Shallow Probes Are Sufficient for Near-Oracle Personalization Depth Allocation in Federated Learning

Overview & Synopsis

Rather than proposing a new federated optimizer, we study whether a small client-specific measurement budget can support cost-aware personalization-depth decisions under a utility that trades Macro-F1 against deployment cost. Exhaustive evaluation of six depths defines an offline oracle that is not deployable. We audit the Probe Sufficiency Hypothesis: three shallow probes (P0--P2) may contain most decision-relevant information for approaching that oracle. FedPBA is a secondary learned instantiation for deep-action extrapolation. On CIFAR-10/100 and patient-disjoint PTB-XL (45 sessions; 900 clients; 2700 evaluations; GroupKFold), training-free greedy probing achieves regret 0.0071 and 98.3 percent oracle recovery, beating metadata-only policies and FedPBA (0.0110 / 97.3 percent). Aggregate shallow-best versus oracle correlation is 0.9818 but falls to 0.578 on deep-oracle rows; PTB-XL deep-oracle cases remain a high-regret boundary without a validated escalation gate.