arXiv Statistics ML
Optimal State-Space Order for Spectral Gaps of Sliding-Window Occupation Counts
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arXiv Machine Learning
Sep 4
Projected Riemannian Gradient Descent for the Bures-Wasserstein Barycenter: Dimension-Independent Linear Convergence at Unit Step Size
arXiv:2609. 03762v1 Announce Type: new Abstract: The computation of the Bures-Wasserstein (BW) barycenter of an ensemble of positive definite matrices arises throughout machine learning, optimal transport, and quantum information.
arXiv Machine Learning
Aug 18
Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Run
arXiv:2608. 16878v1 Announce Type: cross Abstract: For any convex body $\mathcal{K}\subset\mathbb{R}^{n}$ containing a unit ball, the spectral gap of Hit-and-Run is $\Omega(1/(n^2 C_{\mathsf{PI}}))$, where $C_{\mathsf{PI}}$ is the Poincar\'e constant of the uniform distribution $\pi$ over $\mathcal{K}$.
arXiv Machine Learning
Sep 10
Tight Lower Bounds for State Tomography with Limited Entanglement
arXiv:2609.05718v1 Announce Type: cross Abstract: We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower b...
arXiv Machine Learning
Jun 25
Minimax PAC Bounds for Learning in Exogenous Contextual MDPs
arXiv:2606. 25170v1 Announce Type: cross Abstract: We study PAC learning in tabular discounted Markov decision processes with exogenous i.
arXiv Machine Learning
Jul 28
A Resolution of the SS--RS--GD Inequalities
arXiv:2607. 22620v1 Announce Type: cross Abstract: Yun, Sra, and Jadbabaie (COLT 2021, open question) conjectured the SS--RS--GD inequalities: for well-conditioned symmetric matrices $A_1,\dots,A_n$, the operators $W_{ss}$, $W_{rs}$, and $W_{gd}$ that encode the expected iterate of single-shuffle SGD, random-reshuffle SGD, and gradient descent on a quadratic finite sum should satisfy \[ \|W_{ss}\|\le \| W_{rs}\|\le \|W_{gd}\|.
arXiv Machine Learning
Jun 15
Nonlinear Two-Time-Scale Stochastic Approximation: A Sharp Phase Transition and How to Beat It
arXiv:2606. 14488v1 Announce Type: cross Abstract: Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $\beta_k=\Theta(k^{-1})$ and $\alpha_k=\Theta(k^{-a})$, $a\in(1/2,1)$, generally satisfies a mean-square rate of order $k^{-a}$; decoupled $k^{-1}$ rates require strong local linearity.