Action-Directed Information for Distributed Control and Agentic Interaction

Distributed intelligence concerns systems in which semi-autonomous components with local dynamics and partial observations coordinate through information exchange to maintain a shared function. This paper proposes an operational way to study such systems: measure information at the interface where a message changes a receiving action, then connect that measure to function by intervention and disturbance evaluation. We instantiate this proposal in DI-Walker, a two-dimensional four-limb embodied plant controlled by frozen Cross-Entropy-Method policies. We compare a controller using each limb's own realized-force sensor with one using the realized-force sensors of peer limbs. Under limb loss, limb slip, and weak central-control dropout, Peer-Sensor has lower late tracking error in several conditions. A corrected finite-history action-predictive estimator shows a substantially larger peer-message gain under compound failure. A future scalar functional-prediction estimator does not show the same stable advantage. We interpret this discrepancy as a methodological result: information useful for an intermediate control action can be hidden by later plant dynamics, redundancy, and context. The paper relates this result to Predictive Information, Transfer Entropy, Directed Information, information-to-go/IT-PAC ideas, empowerment, and the robust control data-rate perspective, while explicitly distinguishing operational predictive gains from exact Directed Information, channel capacity, and a formal data-rate theorem.