Barrier functions constitute an effective tool for assessing and enforcing safety-critical constraints on dynamical systems. To this end, one is required to find a function h that satisfies a Lyapunov-like differential condition, thereby ensuring the invariance of its zero super-level set h(>= 0). This methodology, however, does not prescribe a general method for finding the function h that satisfies such differential conditions, which, in general, can be a daunting task. In this paper, we seek to overcome this limitation by developing a generalized barrier condition that makes the search for h easier. We do this in two steps. First, we develop integral barrier conditions that reveal equivalent asymptotic behavior to the differential ones, but without requiring differentiability of h. Subsequently, we further replace the stringent invariance requirement on h >= 0 with a more flexible concept known as recurrence. A set is (tau-)recurrent if every trajectory that starts in the set returns to it (within tau seconds) infinitely often. We show that, under mild conditions, a simple sign distance function can satisfy our relaxed condition and that the ( tau-)recurrence of the super-level set h >= 0 is sufficient to guarantee the system's safety.
We study the problem of Symmetric Private Information Retrieval (SPIR) in a scenario with $L$ non-replicated and colluding servers, and $M$ independent files distributed across these servers. In this setting, communication takes place through a noisy multiple-access channel and a noiseless public channel. The client must retrieve one of the $M$ files such that (i) the client's choice must not be revealed to the servers, and (ii) the client must not learn any information about non-selected files. Our main contribution is showing that, for a specific class of channels and without requiring shared randomness among servers, positive rates are achievable even when all the servers collude. Additionally, we present an example of channel where distributing files across multiple servers yields an achievable rate that outperforms a setting where all the files are stored on a single server.
Federated Learning (FL) represents a growing machine learning (ML) paradigm designed for training models across numerous nodes that retain local datasets, all without directly exchanging the underlying private data with the parameter server (PS). Its increasing popularity is attributed to notable advantages in terms of training deep neural network (DNN) models under privacy aspects and efficient utilization of communication resources. Unfortunately, DNNs suffer from high computational and communication costs, as well as memory consumption in intricate tasks. These factors restrict the applicability of FL algorithms in communication-constrained systems with limited hardware resources. In this paper, we develop a novel algorithm that overcomes these limitations by synergistically combining a pruning-based method with the FL process, resulting in low-dimensional representations of the model with minimal communication cost, dubbed Masked Pruning over FL (MPFL). The algorithm operates by initially distributing weights to the nodes through the PS. Subsequently, each node locally trains its model and computes pruning masks. These low-dimensional masks are then transmitted back to the PS, which generates a consensus pruning mask, broadcasted back to the nodes. This iterative process enhances the robustness and stability of the masked pruning model. The generated mask is used to train the FL model, achieving significant bandwidth savings. We present an extensive experimental study demonstrating the superior performance of MPFL compared to existing methods. Additionally, we have developed an open-source software package for the benefit of researchers and developers in related fields.
Linear feature extraction at the presence of nonlinear dependencies among the data is a fundamental challenge in unsupervised learning. We propose using a Gram-Schmidt (GS) type orthogonalization process over function spaces in order to detect and remove redundant dimensions. Specifically, by applying the GS process over a family of functions which presumably captures the nonlinear dependencies in the data, we construct a series of covariance matrices that can either be used to identify new large-variance directions, or to remove those dependencies from the principal components. In the former case, we provide information-theoretic guarantees in terms of entropy reduction. In the latter, we prove that under certain assumptions the resulting algorithms detect and remove nonlinear dependencies whenever those dependencies lie in the linear span of the chosen function family. Both proposed methods extract linear features from the data while removing nonlinear redundancies. We provide simulation results on synthetic and real-world datasets which show improved performance over state-of-the-art feature extraction algorithms.
This paper considers the proportional sharing mechanism [4] from the lens of fairness. Deviating from prior work we consider the net utility to users by incorporating a weighted cost of bidding, one example being the use of power, incurred at user-dependent costs, to competitively bid for throughput in wireless systems. In this context, we analyze the price of anarchy of the equilibrium when the social welfare is measured both by a fair-sharing utility measure, as well as the sum of utility measures. In the context of power bids by users, we consider both continuous and discrete bids. The analysis shows the PoA can be zero and even for a uniform linear utility function when using the sum-total measure, but with distinct costs of bids, is asymptotically zero with increasing number of users indicating that a number of users/clients were starved of resources. This illustrates that accounting for the cost of bids can substantially change the structure of the equilibrium as compared to uniform costs. We also investigate the number of such starved users experimentally. In order to determine equilibrium, we show convex program formulations as well as present approximation methods to determine (1 + epsilon)-approximate equilibrium via an efficient algorithm. We also design methods to compute the optimum solution. Optimization of the social utility in the general case, where multiple resources can be chosen by users, is shown to be NP-hard. Experimental results illustrate the asymptotic behavior of the PoA and of the number of users that are starved of resources when users (competition) increases.
