Information-Theoretic Viewpoints on Optimal Causal Coding-Decoding Problems

—In this paper we consider an interacting two-agent sequential decision-making problem consisting of a Markov source process, a causal encoder with feedback, and a causal decoder. Motivated by a desire to foster links between control and information theory, we augment the standard formulation by considering general alphabets and a cost function operating on current and previous symbols. Using dynamic programming, we provide a structural result whereby an optimal scheme exists that operates on appropriate sufficient statistics. We emphasize an example where the decoder alphabet lies in a space of beliefs on the source alphabet, and the additive cost function is a log likelihood ratio pertaining to sequential information gain. We also consider the inverse optimal control problem, where a fixed encoder/decoder pair satisfying statistical conditions is shown to be optimal for some cost function, using probabilistic matching. We provide examples of the applicability of this framework to...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Siva K. Gorantla, Todd P. Coleman
• Keywords: CORR 2011, Cost Function, Education, Inverse Optimal Control, Two-agent Sequential Decision-making