A Bayesian Rule for Adaptive Control based on Causal Interventions
Pedro A. Ortega, Daniel A. Braun · 2010
Explaining adaptive behavior is a central problem in artificial intelligence research.Here we formalize adaptive agents as mixture distributions over sequences of inputs and outputs (I/O).Each distribution of the mixture constitutes a 'possible world', but the agent does not know which of the possible worlds it is actually facing.The problem is to adapt the I/O stream in a way that is compatible with the true world.A natural measure of adaptation can be obtained by the Kullback-Leibler (KL) divergence between the I/O distribution of the true world and the I/O distribution expected by the agent that is uncertain about possible worlds.In the case of pure input streams, the Bayesian mixture provides a well-known solution for this problem.We show, however, that in the case of I/O streams this solution breaks down, because outputs are issued by the agent itself and require a different probabilistic syntax as provided by intervention calculus.Based on this calculus, we obtain a Bayesian control rule that allows modeling adaptive behavior with mixture distributions over I/O streams.This rule might allow for a novel approach to adaptive control based on a minimum KLprinciple.