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Combining Memory and Landmarks with Predictive State Representations

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.