A Communication-Efficient Distributed Frank-Wolfe Online Algorithm with an Event-Triggered Mechanism

Artificial Intelligence Computer Science Information Science
distributed learning event-triggered online optimization projection-free regret

Academic Background

In the era of big data, distributed learning has become an effective method for solving large-scale online machine learning problems. However, frequent communication and projection operations in distributed learning incur high communication and computational costs. Especially in high-dimensional constrained optimization problems, the computational complexity of projection operations is extremely high, severely impacting algorithm efficiency. To address these issues, this paper proposes a distributed Frank-Wolfe online optimization algorithm based on an event-triggered mechanism, aiming to reduce communication overhead and computational costs.

The Frank-Wolfe algorithm, as a projection-free optimization method, has garnered significant attention due to its simplicity and efficiency. Compared to projection-based methods, the Frank-Wolfe algorithm only requires a linear optimization step in each iteration, avoiding complex projection operations. However, most existing Frank-Wolfe algorithms are implemented in centralized settings and cannot be directly applied to distributed network systems. Therefore, this research aims to combine the Frank-Wolfe algorithm with an event-triggered mechanism to design an efficient online optimization algorithm suitable for distributed networks.

Source of the Paper

This paper is co-authored by Huimin Gao, Muhua Liu, Zhihang Ji, Ruijuan Zheng, and Qingtao Wu, affiliated with the School of Information Engineering, Henan University of Science and Technology and the Longmen Laboratory. The paper was published in Cognitive Computation in 2025, titled “A Communication-Efficient Distributed Frank-Wolfe Online Algorithm with an Event-Triggered Mechanism.”

Research Process

1. Problem Definition and Algorithm Design

This paper studies a distributed online optimization problem where a network consists of multiple nodes (or agents). Each node makes decisions in each iteration and optimizes based on dynamically changing loss functions. The goal is to minimize the global loss function. To reduce communication overhead, the paper introduces an event-triggered mechanism, where information exchange between nodes occurs only when specific conditions are met.

2. Algorithm Implementation

The proposed algorithm is based on the Frank-Wolfe method and incorporates an event-triggered mechanism. The core steps of the algorithm are as follows: - State Fusion: Each node updates its state based on the state information of its neighboring nodes. - Gradient Aggregation: Each node computes a local gradient estimate based on historical gradient information. - Frank-Wolfe Step: The decision variables are updated through a linear optimization step. - Event-Triggered Communication: Nodes communicate with their neighbors only when the change in their state or gradient exceeds a predefined threshold.

3. Theoretical Analysis

The paper provides a rigorous theoretical analysis of the algorithm’s convergence and proves that the algorithm achieves sublinear regret growth for convex objective functions. Specifically, the paper proves that the regret upper bound is O(√T), where T represents the time horizon.

4. Experimental Validation

To validate the algorithm’s performance, numerical experiments were conducted on the News20 and ALOI datasets. The results show that the proposed algorithm performs well under different node counts and triggering thresholds, significantly outperforming baseline methods. Additionally, the experiments validate the effectiveness of the event-triggered mechanism in reducing communication rounds, especially in large-scale networks.

Main Results

1. Algorithm Convergence

The theoretical analysis shows that the proposed algorithm achieves sublinear regret growth for convex objective functions. Specifically, the regret upper bound is O(√T), consistent with existing distributed online optimization algorithms. However, the proposed algorithm significantly reduces communication overhead through the event-triggered mechanism.

2. Experimental Performance

Experiments on the News20 and ALOI datasets demonstrate that the proposed algorithm performs well under different node counts and triggering thresholds. As the number of nodes increases, the average loss gradually increases but eventually converges. Moreover, smaller triggering thresholds accelerate the algorithm’s convergence speed.

3. Effectiveness of the Event-Triggered Mechanism

The experimental results show that the event-triggered mechanism significantly reduces communication rounds, especially in large-scale networks. As the triggering threshold increases, communication rounds are significantly reduced, alleviating network communication pressure.

Conclusions and Significance

This paper proposes a distributed Frank-Wolfe online optimization algorithm based on an event-triggered mechanism, significantly improving the efficiency of distributed network systems by reducing communication overhead and computational costs. Theoretical analysis and experimental validation demonstrate that the algorithm achieves sublinear regret growth for convex objective functions and performs well on real-world datasets.

Scientific Value

This research provides an efficient solution for distributed online optimization problems, particularly in high-dimensional constrained optimization, where projection-free methods avoid complex projection operations and reduce computational costs.

Application Value

The proposed algorithm is suitable for large-scale distributed network systems, such as sensor networks and the Internet of Things (IoT), enabling efficient online optimization with limited communication resources.

Research Highlights

  1. Event-Triggered Mechanism: By introducing an event-triggered mechanism, the algorithm only exchanges information between nodes when necessary, significantly reducing communication overhead.
  2. Projection-Free Method: The Frank-Wolfe algorithm is used as a projection-free method, avoiding complex projection operations in high-dimensional constrained optimization and reducing computational costs.
  3. Theoretical Guarantees: The paper provides a rigorous theoretical analysis of the algorithm’s convergence, proving sublinear regret growth for convex objective functions.
  4. Experimental Validation: Experiments on multiple datasets validate the algorithm’s effectiveness and robustness, particularly in large-scale networks.

Other Valuable Information

The paper also explores the impact of different network topologies on algorithm performance. Experiments show that the algorithm converges fastest in fully connected networks. Additionally, the paper compares the proposed algorithm with other distributed online optimization algorithms, such as DEFW and DGD, demonstrating significant advantages in convergence speed and communication efficiency.

Through this research, we not only provide an efficient solution for distributed online optimization problems but also offer new insights for future research, particularly in further optimizing communication efficiency and computational costs.