Beyond Dirichlet Alpha: Realized Client Heterogeneity for Privacy–Utility–Fairness Evaluation in Federated Learning
Abstract
Abstract Dirichlet concentration parameters are widely used to label statistical heterogeneity in federated learning, but a nominal parameter does not uniquely describe the realized client population. This paper develops a heterogeneity-aware methodology for privacy–utility–fairness evaluation that treats realized client distributions as measured experimental variables. The framework combines quantity imbalance, normalized label entropy, Jensen–Shannon divergence, class coverage, and effective label count with client-level utility and fairness metrics. For symmetric Dirichlet allocation, we derive the expected class-concentration index E[Σkπkc²]=(α+1)/(Kα+1) and show that it is strictly decreasing in α while individual realizations remain random. We further show that Jain’s performance-fairness index is exactly 1/[1+CV(a)²] for nonnegative client accuracies, making explicit why fairness must be interpreted jointly with absolute utility. A controlled five-seed numerical study with 20 clients demonstrates that equal nominal α values still produce nontrivial variation in realized quantity and label structure, and that α changes several heterogeneity dimensions simultaneously. The paper then defines a matched evaluation protocol for FedAvg and FedProx under trusted-server client-level central differential privacy using clipping, Gaussian perturbation, and Rényi differential-privacy accounting. The central result is methodological: privacy–utility–fairness conclusions are more…
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