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

arXiv: https://arxiv.org/abs/2609.23845 · HTML: https://mlsanity.com/paper/2609.23845/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 20 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Decentralized Federated Learning via Mutual Knowledge Transfer](https://mlsanity.com/paper/2012.13063/) (2020)
- [Mobility-Aware Decentralized Federated Learning with Joint Optimization of Local Iteration and Leader Selection for Vehicular Networks](https://mlsanity.com/paper/2503.06443/) (2025)
- [DACFL: Dynamic Average Consensus Based Federated Learning in Decentralized Topology](https://mlsanity.com/paper/2111.05505/) (2021)

## Abstract (arXiv)

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.