PROSE: A Theory of Optimal Stopping with Perishable Evidence for Peer Selection in Intermittently Connected Decentralised Learning

2026-09-20

AI Summary

本文针对去中心化学习中因连接间歇性导致的同伴选择问题，提出了一种基于过期证据的最优停止理论PROSE，通过有限视野马尔可夫最优停止模型来解决。

Abstract

Decentralised federated learning removes the aggregation server but makes collaboration dependent on transient peer availability. In mobile and intermittently connected systems, evaluating a promising peer consumes contact time and may cause the exchange opportunity itself to vanish, so that the evidence a learner gathers about a peer is perishable: it decays because links expire and because peer models drift while old measurements age. This paper develops a self-contained theory of optimal stopping for the resulting peer-selection problem. We formalise a receiver's within-contact decision as a finite-horizon Markov optimal-stopping problem with costly information acquisition and a future-arrival outside option, and prove that it admits an optimal policy characterised by a reservation value (Snell-envelope structure). Around this formulation we prove: (i) stage-uniform, drift-aware concentration and a maximin certification rule that is correct with high probability together with a finite-sample identification bound; (ii) a mobility-aware value of-information stopping rule and comparative statics showing that higher link hazard lowers the value of continued probing and enlarges the stopping region; (iii) a closed-form value of waiting under marked-Poisson contact arrivals, together with a search-theoretic reservation value whose comparative statics we characterise; and (iv) a myopic-optimality theorem establishing that, in sufficiently volatile (monotone) mobility regimes, the one-step confidence-safe rule is a sound surrogate for the optimal policy and never stops prematurely. We instantiate the theory as PROSE (Perishable-evidence Reservation-value Optimal Stopping for Exchange), a lightweight, fully local policy, and delineate the static contact and drift-free limits in which classical sequential decision problems are recovered. The development is entirely analytical.

Problem

• Decentralised Federated Learning
• Peer Selection
• Optimal Stopping
• Perishable Evidence
• Intermittently Connected Systems

Innovation

• Optimal Stopping
• Perishable Evidence
• Decentralised Learning
• Markov Decision Process
• Reservation Value