Online Convex Programming and regularization in adaptive control

Online Convex Programming (OCP) is a recently developed model of sequential decision-making in the presence of time-varying uncertainty. In this framework, a decision-maker selects points in a convex feasible set to respond to a dynamically changing sequence of convex cost functions. A generic algorithm for OCP, often with provably optimal performance guarantees, is inspired by the Method of Mirror Descent (MD) developed by Nemirovski and Yudin in the 1970´s. This paper highlights OCP as a common theme in adaptive control, both in its classical variant based on parameter tuning and in a more modern supervisory approach. Specifically, we show that: (1) MD leads to a generalization of classical adaptive control schemes based on recursive parameter tuning; (2) A supervisory controller switching policy that uses OCP to estimate system parameters from a sequence of appropriately regularized output prediction errors can flexibly adapt to presence or absence of output disturbances in the system.