Modeling Context in Cognition Using Variational Inequalities

Important aspects of human cognition, like creativity and play, involve dealing with multiple divergent views of objects, goals, and plans. We argue in this paper that the current model of optimization that drives much of modern machine learning research is far too restrictive a paradigm to mathematically model the richness of human cognition. Instead, we propose a much more flexible and powerful framework of equilibration, which not only generalizes optimization, but also captures a rich variety of other problems, from game theory, complementarity problems, network equilibrium problems in economics, and equation solving. Our thesis is that creative activity involves dealing not with a single objective function, which optimization requires, but rather balancing multiple divergent and possibly contradictory goals. Such modes of cognition are better modeled using the framework of variational inequalities (VIs). We provide a brief review of this paradigm for readers unfamiliar with the underlying mathematics, and sketch out how VIs can account for creativity and play in human and animal cognition.