Information-Theoretic Limits of Scenario-Based Validation for Agentic Artificial Intelligence
TL;DR
This paper formalizes deployment behavior as a random variable over an expansive scenario space and characterize validation as the acquisition of finite information through observed interaction trajectories, and delineates principled boundaries on certifiable claims for agentic AI systems.
Abstract
Validating agentic artificial intelligence systems that operate through long-horizon interaction with complex environments remains a fundamental and unresolved challenge. Contemporary validation practice relies heavily on scenario-based testing, benchmarking, and large-scale simulation, implicitly assuming that sufficient scenario coverage can approximate the system’s operational behavior. This paper challenges that assumption by framing validation as an inference problem under bounded information and analyzing its limits from an information-theoretic perspective. We formalize deployment behavior as a random variable over an expansive scenario space and characterize validation as the acquisition of finite information through observed interaction trajectories. Under minimal and realistic assumptions, we show that the entropy of the scenario space grows rapidly with interaction horizon, while the information obtainable through finite validation is strictly bounded. As a consequence, exhaustive scenario coverage and complete validation guarantees are, in general, information-theoretically impossible for agentic AI systems. We further demonstrate that empirical coverage metrics may diverge from epistemic certainty, leading to increasing apparent validation confidence without proportional reduction in residual uncertainty. To address these limits constructively, we identify conditions under which scope-limited, conditional guarantees remain attainable when validation is restricted to explicitly defined scenario classes. Theory-confirming empirical illustrations are provided to demonstrate the saturation of validation capacity and the persistence of uncertainty under increasing validation effort. The results delineate principled boundaries on certifiable claims for agentic AI systems, while also clarifying the conditions under which validation evidence remains epistemically interpretable, evaluation, and governance practices.