This work studies the problem of sequential control in an unknown, nonlinear
dynamical system, where we model the underlying system dynamics as an unknown
function in a known Reproducing Kernel Hilbert Space. This framework yields a
general setting that permits discrete and continuous control inputs as well as
non-smooth, non-differentiable dynamics. Our main result, the Lower
Confidence-based Continuous Control ($LC^3$) algorithm, enjoys a near-optimal
$O(\sqrt{T})$ regret bound against the optimal controller in episodic settings,
where $T$ is the number of episodes. The bound has no explicit dependence on
dimension of the system dynamics, which could be infinite, but instead only
depends on information theoretic quantities. We empirically show its
application to a number of nonlinear control tasks and demonstrate the benefit
of exploration for learning model dynamics.

该研究针对未知的非线性动态系统问题，提出了一种基于再生核希尔伯特空间的顺序控制算法，并通过信息理论量来获得近乎最优的遗憾上界，实验结果表明其在多个非线性控制任务中均获得了较好的表现。

在线非线性控制的信息论遗憾界

Information Theoretic Regret Bounds for Online Nonlinear Control

We study the problem of safe learning and exploration in sequential control
problems. The goal is to safely collect data samples from operating in an
environment, in order to learn to achieve a challenging control goal (e.g., an
agile maneuver close to a boundary). A central challenge in this setting is how
to quantify uncertainty in order to choose provably-safe actions that allow us
to collect informative data and reduce uncertainty, thereby achieving both
improved controller safety and optimality. To address this challenge, we
present a deep robust regression model that is trained to directly predict the
uncertainty bounds for safe exploration. We derive generalization bounds for
learning, and connect them with safety and stability bounds in control. We
demonstrate empirically that our robust regression approach can outperform the
conventional Gaussian process (GP) based safe exploration in settings where it
is difficult to specify a good GP prior.

研究在序列控制问题中的安全学习和探索问题，提出了一种深度健壮回归模型来预测安全探索的不确定性界限，证明了该方法在难以指定好的高斯过程先验的情况下优于传统的基于高斯过程的安全探索方法。