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

arXiv:2603.01283v2 Announce Type: replace Abstract: Deployed RL agents operate in closed-loop systems where reliable performance depends on maintaining coherent coupling between observations, actions, and outcomes. Current monitoring approaches rely on reward and task metrics, measures that are reactive by design and blind to structural degradation that precedes performance collapse. We argue that deployment monitoring is fundamentally a question about uncertainty resolution: whether the agent's observations and actions continue to reduce uncertainty about outcomes, and whether outcomes constrain what the agent must have done. Information theory directly operationalizes this question, entropy quantifies uncertainty, and mutual information quantifies its resolution across the loop. We introduce Bipredictability (P), the fraction of the total uncertainty budget converted into shared predictability across the observation, action, outcome loop. A theoretical property is a provable classical upper bound P is less than or equal to 0.5, independent of domain, task, or agent, a structural consequence of Shannon entropy rather than an empirical observation. When agency is present, a penalty suppresses P strictly below this ceiling, confirmed at P equals 0.33 across trained agents. To operationalize P as a real time monitoring signal, we introduce the Information Digital Twin (IDT), an auxiliary architecture that computes P and its directional components from the observable interaction stream without access to model internals. Across 168 perturbation trials spanning eight perturbation types and two policy architectures, IDT based monitoring detected 89.3 percent of coupling degradations versus 44.0 percent for reward based monitoring, with 4.4 times lower median latency. These results establish Bipredictability as a principled, bounded, and computable prerequisite signal for closed loop self regulation in deployed reinforcement learning systems.