The Informational Cost of Agency: A Bounded Measure of Interaction Efficiency for Deployed Reinforcement Learning

TL;DR

This paper introduces Bipredictability, a new information-theoretic metric to quantify the efficiency of interaction in reinforcement learning systems, revealing an inherent informational cost of agency.

Contribution

The paper proposes Bipredictability (P), a formal measure of interaction efficiency, and demonstrates its applicability across diverse systems, providing a new tool for runtime reliability in autonomous agents.

Findings

Bipredictability P is bounded below 0.5, confirming the informational cost of agency.

Empirical results show P ≈ 0.33 in trained agents, matching theoretical predictions.

IDT detects 89.3% of coupling degradations with lower latency than reward-based methods.

Abstract

Deployed reinforcement learning systems lack a principled runtime reliability theory. We close this gap by introducing Bipredictability, P, a closed form information theoretic metric that quantifies how efficiently a closed loop interaction between agent and environment converts uncertainty into shared predictability. P admits a provable classical bound P equal, smaller than 0.5, derived from Shannon entropy subadditivity, and responsive agency necessarily suppresses P below this ceiling, a structural prediction we term the informational cost of agency. Across 21 trained continuous control agents, we confirm this prediction empirically at P = 0.33 plus minus 0.02. The same suppression signature reproduces in language model dialogue, convolutional vision systems, and classical mechanical baselines, indicating that P captures a substrate independent property of agentic interaction rather than an algorithm specific artifact. The Information Digital Twin, IDT, a model agnostic architecture that computes P from the external interaction stream, detects 89.3% of coupling degradations against 44.0% for reward based monitoring, with 4.4 times lower latency. P provides the missing measurement layer for runtime reliability and closed loop self regulation in deployed autonomous systems.