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.

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The best-fit Gaussian distribution is denoted with adashed line.

In this paper, we take a step toward narrowing the gap between model-based and model-free RL methods.

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Whiletheoretical results havebeen obtained for their heavy-tailedness, the full characterization of the prior predictive distribution (i.e. its density, CDF andmoments), remained unknownpriortothiswork.

Our approach leads to better use of hardware resources.

We also develop a new auto-encoding algorithm that finds a latent space to disentangle latent input coordinates intowell-separated clusters, which isamenable tooursample complexityanalysis.

Figure 5: Left: Visualizationofthe Motorcyclesimulator. Right: Performanceacross 10 runs 1 standarddeviation.

Intheoriginalformulation, observations are assumed to be exact (non-noisy), so the GP likelihood only included a small observation noise σ2obs for numerical stability [32].