We tackle the problem of Non-stochastic Control with the aim of obtaining
algorithms that adapt to the controlled environment. Namely, we tailor the FTRL
framework to dynamical systems where the existence of a state, or equivalently
a memory, couples the effect of the online decisions. By designing novel
regularization techniques that take the system's memory into consideration, we
obtain controllers with new sub-linear data adaptive policy regret bounds.
Furthermore, we append these regularizers with untrusted predictions of future
costs, which enables the design of the first Optimistic FTRL-based controller
whose regret bound is adaptive to the accuracy of the predictions, shrinking
when they are accurate while staying sub-linear even when they all fail.

我们通过设计新的正则化技术，并将其与未经验证的未来成本预测相结合，实现了自适应于环境的 Non-stochastic Control 算法，这些算法通过考虑系统的内存具有新的数据自适应策略回归界限，并能在准确预测时收缩，即使全部失败时仍保持次线性。

自适应在线非随机控制

Adaptive Online Non-stochastic Control

We consider the problem of controlling a possibly unknown linear dynamical
system with adversarial perturbations, adversarially chosen convex loss
functions, and partially observed states, known as non-stochastic control. We
introduce a controller parametrization based on the denoised observations, and
prove that applying online gradient descent to this parametrization yields a
new controller which attains sublinear regret vs. a large class of closed-loop
policies. In the fully-adversarial setting, our controller attains an optimal
regret bound of $\sqrt{T}$-when the system is known, and, when combined with an
initial stage of least-squares estimation, $T^{2/3}$ when the system is
unknown; both yield the first sublinear regret for the partially observed
setting.
Our bounds are the first in the non-stochastic control setting that compete
with \emph{all} stabilizing linear dynamical controllers, not just state
feedback. Moreover, in the presence of semi-adversarial noise containing both
stochastic and adversarial components, our controller attains the optimal
regret bounds of $\mathrm{poly}(\log T)$ when the system is known, and
$\sqrt{T}$ when unknown. To our knowledge, this gives the first end-to-end
$\sqrt{T}$ regret for online Linear Quadratic Gaussian controller, and applies
in a more general setting with adversarial losses and semi-adversarial noise.

本文研究非随机控制问题，提出了一种基于降噪观测值的控制器参数化方法，通过在线梯度下降方法得到一个新的控制器，其对一类闭环策略实现了次线性遗憾，为非随机控制领域中第一个可以与所有线性稳定动态控制器竞争的遗憾界。