Certified Task-Conditioned Active Observability

2026-09-21

AI Summary

This study addresses the decision-making challenge for autonomous agents that must passively observe indistinguishable states in unobservable physical systems where interaction is costly. To this end, it proposes a task-conditioned active observability complexity framework. Methodologically, the work constructs minimal sufficient quotient spaces and optimal distinguishing trees, introducing a martingale certificate mechanism to compose risk bounds without independence assumptions. Furthermore, by integrating Bellman recursion with adaptive probing strategies, it establishes a phased certified observer architecture. Experimental results demonstrate that the proposed approach achieves certified state recovery with a zero false-acceptance rate in high-dimensional systems, significantly reducing both sensor reading frequency and computational overhead.

Abstract

Before acting upon an unobservable physical system, an autonomous agent must determine which latent distinctions govern downstream tasks, how many active interventions are necessary to certify them, and when to abstain to prevent catastrophic errors. Classical observability treats state reconstruction as an unconditioned binary predicate, failing when passive observations cannot break latent degeneracies without perturbation, full microscopic inversion is prohibitively costly, and distinguishing task-irrelevant degrees of freedom wastes interaction budgets. We formalize task-conditioned active observability complexity: the minimum worst-case expected interaction cost required to identify task-relevant states under certified error and safe abstention guarantees. We prove that task-predictive equivalence induces the unique minimal sufficient quotient $\mathcal{H}/\!\sim_τ$, leaving active observability complexity strictly invariant while eliminating superfluous distinctions. In deterministic regimes, this complexity is characterized by an optimal adaptive distinguishing tree and Bellman recursion; in noisy regimes, it obeys a stopped-transcript relative-entropy lower bound and adaptive martingale certificates that compose without independence assumptions. We instantiate a prospective certified observer with staged recovery: a nominal verifier defers candidate compilation, triggering active probing only upon evidence, while a history-measurable score shell prunes hypotheses without sacrificing risk bounds. Stress audits across high-dimensional physical systems and thousands of operational trials demonstrate certified state recovery with zero false acceptances and substantial reductions in sensor reads and model steps.

Problem

• active observability
• task-conditioned
• autonomous agent
• interaction cost
• unobservable physical system

Innovation

• Task-Conditioned Active Observability
• Minimal Sufficient Quotient
• Adaptive Martingale Certificates
• Certified Observer
• Safe Abstention