A. M. Hashemi

Antesh Upadhyay, Sang Bin Moon, Abolfazl Hashemi

We introduce FedSGM, a unified framework for federated constrained optimization that addresses four major challenges in federated learning (FL): functional constraints, communication bottlenecks, local updates, and partial client participation. Building on the switching gradient method, FedSGM provides projection-free, primal-only updates, avoiding expensive dual-variable tuning or inner solvers. To handle communication limits, FedSGM incorporates bi-directional error feedback, correcting the bias introduced by compression while explicitly understanding the interaction between compression noise and multi-step local updates. We derive convergence guarantees showing that the averaged iterate achieves the canonical $\boldsymbol{\mathcal{O}}(1/\sqrt{T})$ rate, with additional high-probability bounds that decouple optimization progress from sampling noise due to partial participation. Additionally, we introduce a soft switching version of FedSGM to stabilize updates near the feasibility boundary. To our knowledge, FedSGM is the first framework to unify functional constraints, compression, multiple local updates, and partial client participation, establishing a theoretically grounded foundation for constrained federated learning. Finally, we validate the theoretical guarantees of FedSGM via experimentation on Neyman-Pearson classification and constrained Markov decision process (CMDP) tasks.

Zhankun Luo, Antesh Upadhyay, Sang Bin Moon et al.

This paper addresses the distributed stochastic minimax optimization problem subject to stochastic constraints. We propose a novel first-order Softmax-Weighted Switching Gradient method tailored for federated learning. Under full client participation, our algorithm achieves the standard $\mathcal{O}(ε^{-4})$ oracle complexity to satisfy a unified bound $ε$ for both the optimality gap and feasibility tolerance. We extend our theoretical analysis to the practical partial participation regime by quantifying client sampling noise through a stochastic superiority assumption. Furthermore, by relaxing standard boundedness assumptions on the objective functions, we establish a strictly tighter lower bound for the softmax hyperparameter. We provide a unified error decomposition and establish a sharp $\mathcal{O}(\log\frac{1}δ)$ high-probability convergence guarantee. Ultimately, our framework demonstrates that a single-loop primal-only switching mechanism provides a stable alternative for optimizing worst-case client performance, effectively bypassing the hyperparameter sensitivity and convergence oscillations often encountered in traditional primal-dual or penalty-based approaches. We verify the efficacy of our algorithm via experiment on the Neyman-Pearson (NP) classification and fair classification tasks.

Deepak Ravikumar, Efstathia Soufleri, Abolfazl Hashemi et al.

Deep Neural Nets (DNNs) have become a pervasive tool for solving many emerging problems. However, they tend to overfit to and memorize the training set. Memorization is of keen interest since it is closely related to several concepts such as generalization, noisy learning, and privacy. To study memorization, Feldman (2019) proposed a formal score, however its computational requirements limit its practical use. Recent research has shown empirical evidence linking input loss curvature (measured by the trace of the loss Hessian w.r.t inputs) and memorization. It was shown to be ~3 orders of magnitude more efficient than calculating the memorization score. However, there is a lack of theoretical understanding linking memorization with input loss curvature. In this paper, we not only investigate this connection but also extend our analysis to establish theoretical links between differential privacy, memorization, and input loss curvature. First, we derive an upper bound on memorization characterized by both differential privacy and input loss curvature. Second, we present a novel insight showing that input loss curvature is upper-bounded by the differential privacy parameter. Our theoretical findings are further empirically validated using deep models on CIFAR and ImageNet datasets, showing a strong correlation between our theoretical predictions and results observed in practice.