Convergence of Bayesian Control Rule

TL;DR

This paper proves the convergence of the Bayesian control rule, a new adaptive control method based on relative entropy minimization, under ergodicity and consistency assumptions.

Contribution

It provides the first rigorous proof of convergence for the Bayesian control rule, establishing its theoretical validity.

Findings

Proves convergence under boundedness and consistency assumptions

Establishes the Bayesian control rule as a reliable adaptive control method

Links the rule to relative entropy minimization principles

Abstract

Recently, new approaches to adaptive control have sought to reformulate the problem as a minimization of a relative entropy criterion to obtain tractable solutions. In particular, it has been shown that minimizing the expected deviation from the causal input-output dependencies of the true plant leads to a new promising stochastic control rule called the Bayesian control rule. This work proves the convergence of the Bayesian control rule under two sufficient assumptions: boundedness, which is an ergodicity condition; and consistency, which is an instantiation of the sure-thing principle.