How Much Regularization Survives Averaging? Update Masking in Federated Learning

Federated learning (FL) enables collaborative model training without sharing raw data, but its performance degrades under non-IID data and stochastic client participation. Remedies built on classical Federated Averaging (FedAvg) typically presuppose that client participation probabilities are known to the server, which is rarely the case in deployed systems. We first discuss and then characterize the optimization problem that \emph{distributionally agnostic} FedAvg actually solves when participation is entirely unknown, possibly highly skewed, and of variable size across rounds: uniform aggregation is shown to minimize a well-defined stochastic objective, weighted by the participation-induced marginal, at a standard $\mathcal{O}(1/\sqrt{T})$ rate for convex and possibly nonsmooth losses. Building on this characterization, we propose \emph{Federated Risk-Averse Averaging} (\textsc{FedeRage}), a risk-averse extension of FedAvg that embeds the \emph{Conditional Value-at-Risk} (CVaR) into the local objective within a natural distributionally robust optimization (DRO) framework. \textsc{FedeRage} implicitly upweights high-loss and infrequently participating clients while adding only a \emph{single scalar per-client}, and admits an $\mathcal{O}(κ/\sqrt{T})$ rate in which the factor $κ$ is the upper bound on the ``price" of risk aversion. In contrast with aggregation-alignment schemes based on optimal transport, which require the availability distribution as an input, \textsc{FedeRage} remains agnostic to it. Several experiments on three heterogeneous benchmarks indicate consistent improvements over state-of-the-art methods in accuracy, fairness, and convergence speed.

Federated clients that perform several local optimization steps can return parameter displacements with widely different magnitudes. The quadratic regularization of FedProx grows linearly with displacement and therefore offers limited control over the contrast between ordinary and unusually large client movements. We here introduce HiFedProx, which replaces the quadratic penalty with a scale-matched power-type regularizer indexed by $p\geq2$. All powers have the same regularization-gradient magnitude at a reference displacement $R$, while every $p>2$ gives a weaker response below $R$ and a stronger response above it. An exact affine reference calculation shows that increasing $p$ compresses relative displacement disparities, although very large powers approach fixed-radius behavior and increase local curvature. HiFedProx combines this geometry with finite-budget stochastic client optimization and same-minibatch Armijo backtracking. In paired five-seed experiments on a frozen 60-writer FEMNIST subset, a common-parameter study over $p\in\{2,3,4,5,6,7,8\}$ shows similar clean-training performance but substantial gains under composite stress. The lowest moderate- and severe-stress losses occur at $p=7$ and $p=6$, improving over $p=2$ by $11.44\%$ and $23.16\%$, respectively. Although displacement-tail ratios continue to decrease through $p=8$, predictive performance peaks in an intermediate range and Armijo trial cost increases with $p$. These results indicate that the exponent should be calibrated rather than maximized. In our experiments, $p=5$--$7$ provides the most useful range.

Federated learning systems are increasingly deployed to facilitate collaborative model training across a heterogeneous client population. Existing practice mostly implicitly assumes that the aggregated client data distribution is representative of the learner's target distribution or that learning from all available clients is uniformly beneficial for the learner distribution. However, such an assumption often does not hold in reality. Traditional client selection strategies in FL literature largely overlook such misalignment, while most existing work on multi-source transfer learning either requires direct access to local data or uses one-shot model/feature aggregation. In this paper, we take the initiative to understand and mitigate the impacts of such learner-client population misalignment. In particular, we consider the practical setting where the learner keeps a small proxy dataset. We observe that client contributions vary significantly across training rounds, and traditional technology is insufficient to identify beneficial sources under multi-source transfer diversity. Then, we propose a dynamic, influence-aware client selection framework that estimates each client's potential utility to the learner's optimization objective using proxy influence signals on a learner-specific proxy set. Via using leave-one-out evaluations, we prioritize the most informative sources of knowledge while controlling the negative impacts of statistical noise and data heterogeneity. Experiments on CIFAR-10 under heterogeneous data partitions demonstrate that our approach consistently outperforms static and dynamic baselines, achieving faster convergence and higher accuracy.