惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

MyScale Blog
MyScale Blog
F
Fortinet All Blogs
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
D
Docker
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
爱范儿
爱范儿
V
Visual Studio Blog
Last Week in AI
Last Week in AI
WordPress大学
WordPress大学
aimingoo的专栏
aimingoo的专栏
小众软件
小众软件
L
LangChain Blog
Vercel News
Vercel News
阮一峰的网络日志
阮一峰的网络日志
IT之家
IT之家
P
Proofpoint News Feed
博客园_首页
D
DataBreaches.Net
T
The Blog of Author Tim Ferriss
The GitHub Blog
The GitHub Blog
酷 壳 – CoolShell
酷 壳 – CoolShell
C
Check Point Blog
Engineering at Meta
Engineering at Meta
Microsoft Azure Blog
Microsoft Azure Blog

math.PR updates on arXiv.org

Visibility in the Boolean Model on Harmonic Manifolds Global estimates on the Brenier map Geodesics and Wandering Exponents in Brochette First-Passage Percolation State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits Randomly twisted transfer operators and singular values statistics Generalized Bessel-Dunkl diffusions An almost sure invariance principle for the Takagi-van der Waerden class functions Central limit theorems for high dimensional lattice polytopes: cosmological polytopes Convergence rate estimates for semigroups and heat kernels associated with resistance forms Second-order Poincaré inequalities and localization on the Poisson space Maximum Probability of Independence in Transitive Matroids On global solutions to the semidiscrete stochastic heat equation The Poisson Tail Conjecture for primes in short intervals A Complete Spectral Analysis of the CEV Operator with Applications to Arbitrage Holographic functions and neural networks From Betting to Empirical Bernstein LIL Concentration of General Stochastic Approximation Under Heavy-Tailed Markovian Noise Pointwise Generalization in Deep Neural Networks Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors Wasserstein bounds for denoising diffusion probabilistic models via the Föllmer process A note on connections between the Föllmer process and the denoising diffusion probabilistic model Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights Propagation of Chaos in Contextual Flow Maps Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixtures $α$-TCAV: A Unified Framework for Testing with Concept Activation Vectors Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model On the Limits of Latent Reuse in Diffusion Models State-of-art minibatches via novel DPP kernels: discretization, wavelets, and rough objectives
An $Ω(\log(N)/N)$ Lookahead is Sufficient to Bound Costs ...
Robert L. Bray · 2026-01-21 · via math.PR updates on arXiv.org

I study the simplest model of revenue management with reusable resources: admission control of two customer classes into a loss queue. This model's long-run average collected reward has two natural upper bounds: the deterministic relaxation and the full-information offline problem. With these bounds, we can decompose the costs faced by the online decision maker into (i) the \emph{cost of variability}, given by the difference between the deterministic value and the offline value, and (ii) the \emph{cost of uncertainty}, given by the difference between the offline value and the online value. \cite{Xie2025} established that the sum of these two costs is $Θ(\log N)$, as the number of servers, $N$, goes to infinity. I show that we can entirely attribute this $Θ(\log N)$ rate to the cost of uncertainty, as the cost of variability remains $O(1)$ as $N \rightarrow \infty$. In other words, I show that anticipating future fluctuations is sufficient to bound operating costs -- smoothing out these fluctuations is unnecessary. In fact, I show that an $Ω(\log(N)/N)$ lookahead window is sufficient to bound operating costs.