Controllable Information Production

Intrinsic Motivation (IM) is a paradigm for generating intelligent behavior without external utilities. The existing information-theoretic methods for IM are predominantly based on information transmission, which explicitly depends on the designer's choice of which random variables engage in transmission. In this work, we introduce a novel IM principle, Controllable Information Production (CIP), that avoids both external utilities and designer-specified variables. We derive the CIP objective from Optimal Control, showing a connection between extrinsic and intrinsic behaviors. CIP appears as the gap between open-loop and closed-loop Kolmogorov-Sinai entropies, which simultaneously rewards the pursuit and regulation of chaos. We establish key theoretical properties of CIP and demonstrate its effectiveness on standard IM benchmarks.