A particle scheme based on implicit Euler time stepping and spatial sampling is proved to converge for first-order MFGs under displacement monotonicity, handling non-separable Hamiltonians and singular data for arbitrary horizons.
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Derives adaptive generalization bounds {c_m / N^{1/(2∨m)}} for digital ML models via new concentration of measure results on finite metric spaces, with c_m = O(sqrt(m)).
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Numerical analysis of first-order mean field games under displacement monotonicity
A particle scheme based on implicit Euler time stepping and spatial sampling is proved to converge for first-order MFGs under displacement monotonicity, handling non-separable Hamiltonians and singular data for arbitrary horizons.
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Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces
Derives adaptive generalization bounds {c_m / N^{1/(2∨m)}} for digital ML models via new concentration of measure results on finite metric spaces, with c_m = O(sqrt(m)).