Decentralized Optimization in Networks : Algorithmic Efficiency and Privacy Preservation

Decentralized Optimization in Networks: Algorithmic Efficiency and Privacy Preservation provides the reader with theoretical foundations, practical guidance, and solutions to decentralized optimization problems. The book demonstrates the application of decentralized optimization algorithms to enhance communication and computational efficiency, solve large-scale datasets, maintain privacy preservation, and address challenges in complex decentralized networks. The book covers key topics such as event-triggered communication, random link failures, zeroth-order gradients, variance-reduction, Polyak’s projection, stochastic gradient, random sleep, and differential privacy. It also includes simulations and practical examples to illustrate the algorithms' effectiveness and applicability in real-world scenarios.

Decentralized algorithms are useful for solving large-scale complex optimization problems, which not only alleviate the single-point resource bottleneck problem of centralized algorithms, but also possess higher scalability. Decentralized Optimization in Networks: Algorithmic Efficiency and Privacy Preservation provides the reader with theoretical foundations, practical guidance, and problem-solving approaches to decentralized optimization. It teaches how to apply decentralized optimization algorithms to improve optimization efficiency (communication efficiency, computational efficiency, fast convergence), solve large-scale problems (training for large-scale datasets), achieve privacy preservation (effectively counter external eavesdropping attacks, differential attacks, etc), and overcome a range of challenges in complex decentralized network environments (random sleep, random link failures, time-varying, directed, etc). It focuses on: 1) communication-efficiency: event-triggered communication, random link failures, zeroth-order gradients. 2) computation-efficiency: variance-reduction, Polyak’s projection, stochastic gradient, random sleep. 3) privacy preservation: differential privacy, edge-based correlated perturbations, conditional noises. It uses simulation results, including practical application examples, to illustrate the effectiveness and the practicability of decentralized optimization algorithms.