Bellman Contraction under MMD: A Unified Framework
The paper identifies 11 new kernels that induce Bellman contraction, while finding that faster contraction tends to weaken discrimination between distributions.
The framework reduces contraction under Maximum Mean Discrepancy to a mathematical condition on an associated “Bellman difference kernel.” For radial kernels, it provides criteria that hold in any dimension and can be checked analytically or numerically. The authors also introduce “chaining,” a construction that produces kernels with any prescribed contraction factor. Their analysis explains why Gaussian RBF kernels can remain valid with bounded rewards despite lacking global contraction.
ArXiv · AI/CL/LG's note
The framework reduces contraction under Maximum Mean Discrepancy to a mathematical condition on an associated “Bellman difference kernel.” For radial kernels, it provides criteria that hold in any dimension and can be checked analytically or numerically. The authors also introduce “chaining,” a construction that produces kernels with any prescribed contraction factor. Their analysis explains why Gaussian RBF kernels can remain valid with bounded rewards despite lacking global contraction.
ArXiv · AI/CL/LG's note
score 4