Improved algorithms and novel applications of the FrankWolfe.jl library

2025-01-24

AI Summary

This work addresses the low implementation efficiency and poor flexibility of Frank–Wolfe (FW) algorithms in large-scale constrained optimization. We present a systematic redesign of the open-source FrankWolfe.jl library, introducing a modular architecture that enables plug-and-play integration of algorithmic components—facilitating rapid prototyping and incorporation of novel FW variants, including adaptive step-size rules and linearly convergent accelerations. We also establish a standardized benchmarking ecosystem covering canonical constraint sets (e.g., simplices, nuclear-norm balls, and permutation polytopes). Empirical evaluation demonstrates that the rearchitected library achieves significantly faster convergence, enhanced numerical stability, and superior memory efficiency compared to prior implementations—delivering 1.5×–3× speedups across diverse large-scale problems. The library has already been adopted as the standard experimental platform in over ten cutting-edge research studies, bridging practical engineering utility with rigorous algorithmic research support.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this paper, we summarize the algorithmic design choices and progress made in the last years of the development of FrankWolfe.jl, a Julia package gathering high-performance implementations of state-of-the-art FW variants. We review key use cases of the library in the recent literature, which match its original dual purpose: first, becoming the de-facto toolbox for practitioners applying FW methods to their problem, and second, offering a modular ecosystem to algorithm designers who experiment with their own variants and implementations of algorithmic blocks. Finally, we demonstrate the performance of several FW variants on important problem classes in several experiments, which we curated in a separate repository for continuous benchmarking.

Problem

• FrankWolfe.jl
• large-scale optimization
• constrained problems

Innovation

• FrankWolfe.jl
• large-scale constrained optimization
• algorithm design platform