Network Economics, Variational Inequalities and Deep Learning

Abstract

Increasingly, much work in AI – from machine learning and natural language processing to planning, perception, and robotics – is based on classical (continuous) optimization. While this foundation has proved to be of considerable practical utility, the increasingly decentralized and networked nature of computation in the 21st century, implies that classical optimization may prove increasingly restrictive, as AI tackles applications that involve massively large networked environments, where data is stored heterogeneously in the “cloud”, and computation involves balancing multiple competing objectives, including cost, privacy, reliability, and security. The aim of this tutorial is to present an elegant mathematical formalism for solving large games that has been extensively studied in network economics, but so far, has not yet played a major role in multiagent AI. The framework is based on variational inequalities, a formalism that extends classical optimization to vector fields. We use a variety of real-world problems, from modeling traffic flow to content distribution on the Internet and green supply chains in sustainable manufacturing, to illustrate the power of this formalism. We also show that work in deep learning on generative adversarial networks results in complex network dynamics, and can be profitably studied this framework. The tutorial will introduce all the necessary mathematics, and should be of interest to AAMAS researchers from a wide variety of backgrounds.