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Dimension-Independent Convergence Rate for Adagrad with Heavy-Ball Momentum

Author

Listed:
  • Kyunghun Nam

    (Department of Artificial Intelligence, Korea University, Seoul 02841, Republic of Korea)

  • Sejun Park

    (Department of Artificial Intelligence, Korea University, Seoul 02841, Republic of Korea)

Abstract

In this study, we analyze the convergence rate of Adagrad with momentum for non-convex optimization problems. We establish the first dimension-independent convergence rate under the ( L 0 , L 1 ) -smoothness assumption, which is a generalization of the standard L -smoothness. We show the O ( 1 / T ) convergence rate under bounded noise in stochastic gradients, where the bound can scale with the current optimality gap and gradient norm.

Suggested Citation

  • Kyunghun Nam & Sejun Park, 2025. "Dimension-Independent Convergence Rate for Adagrad with Heavy-Ball Momentum," Mathematics, MDPI, vol. 13(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:681-:d:1594925
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