핵심 개념

Push-LSVRG-UP achieves linear convergence in resolving large-scale optimization problems over unbalanced directed networks.

요약

The paper introduces Push-LSVRG-UP, a distributed stochastic optimization algorithm for large-scale convex finite-sum optimization problems in multi-agent systems over unbalanced directed networks. It focuses on efficient computation, communication, and convergence analysis. The algorithm combines the push-sum technique and a distributed loopless stochastic variance-reduced gradient method with uncoordinated triggered probabilities. Theoretical results demonstrate its linear convergence, low storage costs, and reduced computational complexity compared to existing methods. Simulations validate its performance on real-world datasets.

에서 추출된 핵심 인사이트

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

통계

- "The convergence analysis of Push-LSVRG-UP is relied on analyzing the contraction relationships between four error terms associated with the multi-agent system."
- "The step-size condition for linear convergence is 0 < α ≤ min((1 − σ) p / 6µ, (1 − σ)2p / 480δLQ¯p)."

인용구

- "The convergence analysis of Push-LSVRG-UP is relied on analyzing the contraction relationships between four error terms associated with the multi-agent system."
- "The step-size condition for linear convergence is 0 < α ≤ min((1 − σ) p / 6µ, (1 − σ)2p / 480δLQ¯p)."

더 깊은 문의

Push-LSVRG-UP introduces an uncoordinated probabilistic triggered mechanism that allows each agent in the system to compute local batch gradients independently based on a predefined probability. This mechanism impacts the independence and flexibility of agents by allowing them to operate autonomously without the need for synchronization or coordination in triggering the local batch gradient computation. Each agent can decide when to compute the local batch gradient based on its own triggered probability, enhancing its independence in the optimization process. This flexibility enables agents to adapt to varying computational loads or network conditions, leading to a more efficient and decentralized optimization process.

The reduced per-iteration computational complexity in Push-LSVRG-UP has significant implications for practical applications. By eliminating the need for each agent to compute local batch gradients at every iteration, the algorithm reduces the computational burden on individual agents. This reduction in computational complexity not only improves the efficiency of each agent's computation but also lightens the overall computational load on the multi-agent system. As a result, agents can process and exchange information more efficiently, leading to faster convergence and lower resource requirements in practical applications.

The network-independent computational complexity of Push-LSVRG-UP plays a crucial role in enhancing its efficiency in resolving large-scale optimization problems. By allowing the algorithm to work in a class of generic unbalanced directed networks, Push-LSVRG-UP can handle a wide range of network structures without being limited to specific communication patterns. This flexibility enables the algorithm to adapt to diverse network configurations and communication capabilities, making it suitable for real-world scenarios where network conditions may vary. The network-independent computational complexity also ensures that the algorithm can achieve optimal performance across different network setups, contributing to its efficiency in resolving large-scale optimization problems.

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