Spectral Learning from a Single Trajectory under Finite-State Policies

Borja Balle 1 Odalric-Ambrym Maillard 2
2 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : We present spectral methods of moments for learning sequential models from a single trajec-tory, in stark contrast with the classical literature that assumes the availability of multiple i.i.d. trajectories. Our approach leverages an efficient SVD-based learning algorithm for weighted au-tomata and provides the first rigorous analysis for learning many important models using dependent data. We state and analyze the algorithm under three increasingly difficult scenarios: proba-bilistic automata, stochastic weighted automata, and reactive predictive state representations controlled by a finite-state policy. Our proofs include novel tools for studying mixing properties of stochastic weighted automata.
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https://hal.archives-ouvertes.fr/hal-01590940
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Submitted on : Wednesday, September 20, 2017 - 2:44:29 PM
Last modification on : Friday, March 22, 2019 - 1:34:36 AM

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Borja Balle, Odalric-Ambrym Maillard. Spectral Learning from a Single Trajectory under Finite-State Policies. International conference on Machine Learning, Jul 2017, Sidney, France. ⟨hal-01590940⟩

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