Regret Bounds for Adaptive Nonlinear Control
We study the problem of adaptively controlling a known discrete-time nonlinear system subject to unmodeled disturbances. We prove the first finite-time regret bounds for adaptive nonlinear control with matched uncertainty in the stochastic setting, showing that the regret suffered by certainty equivalence adaptive control, compared to an oracle controller with perfect knowledge of the unmodeled disturbances, is upper bounded by $\widetilde{O}(\sqrt{T})$ in expectation. Furthermore, we show that when the input is subject to a $k$ timestep delay, the regret degrades to $\widetilde{O}(k \sqrt{T})$. Our analysis draws connections between classical stability notions in nonlinear control theory (Lyapunov stability and contraction theory) and modern regret analysis from online convex optimization. The use of stability theory allows us to analyze the challenging infinite-horizon single trajectory setting.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Adaptive Regret for Control of Time-Varying Dynamics
We consider the problem of online control of systems with time-varying linear dynamics. This is a general formulation that is motivated by the use of local linearization in control of nonlinear dynamical systems. To stat…
Online Stackelberg Optimization via Nonlinear Control
In repeated interaction problems with adaptive agents, our objective often requires anticipating and optimizing over the space of possible agent responses. We show that many problems of this form can be cast as instances…
Logarithmic Regret for Nonlinear Control
We address the problem of learning to control an unknown nonlinear dynamical system through sequential interactions. Motivated by high-stakes applications in which mistakes can be catastrophic, such as robotics and healt…
continuous-controlContinuous ControlSmart Predict-Then-Control: Integrating identification and control via decision regret
This paper presents Smart Predict-Then-Control (SPC) framework for integrating system identification and control. This novel SPC framework addresses the limitations of traditional methods, the unaligned modeling error an…
Finite Time Regret Bounds for Minimum Variance Control of Autoregressive Systems with Exogenous Inputs
Minimum variance controllers have been employed in a wide-range of industrial applications. A key challenge experienced by many adaptive controllers is their poor empirical performance in the initial stages of learning. …