mlsanityData to 14 Oct 2026

Primal and Dual Analysis of Entropic Fictitious Play for Finite-sum Problems

arXiv 2303.02957 ↗First posted 6 Mar 2023stat.ML cs.LG math.OCcited by 4

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Abstract (arXiv)

The entropic fictitious play (EFP) is a recently proposed algorithm that minimizes the sum of a convex functional and entropy in the space of measures -- such an objective naturally arises in the optimization of a two-layer neural network in the mean-field regime. In this work, we provide a concise primal-dual analysis of EFP in the setting where the learning problem exhibits a finite-sum structure. We establish quantitative global convergence guarantees for both the continuous-time and discrete-time dynamics based on properties of a proximal Gibbs measure introduced in Nitanda et al. (2022). Furthermore, our primal-dual framework entails a memory-efficient particle-based implementation of the EFP update, and also suggests a connection to gradient boosting methods. We illustrate the efficiency of our novel implementation in experiments including neural network optimization and image synthesis.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 22 of its 34 references that are in the map. First posted on arXiv 6 Mar 2023.

Builds on

22 of 34 references.

References · 22

  1. 2018A Mean Field View of the Landscape of Two-Layers Neural Networkscited by 466
  2. 2020Modular Primitives for High-Performance Differentiable Renderingcited by 441
  3. 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 426
  4. 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 227
  5. 2022High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representationcited by 150
  6. 2022The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networkscited by 142
  7. 2015On the Equivalence between Kernel Quadrature Rules and Random Feature Expansionscited by 138
  8. 2018Mean Field Analysis of Neural Networks: A Central Limit Theoremcited by 107
  9. 2019Limitations of Lazy Training of Two-layers Neural Networkscited by 87
  10. 2020Fictitious Play for Mean Field Games: Continuous Time Analysis and Applicationscited by 62
  11. 2022Mean-Field Langevin Dynamics: Exponential Convergence and Annealingcited by 61
  12. 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 55
10 more
  1. 2017Stochastic Particle Gradient Descent for Infinite Ensemblescited by 52
  2. 2019Mean-Field Langevin Dynamics and Energy Landscape of Neural Networkscited by 50
  3. 2018Stein Pointscited by 43
  4. 2021Modern Evolution Strategies for Creativity: Fitting Concrete Images and Abstract Conceptscited by 40
  5. 2015Learning in Mean Field Games: the Fictitious Playcited by 38
  6. 2022Uniform-in-time propagation of chaos for mean field Langevin dynamicscited by 23
  7. 2020Particle Dual Averaging: Optimization of Mean Field Neural Networks with Global Convergence Rate Analysiscited by 21
  8. 2022Entropic Fictitious Play for Mean Field Optimization Problemcited by 12
  9. 2018Finite mean field games: fictitious play and convergence to a first order continuous mean field gamecited by 9
  10. 2022Generalized conditional gradient and learning in potential mean field gamescited by 5

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Cited by year

Citing papers per year: 2023: 1; 2024: 1; 2025: 2.

4 papers.

  1. 2023Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reductioncited by 20
  2. 2024Provably Neural Active Learning Succeeds via Prioritizing Perplexing Samplescited by 5
  3. 2025Direct Distributional Optimization for Provable Alignment of Diffusion Modelscited by 5
  4. 2025Non-convex entropic mean-field optimization via Best Response flowcited by 2