Zeroth-order gradient tracking for decentralized learning with privacy guarantees.

Area of Science:

• Optimization Theory
• Distributed Systems
• Cybersecurity

Background:

• Decentralized systems often face challenges with unknown gradient information, hindering optimization.
• Protecting individual agent privacy is crucial in distributed machine learning and smart grids.
• Existing methods may not adequately balance privacy preservation with optimization efficiency.

Purpose of the Study:

• To propose a novel algorithm for decentralized optimization with unknown gradients.
• To incorporate differential privacy mechanisms to safeguard agent data.
• To ensure the convergence and effectiveness of the proposed algorithm in practical applications.

Main Methods:

• Development of a differential privacy decentralized zeroth-order gradient tracking (DP-DZOGT) algorithm.
• Construction of a one-point zeroth-order gradient estimator (OPZOGE) for gradient estimation.
• Introduction of random noise into agent states and gradients for enhanced privacy.

Main Results:

• The DP-DZOGT algorithm guarantees linear convergence under a fixed step size.
• The proposed method effectively estimates gradients using only function values.
• Demonstrated application and validation in smart grid and decentralized federated learning scenarios.

Conclusions:

• The DP-DZOGT algorithm offers a robust solution for private optimization in decentralized systems.
• The integration of differential privacy effectively protects sensitive agent information.
• The algorithm shows promise for enhancing security and performance in smart grids and decentralized federated learning.