Iterative Linearized Control: Stable Algorithms and Complexity Guarantees

TL;DR

This paper analyzes gradient-based algorithms for nonlinear control, linking their complexity to dynamic programming oracles, and introduces a regularized Gauss-Newton method with theoretical guarantees and practical improvements.

Contribution

It provides a complexity analysis framework for control algorithms and proposes a new regularized Gauss-Newton method with proven bounds and better convergence.

Findings

Complexity bounds relate to dynamic programming oracles.

Proposed Gauss-Newton algorithm has worst-case complexity guarantees.

Software implementation available in PyTorch.

Abstract

We examine popular gradient-based algorithms for nonlinear control in the light of the modern complexity analysis of first-order optimization algorithms. The examination reveals that the complexity bounds can be clearly stated in terms of calls to a computational oracle related to dynamic programming and implementable by gradient back-propagation using machine learning software libraries such as PyTorch or TensorFlow. Finally, we propose a regularized Gauss-Newton algorithm enjoying worst-case complexity bounds and improved convergence behavior in practice. The software library based on PyTorch is publicly available.