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FastPart: Over-Parameterized Stochastic Gradient Descent for Sparse optimisation on Measures

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  • Gadat, Sébastien
  • De Castro, Yohann
  • Marteau, Clément

Abstract

This paper presents a novel algorithm that leverages Stochastic Gradient Descent strategies in con-junction with Random Features to augment the scalability of Conic Particle Gradient Descent (CPGD) specifically tailored for solving sparse optimisation problems on measures. By formulating the CPGD steps within a variational framework, we provide rigorous mathematical proofs demonstrating the fol-lowing key findings: (i) The total variation norms of the solution measures along the descent trajectory remain bounded, ensuring stability and preventing undesirable divergence; (ii) We establish a global convergence guarantee with a convergence rate of O(log(K)/√K) over K iterations, showcasing the efficiency and effectiveness of our algorithm, (iii) Additionally, we analyze and establish local control over the first-order condition discrepancy, contributing to a deeper understanding of the algorithm’s behavior and reliability in practical applications.

Suggested Citation

  • Gadat, Sébastien & De Castro, Yohann & Marteau, Clément, 2023. "FastPart: Over-Parameterized Stochastic Gradient Descent for Sparse optimisation on Measures," TSE Working Papers 23-1494, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:128771
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    References listed on IDEAS

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    1. Miclo, Laurent, 2023. "On the convergence of global-optimization fraudulent stochastic algorithms," TSE Working Papers 23-1437, Toulouse School of Economics (TSE).
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