Self-Balancing Sequential Sampling: Fast Convergence with Controlled Predictability

[2607.20818] Self-Balancing Sequential Sampling: Fast Convergence with Controlled Predictability Skip to main content Search Submit Donate Log in Mathematics > Probability arXiv:2607.20818 (math) [Submitted on 23 Jul 2026 ( v1 ), last revised 24 Aug 2026 (this version, v2)] Title: Self-Balancing Sequential Sampling: Fast Convergence with Controlled Predictability Authors: Zachary McNulty , Daniel Raban View PDF HTML (experimental) Abstract: Many instances of sequential sampling, including audit and inspection scheduling, representative sampling, and treatment assignment, require selections to be distributed evenly without becoming easy to anticipate or exploit. We study a family of sequential sampling rules that adaptively bias sampling probabilities in order to achieve faster convergence of the empirical distribution to a desired target law, while keeping the resulting samples as unpredictable as possible. The resulting self-balancing sampler is simple to implement, arises naturally among a class of Markovian samplers sharing a certain invariance property, and admits a stochastic mirror-descent interpretation. Our main results show that (i) this self-balancing sampler converges at the fastest possible $O(n^{-1})$ rate with explicit dependence on biasing parameters, beating the standard $O(n^{-1/2})$ rate of IID sampling, (ii) it is the unique solution to a natural entropy-regularized optimization problem which balances the convergence rate of the empirical law and the unpredictability of the samples, and (iii) in the weak-biasing regime, the properly centered counts process converges to an Ornstein-Uhlenbeck process in the diffusive limit. Together, these results support a practical framework for reducing repeated selections and long gaps in coverage without making future selections overly predictable. Comments: 53 pages, 5 figures Subjects: Probability (math.PR) ; Methodology (stat.ME); Machine Learning (stat.ML) MSC classes: 60J10 (Primary), 62L05, 90C25, 60F17 (Secondary) Cite as: arXiv:2607.20818 [math.PR] (or arXiv:2607.20818v2 [math.PR] for this version) https://doi.org/10.48550/arXiv.2607.20818 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Daniel Raban [ view email ] [v1] Thu, 23 Jul 2026 01:10:42 UTC (376 KB) [v2] Mon, 24 Aug 2026 22:40:18 UTC (382 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2026-07 Change to browse by: math stat stat.ME stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Self-Balancing Sequential Sampling: Fast Convergence with Controlled Predictability#670696
• Bagging Robustly Learns VC Classes with Linear Sample Complexity#451279
• Strategically Diverse Sampling for Self-Training#1106270
• Truthful Calibration Measures for Sequential Prediction#480035
• Exploring Randomness#762117