  Predictive state representations (PSRs) offer an expressive framework for
modelling partially observable systems. By compactly representing systems as
functions of observable quantities, the PSR learning approach avoids using
local-minima prone expectation-maximization and instead employs a globally
optimal moment-based algorithm. Moreover, since PSRs do not require a
predetermined latent state structure as an input, they offer an attractive
framework for model-based reinforcement learning when agents must plan without
a priori access to a system model. Unfortunately, the expressiveness of PSRs
comes with significant computational cost, and this cost is a major factor
inhibiting the use of PSRs in applications. In order to alleviate this
shortcoming, we introduce the notion of compressed PSRs (CPSRs). The CPSR
learning approach combines recent advancements in dimensionality reduction,
incremental matrix decomposition, and compressed sensing. We show how this
approach provides a principled avenue for learning accurate approximations of
PSRs, drastically reducing the computational costs associated with learning
while also providing effective regularization. Going further, we propose a
planning framework which exploits these learned models. And we show that this
approach facilitates model-learning and planning in large complex partially
observable domains, a task that is infeasible without the principled use of
compression.
