Summary
In networks where devices connect briefly and unpredictably, deciding when to stop checking a potential peer for data sharing is tricky because connections can disappear and information gets outdated. The authors develop a mathematical framework to optimally decide when to stop gathering evidence about another device before the connection ends, balancing costs and risks. Their solution accounts for changing connections and drifting data, and provides rules that work well even in volatile mobile environments. This leads to a simple local decision policy for devices that helps them choose peers efficiently in decentralized learning setups.
What this means in practice
- •For mobile network engineers: Optimize timing for peer-to-peer model exchange in mobile networks with unstable connections using a theory-based stopping rule.
- •For distributed system designers: Design decentralized learning systems that decide when to stop probing peers in scenarios with limited and quickly fading data.
A theory result. No direct application yet.
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.