The paper investigates the mixing time of weighted Dikin walks used for sampling from exponential distributions on polytopes and truncated positive-semidefinite cones. It presents a general total-variation mixing bound under conditions of strong self-concordance, ν-symmetry, and mixed-trace regularity, achieving an “~O(d^2)" bound for polytopes and “~O(d^4)" for truncated PSD cones. A second result introduces a fourth-order bootstrap condition that yields stronger χ^2-divergence guarantees and an improved “~O(d^2)" mixing bound for a scaled Lee–Sidford metric.
By Yuansi Chen, Yunbum Kook
arXiv:2608. 25273v1 Announce Type: cross Abstract: We analyze exact-metric, Metropolis-adjusted Dikin walks by keeping the proposal determinant and reverse quadratic form together.
By Zhao Song, Lichen Zhang
arXiv:2609.40193v1 Announce Type: new
Abstract: We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, w...
By Yuchen Xin, Zhihua Zhang
arXiv:2608.25279v1 Announce Type: cross
Abstract: The OBABO and BAOAB schemes and the other standard Strang splittings of kinetic (underdamped) Langevin dynamics are widely used Markov chain Monte Ca...
By Nawaf Bou-Rabee
arXiv:2606. 24981v1 Announce Type: new Abstract: We study linear TD(0) under Markovian sampling, where data are generated along a single trajectory.
By Wei-Cheng Lee, Francesco Orabona
arXiv:2606. 26316v1 Announce Type: new Abstract: We study first-order methods for smooth objectives satisfying the Polyak-\L{}ojasiewicz (PL) condition when gradient samples are generated by an exogenous Markov chain.
By Dhruv Sarkar, Aprameyo Chakrabartty, Vaneet Aggarwal
While entropy regularization is widely used to stabilize and accelerate Natural Policy Gradient methods, its ability to yield faster convergence rates for the unregularized objective remains underexplored. Existing analyses often rely on double-loop architectures and invoke a linear entropy penalty.
arXiv:2609. 12594v1 Announce Type: new Abstract: We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for $\pi(\,\mathrm{d} x)\propto e^{-f(x)-g(x)}\,\mathrm{d} x$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g:\mathbb{R}^d\to\mathbb{R}$ is convex and globally $G$-Lipschitz.
By Yuchen Xin, Zhihua Zhang
arXiv:2607. 26285v1 Announce Type: cross Abstract: Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees.
By Martin J. Wainwright
arXiv:2608. 19587v1 Announce Type: new Abstract: While entropy regularization is widely used to stabilize and accelerate Natural Policy Gradient methods, its ability to yield faster convergence rates for the unregularized objective remains underexplored.
By Zhiqiang Tan
The paper introduces a parallel architecture for stochastic gradient methods that adaptively selects the number of iterations. An algorithm A(x₀, y) takes an initial point and a step limit y, and p processors search for an appropriate iteration count T using a prescribed function h. The framework guarantees a (p, αₚ)-approximation, meaning for any T ≥ T₀ there exists a processor and stage where the cumulative iterations lie within a factor αₚ of T, and the authors prove tight lower bounds for αₚ while presenting simple arithmetic stochastic gradient methods that use only divisions by powers of two.
By Bin Fu
arXiv:2605. 01928v2 Announce Type: replace Abstract: We optimize losses that jump: spiking thresholds, quantized layers, and discrete routing put jumps in the forward pass, where backpropagation does not apply.
By An T. Le