A Lower Bound on the Guaranteed Tolerance for a Latent Target Quantity in Closed Management Loops of Autonomous Electronic Communication Networks
Year: 2026
Type: preprint
Abstract: Autonomy-level scales for electronic communication networks (ECN) define the level by the degree to which the operational cycle is delegated to the system. They impose no condition on the nature of the target quantity of a closed loop. Yet some targets of autonomous loops are latent: they cannot be recovered uniquely even from exact values of all observations available to the loop and with exact knowledge of the network state. Examples are perceived quality, the trustworthiness of a strategic counterparty, and the catastrophic tail of losses. For a loop in which the target depends affinely on a latent component, we derive a lower bound on the guaranteed band of target values: the product of the target's sensitivity to the latent component and the width of the section of the component's identification region at a given state. The bound holds for any deterministic or randomized policy, including active probing, and does not require the latent component to be independent of the state. A necessary condition for guaranteed keeping of the target within a tolerance follows. If no channel of the loop identifies the target under the assumptions accepted by the field, and the necessary condition is violated, then no guarantee is possible within the existing channels, policies, controls and assumptions. It can be restored only by a change of the problem data of one of three kinds: a new source of information about the latent component; robust design without such information; a change of the requirement. For partial and delayed identification, quantitative necessary conditions are obtained. The statements are verified by computations that are bit-for-bit reproducible on three computing platforms. On an illustrative model the computations exhibit two possible applied dependencies: training an estimator on the proxy under an unidentified target may worsen the guarantee; the average quality of keeping may mask a systematic violation of the tolerance. As examples of application, a classification of nine subsystems of autonomous ECN with a latent target by identifiability rung is given – a snapshot of the author's research as of 2026-10-04. Practical significance: before a loop is deployed, the result makes it possible to check whether tuning within the existing channels can give a guarantee and, if not, to choose a remedy by quantitative thresholds. It also sets a bound on the delay of the reporting channel and warns against acceptance criteria based on averages. The preprint is deposited in two language versions: Ukrainian (master text) and English. Formula numbers, notation and numerical values coincide; if the versions diverge, the Ukrainian version prevails. The main title of the record is English for discoverability. The archive PP-1_code.zip contains the verification code (MIT), its reference results on three platforms (CC BY 4.0) and a README with checksums and the run command. Declaration on artificial intelligence. Artificial intelligence tools were used for searching and verifying sources, for linguistic and stylistic editing, for formatting the text in accordance with the requirements of the publication and for writing the code of the computational verification (Section 6) to the author's specification. They did not affect the problem statement, the statements or their proofs.
Author: Vakulenko, Oleksandr
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225316400