SAGE: Optimal-Stopping Peer Selection for Decentralised Federated Learning

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.

Federated Learning enables collaborative model training across decentralized data sources without data transfer. Averaging-based FL is limited by the presence of non-IID data, which negatively impacts convergence speed and final model accuracy. Conventional alternatives suffer from significant inefficiency. Clients with noisy or highly heterogeneous data contribute expensive gradient computations that are either discarded or heavily down-weighted before aggregation. These reactive approaches waste computational resources, require more communication rounds and result in unnecessary privacy exposure. In this paper, we propose a proactive client selection framework that aims to find an optimal federation of clients whose combined data match utility and fairness requirements before training begins. Our method relies on mutual information computed from differentially private contingency tables to quantify the relevance of cross-feature correlations in the union dataset. We introduce a Potential Federation Loss (PFL) over the set of fixed-size federations, which balances two objectives. Maximizing collective data utility while ensuring fair cross-features correlations to prevent group unfairness. Client selection is expressed as an optimal subset search problem over the PFL objective, which we solve using simulated annealing under strong differential privacy guarantees for clients' local statistics. Experimental results on four benchmarks show faster, fairer, and more accurate models trained on optimally found federations, compared to uniform sampling, even when state-of-the-art adaptive aggregation or sampling strategies are employed.

Decentralized federated learning (DFL) removes the central server by letting nodes exchange model updates through peer-to-peer gossip, but existing gossip-based methods often lack provenance finality and resilience to Byzantine or lazy participants. Ledger-assisted federated learning (FL) improves auditability, yet blockchains, shards, or settlement committees can reintroduce global coordination costs that conflict with DFL locality. This paper proposes \emph{gspDAG-FL}, a secure DFL framework that derives consensus from the same gossip history used to disseminate models. Nodes exchange model payloads only with neighbors, while full nodes collect event certificates and receiver-endorsed accepted gossip proofs, reconstruct a compact Topology directed acyclic graph (DAG), and run Hashgraph-style virtual voting followed by compact full-node certificates. Finality is over unique model-origin tuples, not identical local parameter states. To improve resilience, gspDAG-FL combines payload validation, accepted-proof validation, and private semantic audit before aggregation. We formalize the adversarial setting, prove safety and conditional liveness of the control plane, and give a convergence guarantee for certified perturbed gossip under time-varying effective mixing. Experiments on MNIST classification and Penn Treebank language modeling, using fair held-out validation/audit data and networks up to $N=100$, show that gspDAG-FL achieves learning quality close to validation-based ledger FL while reducing coordination bottlenecks, improving throughput, and maintaining high invalid-origin detection under mixed Byzantine and lazy participation.