The Gaussian process state space model (GPSSM) is a non-linear dynamical
system, where unknown transition and/or measurement mappings are described by
GPs. Most research in GPSSMs has focussed on the state estimation problem,
i.e., computing a posterior of the latent state given the model. However, the
key challenge in GPSSMs has not been satisfactorily addressed yet: system
identification, i.e., learning the model. To address this challenge, we impose
a structured Gaussian variational posterior distribution over the latent
states, which is parameterised by a recognition model in the form of a
bi-directional recurrent neural network. Inference with this structure allows
us to recover a posterior smoothed over sequences of data. We provide a
practical algorithm for efficiently computing a lower bound on the marginal
likelihood using the reparameterisation trick. This further allows for the use
of arbitrary kernels within the GPSSM. We demonstrate that the learnt GPSSM can
efficiently generate plausible future trajectories of the identified system
after only observing a small number of episodes from the true system.

本文介绍了 Gaussian 过程状态空间模型，并探讨最大的挑战 —— 系统识别，提出了基于双向循环神经网络的结构化高斯变分后验分布来处理推断问题，并使用重参数化技巧有效计算边缘似然的下界，可以在观察到真实系统的少量数据后生成可信赖的未来轨迹。

高斯过程状态空间模型的识别

Identification of Gaussian Process State Space Models

This paper considers linear-quadratic control of a non-linear dynamical
system subject to arbitrary cost. I show that for this class of stochastic
control problems the non-linear Hamilton-Jacobi-Bellman equation can be
transformed into a linear equation. The transformation is similar to the
transformation used to relate the classical Hamilton-Jacobi equation to the
Schr\"odinger equation. As a result of the linearity, the usual backward
computation can be replaced by a forward diffusion process, that can be
computed by stochastic integration or by the evaluation of a path integral. It
is shown, how in the deterministic limit the PMP formalism is recovered. The
significance of the path integral approach is that it forms the basis for a
number of efficient computational methods, such as MC sampling, the Laplace
approximation and the variational approximation. We show the effectiveness of
the first two methods in number of examples. Examples are given that show the
qualitative difference between stochastic and deterministic control and the
occurrence of symmetry breaking as a function of the noise.

本文讨论了非线性动态系统的线性二次控制问题，并将其转化为线性方程。通过使用路径积分方法，解决了传统反向计算的问题，并给出了路径积分方法的有效计算方法，如 MC 抽样、Laplace 逼近和变分逼近。通过例子来说明了随机和确定性控制的区别以及噪声的对称性破坏现象的发生。