Bayesian Adaptive Control with I/O Streams

A Bayesian Rule for Adaptive Control based on Causal Interventions

We formalize adaptive agents as mixture distributions over sequences of inputs and outputs (i/o).Each distribution of the mixtureconstitutes a `possible world', but the agent does not know which of the `possible worlds' it is actually facing.The problem is to adapt the stream in a way that is compatible with the true world.We show that in the case of pure inputstreams, the bayesian mixture provides a well-known solution for this problem.We show, however, that in the case of pure inputstreams this solution breaks down, because outputs are issued by the agent itself and require a different probabilistic syntax as provided by intervention calculus.We obtain a bayesian control rule that allows modeling adaptive behavior with mixture distributions over streams of inputs and outputs.This rule might allow for a novel approach to adaptive control based on a minimum kl-principle.