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Oracle Complexity Separation in Convex Optimization

Author

Listed:
  • Anastasiya Ivanova

    (National Research University Higher School of Economics
    Grenoble Alpes University)

  • Pavel Dvurechensky

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • Evgeniya Vorontsova

    (Catholic University of Louvain)

  • Dmitry Pasechnyuk

    (Moscow Institute of Physics and Technology
    ISP RAS Research Center for Trusted Artificial Intelligence)

  • Alexander Gasnikov

    (National Research University Higher School of Economics
    Moscow Institute of Physics and Technology
    ISP RAS Research Center for Trusted Artificial Intelligence
    Institute for Information Transmission Problems)

  • Darina Dvinskikh

    (National Research University Higher School of Economics
    Moscow Institute of Physics and Technology
    ISP RAS Research Center for Trusted Artificial Intelligence)

  • Alexander Tyurin

    (National Research University Higher School of Economics)

Abstract

Many convex optimization problems have structured objective functions written as a sum of functions with different oracle types (e.g., full gradient, coordinate derivative, stochastic gradient) and different arithmetic operations complexity of these oracles. In the strongly convex case, these functions also have different condition numbers that eventually define the iteration complexity of first-order methods and the number of oracle calls required to achieve a given accuracy. Motivated by the desire to call more expensive oracles fewer times, we consider the problem of minimizing the sum of two functions and propose a generic algorithmic framework to separate oracle complexities for each function. The latter means that the oracle for each function is called the number of times that coincide with the oracle complexity for the case when the second function is absent. Our general accelerated framework covers the setting of (strongly) convex objectives, the setting when both parts are given through full coordinate oracle, as well as when one of them is given by coordinate derivative oracle or has the finite-sum structure and is available through stochastic gradient oracle. In the latter two cases, we obtain accelerated random coordinate descent and accelerated variance reduced methods with oracle complexity separation.

Suggested Citation

  • Anastasiya Ivanova & Pavel Dvurechensky & Evgeniya Vorontsova & Dmitry Pasechnyuk & Alexander Gasnikov & Darina Dvinskikh & Alexander Tyurin, 2022. "Oracle Complexity Separation in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 462-490, June.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-022-02038-7
    DOI: 10.1007/s10957-022-02038-7
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    References listed on IDEAS

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    1. Yurii Nesterov, 2018. "Lectures on Convex Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-91578-4, December.
    2. NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Yurii NESTEROV & Sebastian U. STICH, 2017. "Efficiency of the accelerated coordinate descent method on structured optimization problems," LIDAM Reprints CORE 2845, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Dvurechensky, Pavel & Gorbunov, Eduard & Gasnikov, Alexander, 2021. "An accelerated directional derivative method for smooth stochastic convex optimization," European Journal of Operational Research, Elsevier, vol. 290(2), pages 601-621.
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