mlsanityData to 14 Oct 2026

Analysis of Kernel Mirror Prox for Measure Optimization

arXiv 2403.00147 ↗First posted 29 Feb 2024math.OC cs.LGcited by 4

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Abstract (arXiv)

By choosing a suitable function space as the dual to the non-negative measure cone, we study in a unified framework a class of functional saddle-point optimization problems, which we term the Mixed Functional Nash Equilibrium (MFNE), that underlies several existing machine learning algorithms, such as implicit generative models, distributionally robust optimization (DRO), and Wasserstein barycenters. We model the saddle-point optimization dynamics as an interacting Fisher-Rao-RKHS gradient flow when the function space is chosen as a reproducing kernel Hilbert space (RKHS). As a discrete time counterpart, we propose a primal-dual kernel mirror prox (KMP) algorithm, which uses a dual step in the RKHS, and a primal entropic mirror prox step. We then provide a unified convergence analysis of KMP in an infinite-dimensional setting for this class of MFNE problems, which establishes a convergence rate of O(1/N) in the deterministic case and O(1/√N) in the stochastic case, where N is the iteration counter. As a case study, we apply our analysis to DRO, providing algorithmic guarantees for DRO robustness and convergence.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 43 of its 86 references that are in the map. First posted on arXiv 29 Feb 2024.

Builds on

43 of 86 references.

References · 43

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31 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 1.

4 papers.

  1. 2025Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuningcited by 17
  2. 2025Provable Maximum Entropy Manifold Exploration via Diffusion Modelscited by 14
  3. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  4. 2026A Unified Density Operator View of Flow Control and Mergingcited by 2