Introduction to Online Control

This book introduces readers with a background in linear algebra to a robust new framework for developing control algorithms. Rather than making probabilistic assumptions about the world, nonstochastic online control provides efficient gradient-based algorithms that can operate in the presence of uncertainty and unforeseeable disturbances.

This tutorial guide introduces online nonstochastic control, an emerging paradigm in control of dynamical systems and differentiable reinforcement learning that applies techniques from online convex optimization and convex relaxations to obtain new methods with provable guarantees for classical settings in optimal and robust control. In optimal control, robust control, and other control methodologies that assume stochastic noise, the goal is to perform comparably to an offline optimal strategy. In online control, both cost functions and perturbations from the assumed dynamical model are chosen by an adversary. Thus, the optimal policy is not defined a priori and the goal is to attain low regret against the best policy in hindsight from a benchmark class of policies. The resulting methods are based on iterative mathematical optimization algorithms and are accompanied by finite-time regret and computational complexity guarantees. This book is ideal for graduate students and researchers interested in bridging classical control theory and modern machine learning.