Kernel-based potential mean-field games with unbiased random Fourier $U$-statistics
We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed through reproducing-kernel maximum mean discrepancy (MMD) penalties, and develop a computational framework that exploits this kernel structure. Both costs are estimated from finite-sample empirical distributions using a random Fourier U-statistic representation that is unbiased and has linear cost in the batch size. The drift of the controlled diffusion is parametrized by a neural network and trained via stochastic gradient descent. For population near-minimizers we prove convergence to the terminal-constrained problem as the penalty diverges, and show ...
| Authors | Yumiharu Nakano |
|---|---|
| Primary category | math.OC |
| Published | 28 May 2026 |
| Last updated at source | 20 September 2026 |
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