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.
Predictive state representations (PSRs) are a recently proposed way of modeling controlled dynamical systems. PSR-based models use predictions of observable outcomes of tests that could be done on the system as their state representation, and have model parameters that define how the predictive state representation changes over time as actions are taken and observations noted. Learning PSR-based models requires solving two subproblems: 1) discovery of the tests whose predictions constitute state, and 2) learning the model parameters that define the dynamics. So far, there have been no results available on the discovery subproblem while for the learning subproblem an approximate-gradient algorithm has been proposed (, 2003) with mixed results (it works on some domains and not on others). In this paper, we provide the first discovery algorithm and a new learning algorithm for linear PSRs for the special class of controlled dynamical systems that have a reset operation. We provide experimental verification of our algorithms. Finally, we also distinguish our work from prior work by Jaeger (2000) on observable operator models (OOMs). It has recently been proposed that it is advantageous to have models of dynamical systems be based solely on observable quantities. Predictive state representations (PSRs) are a type of model that uses predictions about future observations to capture the state of a dynamical system. However, PSRs do not use memory of past observations. We propose a model called memory-PSRs that uses both memories of the past, and predictions of the future. We show that the use of memories provides a number of potential advantages. It can reduce the size of the model (in comparison to a PSR model). In addition many dynamical systems have memories that can serve as landmarks that completely determine the current state. The detection and recognition of landmarks is advantageous because they can serve to reset a model that has gotten off-track, as often happens when the model is learned from samples. This paper develops both memory-PSRs and the use and detection of landmarks.