mlsanityData to 7 Oct 2026

Minimisation of Polyak-Lojasewicz Functions Using Random Zeroth-Order Oracles

arXiv 2405.09106 ↗First posted 15 May 2024math.OC cs.LGcited by 4

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Abstract (arXiv)

The application of a zeroth-order scheme for minimising Polyak-Lojasewicz (PL) functions is considered. The framework is based on exploiting a random oracle to estimate the function gradient. The convergence of the algorithm to a global minimum in the unconstrained case and to a neighbourhood of the global minimum in the constrained case along with their corresponding complexity bounds are presented. The theoretical results are demonstrated via numerical examples.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 7 of its 11 references that are in the map. First posted on arXiv 15 May 2024.

Builds on

7 of 11 references.

References · 7

  1. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,140
  2. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 526
  3. 2020Loss landscapes and optimization in over-parameterized non-linear systems and neural networkscited by 231
  4. 2013Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimizationcited by 142
  5. 2018Zeroth-Order Stochastic Variance Reduction for Nonconvex Optimizationcited by 109
  6. 2016Automatic LQR Tuning Based on Gaussian Process Global Optimizationcited by 29
  7. 2021Direct-Search for a Class of Stochastic Min-Max Problemscited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 2.

4 papers.

  1. 2025Minimisation of Quasar-Convex Functions Using Random Zeroth-Order Oraclescited by 3
  2. 2025Minimisation of Submodular Functions Using Gaussian Zeroth-Order Random Oraclescited by 2
  3. 2026Solving the Offline and Online Min-Max Problem of Non-smooth Submodular-Concave Functions: A Zeroth-Order Approachcited by 2
  4. 2026From Cursed to Competitive: Closing the ZO-FO Gap via Input-to-State Stabilitycited by 0