Push-LSVRG-UP: Distributed Stochastic Optimization over Unbalanced Directed Networks with Uncoordinated Triggered Probabilities

Khái niệm cốt lõi

The author presents Push-LSVRG-UP as a distributed stochastic optimization algorithm for large-scale convex finite-sum optimization problems over unbalanced directed networks, emphasizing accelerated linear convergence and reduced computational complexity.

Tóm tắt

The paper introduces Push-LSVRG-UP, a novel distributed stochastic optimization algorithm for resolving large-scale optimization problems over unbalanced directed networks. It focuses on achieving accelerated linear convergence, reducing storage costs, and improving computational efficiency compared to existing methods. The algorithm incorporates an uncoordinated probabilistic triggered mechanism to enhance agent independence and flexibility in computing local batch gradients.
Key points include:

Introduction of Push-LSVRG-UP for large-scale convex finite-sum optimization.
Utilization of push-sum technique and LSVRG method with uncoordinated triggered probabilities.
Emphasis on accelerated linear convergence, reduced storage costs, and lower computational complexity.
Theoretical analysis providing step-size range, convergence rate, and iteration complexity.
Superiority of Push-LSVRG-UP demonstrated through simulations on real-world datasets.

Thống kê

Each agent performs only local computation without leaking private information.
Explicit feasible range of the constant step-size provided.
Linear convergence rate achieved by Push-LSVRG-UP when obtaining the globally optimal solution.

Trích dẫn

"Push-LSVRG-UP achieves superior characteristics of accelerated linear convergence."
"The introduction of an uncoordinated probabilistic triggered mechanism allows for agent independence."

Thông tin chi tiết chính được chắt lọc từ

(Rectified Version) Push-LSVRG-UP

by Jinhui Hu,Gu... lúc arxiv.org 03-05-2024

https://arxiv.org/pdf/2305.09181.pdf

Yêu cầu sâu hơn

How does the uncoordinated probabilistic triggered mechanism impact the overall performance

The uncoordinated probabilistic triggered mechanism in the Push-LSVRG-UP algorithm plays a crucial role in improving the independence and flexibility of each agent in the system. By allowing agents to trigger local batch gradient computations based on individual probabilities, rather than a coordinated probability for all agents, it enhances adaptability and efficiency. This mechanism enables agents to operate autonomously without being constrained by a uniform triggering rule, leading to more efficient computation and communication processes. Additionally, it facilitates better scalability and robustness in handling large-scale optimization problems over unbalanced directed networks.

What are the implications of reduced per-agent computational complexity in practical applications

Reducing per-agent computational complexity has significant implications for practical applications of distributed optimization algorithms. In real-world scenarios where each agent may have limited computational resources or processing capabilities, lowering the per-iteration computational burden can lead to improved overall performance and faster convergence rates. By minimizing the amount of computation required at each iteration for individual agents, Push-LSVRG-UP allows for smoother execution within resource-constrained environments. This reduction in computational complexity not only enhances efficiency but also contributes to lower energy consumption and operational costs.

How might the findings of this study be applied to other fields beyond distributed optimization

The findings of this study on distributed stochastic optimization over unbalanced directed networks can be applied beyond its immediate domain to various other fields:

Machine Learning: The insights gained from developing Push-LSVRG-UP could be leveraged in machine learning tasks that involve large datasets distributed across multiple nodes or devices. The algorithm's ability to handle unbalanced information exchange could improve training efficiency and model accuracy.

Network Security: The concepts introduced in this study could be adapted for enhancing security protocols in network systems by optimizing communication strategies among different components while maintaining privacy constraints.

Internet of Things (IoT): In IoT environments with decentralized data processing requirements, implementing similar decentralized optimization techniques could streamline data analysis processes while ensuring efficient resource utilization across interconnected devices.

Supply Chain Management: Applying distributed optimization methods like Push-LSVRG-UP could optimize supply chain operations by enabling collaborative decision-making among diverse stakeholders while considering network dynamics and information imbalances.