arXiv subjects

Othmane Safsafi

Publications and source records attributed to Othmane Safsafi.

5 recordsLinked to original sources

arXiv2025

Fast In-Spectrum Graph Watermarks

We address the problem of watermarking graph objects, which consists in hiding information within them, to prove their origin. The two existing methods to watermark graphs use subgraph matching or graph isomorphism techniques, which are known to be intractable for large graphs. To reduce the operational complexity, we propose FFG, a new graph watermarking scheme adapted from an image watermarking scheme, since graphs and images can be represented as matrices. We analyze and compare FFG, whose novelty lies in embedding the watermark in the Fourier transform of the adjacency matrix of a graph. Our technique enjoys a much lower complexity than that of related works (i.e. in $\mathcal{O}\left(N^2 \log N\right)$), while performing better or at least as well as the two state-of-the-art methods.

cs.DS↗

arXiv2025

Boosting Resource-Constrained Federated Learning Systems with Guessed Updates

Federated learning (FL) enables a set of client devices to collaboratively train a model without sharing raw data. This process, though, operates under the constrained computation and communication resources of edge devices. These constraints combined with systems heterogeneity force some participating clients to perform fewer local updates than expected by the server, thus slowing down convergence. Exhaustive tuning of hyperparameters in FL, furthermore, can be resource-intensive, without which the convergence is adversely affected. In this work, we propose GEL, the guess and learn algorithm. GEL enables constrained edge devices to perform additional learning through guessed updates on top of gradient-based steps. These guesses are gradientless, i.e., participating clients leverage them for free. Our generic guessing algorithm (i) can be flexibly combined with several state-of-the-art algorithms including FEDPROX, FEDNOVA, FEDYOGI or SCALEFL; and (ii) achieves significantly improved performance when the learning rates are not best tuned. We conduct extensive experiments and show that GEL can boost empirical convergence by up to 40% in resource constrained networks while relieving the need for exhaustive learning rate tuning.

cs.LG↗

arXiv2021

Batched Bandits with Crowd Externalities

In Batched Multi-Armed Bandits (BMAB), the policy is not allowed to be updated at each time step. Usually, the setting asserts a maximum number of allowed policy updates and the algorithm schedules them so that to minimize the expected regret. In this paper, we describe a novel setting for BMAB, with the following twist: the timing of the policy update is not controlled by the BMAB algorithm, but instead the amount of data received during each batch, called \textit{crowd}, is influenced by the past selection of arms. We first design a near-optimal policy with approximate knowledge of the parameters that we prove to have a regret in $\mathcal{O}(\sqrt{\frac{\ln x}{x}}+ε)$ where $x$ is the size of the crowd and $ε$ is the parameter error. Next, we implement a UCB-inspired algorithm that guarantees an additional regret in $\mathcal{O}\left(\max(K\ln T,\sqrt{T\ln T})\right)$, where $K$ is the number of arms and $T$ is the horizon.

cs.LG↗

arXiv2021

Exponential bounds for inhomogeneous random graphs in a Gaussian case

Rank 1 inhomogeneous random graphs are a natural generalization of Erdős Rényi random graphs. In this generalization each node is given a weight. Then the probability that an edge is present depends on the product of the weights of the nodes it is connecting. In this article, we give precise and uniform exponential bounds on the size, weight and surplus of rank 1 inhomogeneous random graphs where the weights of the nodes behave like a random variable with finite fourth moment. We focus on the case where the mean degree of a random node is slightly larger than 1, we call that case the barely supercritical regime. These bounds will be used in follow up articles to study a general class of random minimum spanning trees. They are also of independent interest since they show that these inhomogeneous random graphs behave like Erdős Rényi random graphs even in a barely supercritical regime. The proof relies on novel concentration bounds for sampling without replacement and a careful study of the exploration process.

math.PR↗

arXiv2020

The diameter of the minimum spanning tree of the complete graph with inhomogeneous random weights

We study a new type of random minimum spanning trees. It is built on the complete graph where each vertex is given a weight, which is a positive real number. Then, each edge is given a capacity which is a random variable that only depends on the product of the weights of its endpoints. We then study the minimum spanning tree corresponding to the edge capacities. Under a condition of finite moments on the node weights, we show that the expected diameter and typical distances of this minimum spanning tree are of order $n^{1/3}$. This is a generalization of the results of Addario-Berry, Broutin, and Reed [2009]. We then use our result to answer a conjecture in statistical physics about typical distances on a closely related object. This work also sets the ground for proving the existence of a non-trivial scaling limit of this spanning tree (a generalization of the result of Addario-Berry, Broutin, Goldschmidt, and Miermont [2017])). Our proof is based on a detailed study of rank-1 critical inhomogeneous random graphs, done in Safsafi [2020], and novel couplings between exploration trees related to those graphs and Galton-Watson trees.

math.PR↗