  This paper proposes an online learning method of Gaussian process state-space
model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that
represents unknown state transition and/or measurement models as Gaussian
processes (GPs). While the majority of prior literature on learning of GP-SSM
are focused on processing a given set of time series data, data may arrive and
accumulate sequentially over time in most dynamical systems. Storing all such
sequential data and updating the model over entire data incur large amount of
computational resources in space and time. To overcome this difficulty, we
propose a practical method, termed \textit{onlineGPSSM}, that incorporates
stochastic variational inference (VI) and online VI with novel formulation. The
proposed method mitigates the computational complexity without catastrophic
forgetting and also support adaptation to changes in a system and/or a real
environments. Furthermore, we present application of onlineGPSSM into the
reinforcement learning (RL) of partially observable dynamical systems by
integrating onlineGPSSM with Bayesian filtering and trajectory optimization
algorithms. Numerical examples are presented to demonstrate applicability of
the proposed method.
