arXiv subjects

Xiaomeng Chen

Publications and source records attributed to Xiaomeng Chen.

24 records · Page 2Linked to original sources

arXiv2023

Tight Upper Bounds on the Error Probability of Spinal Codes over Fading Channels

Spinal codes, a family of rateless codes introduced in 2011, have been proved to achieve Shannon capacity over both the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). In this paper, we derive explicit tight upper bounds on the error probability of Spinal codes under maximum-likelihood (ML) decoding and perfect channel state information (CSI) over three typical fading channels, including the Rayleigh channel, the Nakagami-m channel and the Rician channel. Simulation results verify the tightness of the derived upper bounds.

cs.IT↗

arXiv2022

Improving Primal Heuristics for Mixed Integer Programming Problems based on Problem Reduction: A Learning-based Approach

In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is employed to predict binary variables' values. After that, a subset of binary variables is fixed to the predicted value by a greedy method conditioned on the predicted probabilities. By exploring the logical consequences, a learning-based problem reduction method is proposed, significantly reducing the variable and constraint sizes. With the reductive sub-MIP problem, the second layer GCN framework is employed to update the prediction for the remaining binary variables' values and to determine the selection of variables which are then used for branching to generate the Branch and Bound (B&B) tree. Numerical examples show that our BP-RB framework speeds up the primal heuristic and finds the feasible solution with high quality.

math.OC↗

arXiv2022

A Differential Private Method for Distributed Optimization in Directed Networks via State Decomposition

In this paper, we study the problem of consensus-based distributed optimization where a network of agents, abstracted as a directed graph, aims to minimize the sum of all agents' cost functions collaboratively. In existing distributed optimization approaches (Push-Pull/AB) for directed graphs, all agents exchange their states with neighbors to achieve the optimal solution with a constant stepsize, which may lead to the disclosure of sensitive and private information. For privacy preservation, we propose a novel state-decomposition based gradient tracking approach (SD-Push-Pull) for distributed optimzation over directed networks that preserves differential privacy, which is a strong notion that protects agents' privacy against an adversary with arbitrary auxiliary information. The main idea of the proposed approach is to decompose the gradient state of each agent into two sub-states. Only one substate is exchanged by the agent with its neighbours over time, and the other one is kept private. That is to say, only one substate is visible to an adversary, protecting the privacy from being leaked. It is proved that under certain decomposition principles, a bound for the sub-optimality of the proposed algorithm can be derived and the differential privacy is achieved simultaneously. Moreover, the trade-off between differential privacy and the optimization accuracy is also characterized. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed approach.

eess.SY↗

arXiv2021

Branch and Bound in Mixed Integer Linear Programming Problems: A Survey of Techniques and Trends

In this paper, we surveyed the existing literature studying different approaches and algorithms for the four critical components in the general branch and bound (B&B) algorithm, namely, branching variable selection, node selection, node pruning, and cutting-plane selection. However, the complexity of the B&B algorithm always grows exponentially with respect to the increase of the decision variable dimensions. In order to improve the speed of B&B algorithms, learning techniques have been introduced in this algorithm recently. We further surveyed how machine learning can be used to improve the four critical components in B&B algorithms. In general, a supervised learning method helps to generate a policy that mimics an expert but significantly improves the speed. An unsupervised learning method helps choose different methods based on the features. In addition, models trained with reinforcement learning can beat the expert policy, given enough training and a supervised initialization. Detailed comparisons between different algorithms have been summarized in our survey. Finally, we discussed some future research directions to accelerate and improve the algorithms further in the literature.

cs.LG↗

arXiv2021

Remarks on Liouville type theorems for the steady MHD and Hall-MHD equations

In this note we investigate Liouville type theorems for the steady three dimensional MHD and Hall-MHD equations, and show that the velocity field $u$ and the magnetic field $B$ are vanishing provided that $B\in L^{6,\infty}(\mathbb{R}^3)$ and $u\in BMO^{-1}(\mathbb{R}^3)$, which state that the velocity field plays an important role. Moreover, the similar result holds in the case of partial viscosity or diffusivity for the three dimensional MHD equations.

math.AP↗

arXiv2021

Privacy-Preserving Push-sum Average Consensus via State Decomposition

Average consensus is extensively used in distributed networks for computation and control, where all the agents constantly communicate with each other and update their states in order to reach an agreement. Under a general average consensus algorithm, information exchanged through wireless or wired communication networks could lead to the disclosure of sensitive and private information. In this paper, we propose a privacy-preserving push-sum approach for directed networks that can protect the privacy of all agents while achieving average consensus simultaneously. Each node decomposes its initial state arbitrarily into two substates, and their average equals to the initial state, guaranteeing that the agent's state will converge to the accurate average consensus. Only one substate is exchanged by the node with its neighbours over time, and the other one is reserved. That is to say, only the exchanged substate would be visible to an adversary, preventing the initial state information from leakage. Different from the existing state-decomposition approach which only applies to undirected graphs, our proposed approach is applicable to strongly connected digraphs. In addition, in direct contrast to offset-adding based privacy-preserving push-sum algorithm, which is vulnerable to an external eavesdropper, our proposed approach can ensure privacy against both an honest-but-curious node and an external eavesdropper. A numerical simulation is provided to illustrate the effectiveness of the proposed approach.

eess.SY↗