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Federated Learning (FL) is a promising distributed machine learning framework that emphasizes privacy protection. However, inconsistencies between local optimization objectives and the global objective, commonly referred to as client drift, primarily arise due to non-independently and identically distributed (Non-IID) data, multiple local training steps, and partial client participation in training. The majority of current research tackling this challenge is mainly based on the empirical risk minimization (ERM) principle, while giving little consideration to the connection between the global loss landscape and generalization capability. This study proposes FedGAM, an innovative FL algorithm that incorporates Gradient Norm-Aware Minimization (GAM) to efficiently search for a local flat landscape. FedGAM specifically modifies the client model training objective to simultaneously minimize the loss value and first-order flatness, thereby seeking flat minima. To directly smooth the global flatness, we propose the more significant FedGAM-CV, which employs control variables to correct local updates, guiding each client to train models in a globally flat direction. Experiments on three datasets (CIFAR-10, MNIST, and FashionMNIST) demonstrate that our proposed algorithms outperform existing FL baselines, effectively finding flat minima and addressing the client drift problem. [ABSTRACT FROM AUTHOR]

We propose and study the M p UFLP (universal facility location problem in the p -th power of metric space) in this paper, where the universal facility location problem (UFLP) extends several classical facility location problems like the uncapacitated facility location, hard-capacitated facility location, soft-capacitated facility location, incremental-cost facility location, concave-cost facility location, etc. In UFLP, a set of facilities, a set of clients, as well as the distances between them are given. Each facility has its specific cost function w.r.t. the amount of clients assigned to that facility. The goal is to assign the clients to facilities such that the sum of facility cost and service cost is minimized. In traditional facility location problems, the unit service cost is proportional to the distance between the client and its assigned facility and thus metric. However, in our work, this assumption is removed and a generalized version of universal facility location problem is proposed, which is the so-called M n UFLP. When p = 2 , it is also known as l 2 2 measure considered by Jain and Vazirani [J. ACM'01] and Fernandes et al. [Math. Program.'15]. Particularly in this case, we extend their work to include the aforementioned variants of facility location and a local search based (11.18 + ε) -approximation algorithm is proposed. Furthermore, the reanalysis of the proposed algorithm gives a p -related performance guarantee for general p. [ABSTRACT FROM AUTHOR]

The kk-center clustering is one of the well-studied clustering problems in computer science. We are given a set of data points P⊆RdP⊆Rd, where RdRd is dd dimensional Euclidean space. We need to select k≤|P|k≤|P| points as centers and partition the set PP into kk clusters with each point connecting to its nearest center. The goal is to minimize the maximum radius. We consider the so-called online kk-center clustering model where the data points in RdRd arrive over time. We present the bi-criteria (nk,(logU∗L∗)2)(nk,(log⁡U∗L∗)2)-competitive algorithm and (nk,logγlognγk)(nk,log⁡γlog⁡nγk)-competitive algorithm for semi-online and fully-online kk-center clustering respectively, where U∗U∗ is the maximum cluster radius of optimal solution, L∗L∗ is the minimum distance of two distinct points of PP, γγ is the ratio of the maximum distance of two distinct points and the minimum distance of two distinct points of PP and nn is the number of points that will arrive in total. [ABSTRACT FROM AUTHOR]

• NP-hardness proof for the partial assignment problem. • A 1 / m -approximation for the partial assignment problem with general value functions. • A (1 − 1 / e) -approximation for the partial assignment problem with sub- modular value functions. In the partial assignment problem, a seller has an item set M = { i 1 , i 2 , ... , i m } , the amount of each item is exactly one. There are n buyers N = { b 1 , b 2 ,... , b n } , each buyer b p has a preferred bundle B p ⊆ M and a value function f p (⋅). Assume that each item should be sold integrally and thus can be only assigned to at most one buyer. In previous works, buyers are often considered to be single-minded, i.e., a buyer can be either assigned the whole preferred bundle, or nothing. In this paper, we consider a more generalized and realistic model where the buyer can be partially satisfied, i.e., buyer b p can have some positive value if the seller assigns a subset of b p 's preferred bundle. However, there might be exponential number of subsets, to tackle this situation, a value oracle is implemented. We can get the value f p (S p) for buyer b p and S p ⊆ B p by querying the value oracle. The objective is to assign items to buyers such that the total values are maximized, i.e., max ⁡ ∑ p = 1 n f p (S p). We first show that in this model, maximizing the total values is NP-hard. We then propose provably efficient approximation algorithms for general and submodular value functions respectively. If the value function satisfies non-negative, monotone and normalized, an 1 / m -approximation algorithm can be achieved. If the value function is submodular, the total values can be approximated within a factor of (1 − 1 / e). [ABSTRACT FROM AUTHOR]