynamics. Variational inference remains largely the province of Bayesian machine learning, focused on posterior approximation. Reinforcement learning pursues optimal control through policy gradients and value function estimation. These communities publish in separate venues, employ distinct mathematical notations, and rarely transfer algorithmic innovations across domain boundaries.

Yet a 2019 paper by Casey Chu, Jose Blanchet, and Peter Glynn, titled Probability Functional Descent: A Unifying Perspective on GANs, Variational Inference, and Reinforcement Learning, challenges this compartmentalization. The authors demonstrate that these three domains are instances