Approximate information state for approximate planning and reinforcement learning in partially observed systems
Abstract
We propose a theoretical framework for approximate planning and learning in partially observed systems. Our framework is based on the fundamental notion of information state. We provide two equivalent definitions of information state  i) a function of history which is sufficient to compute the expected reward and predict its next value; ii) equivalently, a function of the history which can be recursively updated and is sufficient to compute the expected reward and predict the next observation. An information state always leads to a dynamic programming decomposition. Our key result is to show that if a function of the history (called approximate information state (AIS)) approximately satisfies the properties of the information state, then there is a corresponding approximate dynamic program. We show that the policy computed using this is approximately optimal with bounded loss of optimality. We show that several approximations in state, observation and action spaces in literature can be viewed as instances of AIS. In some of these cases, we obtain tighter bounds. A salient feature of AIS is that it can be learnt from data. We present AIS based multitime scale policy gradient algorithms. and detailed numerical experiments with low, moderate and high dimensional environments.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 DOI:
 10.48550/arXiv.2010.08843
 arXiv:
 arXiv:2010.08843
 Bibcode:
 2020arXiv201008843S
 Keywords:

 Computer Science  Machine Learning;
 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Optimization and Control
 EPrint:
 83 pages