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The paper establishes a universal minimax regret lower bound Ω(√(Tγ_T / log T)) for non-constant continuous kernel functions on compact domains.
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10/9/2026
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UnverifiedPrior to this paper, regret lower bounds for general kernels had been missing, with nearly matching lower bounds derived only for specific kernels such as the squared exponential kernel and the Matérn kernel.69% similarUnverifiedThe Marčenko–Pastur law states that the upper bound of the support interval for the eigenvalue distribution of a purely random matrix is λ_max = σ²(1+√q)², where q = N/T.64% similarUnverifiedIn a Reproducing Kernel Hilbert Space, every function can be uniquely determined by a kernel function, and the point evaluation operation is a continuous linear functional.63% similarUnverifiedThe squared exponential kernel corresponds to the class of infinitely smooth functions, while the Matérn-ν kernel corresponds to the class of ν-times differentiable functions, with smaller ν yielding rougher function classes.61% similarUnverifiedThe push-forward curve is defined as ρ_t = ((1-t)id + tT)_#ρ, whose tangent vector at t=0 is T-id, corresponding to the displacement direction in Wasserstein space61% similar
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