ABGD parametrizes piecewise linear functions as difference of max-affine functions and converges linearly to an epsilon-accurate solution with O(d max(sigma/epsilon,1)^2) samples under sub-Gaussian noise, which is minimax optimal up to logs.
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The sharp MSE bound for the ℓ1-minimum-norm interpolator under isotropic Gaussian covariates is recovered via the geometry of symmetric Gaussian polytopes, without the convex Gaussian min-max theorem.
A learning algorithm achieves tight Õ(√T) regret for profit maximization in bilateral trade against smooth adversaries, matching stochastic rates via continuity and algorithmic chaining.
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Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions
ABGD parametrizes piecewise linear functions as difference of max-affine functions and converges linearly to an epsilon-accurate solution with O(d max(sigma/epsilon,1)^2) samples under sub-Gaussian noise, which is minimax optimal up to logs.
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Minimum Norm Interpolation via The Local Theory of Banach Spaces: The Role of Gaussianity
The sharp MSE bound for the ℓ1-minimum-norm interpolator under isotropic Gaussian covariates is recovered via the geometry of symmetric Gaussian polytopes, without the convex Gaussian min-max theorem.
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Profit Maximization in Bilateral Trade against a Smooth Adversary
A learning algorithm achieves tight Õ(√T) regret for profit maximization in bilateral trade against smooth adversaries, matching stochastic rates via continuity and algorithmic chaining.