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Predictive State Representations (PSRs) are an expressive class of models forcontrolled stochastic processes. PSRs represent state as a set of predictionsof future observable events. Because PSRs are defined entirely in terms ofobservable data, statistically consistent estimates of PSR parameters can belearned efficiently by manipulating moments of observed training data. Mostlearning algorithms for PSRs have assumed that actions and observations arefinite with low cardinality. In this paper, we generalize PSRs to infinite setsof observations and actions, using the recent concept of Hilbert spaceembeddings of distributions. The essence is to represent the state as anonparametric conditional embedding operator in a Reproducing Kernel HilbertSpace (RKHS) and leverage recent work in kernel methods to estimate, predict,and update the representation. We show that these Hilbert space embeddings ofPSRs are able to gracefully handle continuous actions and observations, andthat our learned models outperform competing system identification algorithmson several prediction benchmarks.

Hilbert Space Embeddings of Predictive State Representations