mlsanityData to 7 Oct 2026

Time-uniform, nonparametric, nonasymptotic confidence sequences

arXiv 1810.08240 ↗First posted 18 Oct 2018math.ST math.PR stat.MEcited by 220

Not on the map. Why?

Abstract (arXiv)

A confidence sequence is a sequence of confidence intervals that is uniformly valid over an unbounded time horizon. Our work develops confidence sequences whose widths go to zero, with nonasymptotic coverage guarantees under nonparametric conditions. We draw connections between the Cram'er-Chernoff method for exponential concentration, the law of the iterated logarithm (LIL), and the sequential probability ratio test -- our confidence sequences are time-uniform extensions of the first; provide tight, nonasymptotic characterizations of the second; and generalize the third to nonparametric settings, including sub-Gaussian and Bernstein conditions, self-normalized processes, and matrix martingales. We illustrate the generality of our proof techniques by deriving an empirical-Bernstein bound growing at a LIL rate, as well as a novel upper LIL for the maximum eigenvalue of a sum of random matrices. Finally, we apply our methods to covariance matrix estimation and to estimation of sample average treatment effect under the Neyman-Rubin potential outcomes model.

Key facts. Cited by 220 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Oct 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 15; 2022: 27; 2023: 27; 2024: 23; 2025: 31; 2026: 97.

220 papers.

Sort:

By area:

  1. 2021Dueling RL: Reinforcement Learning with Trajectory Preferencescited by 105
  2. 2023DoG is SGD's Best Friend: A Parameter-Free Dynamic Step Size Schedulecited by 85
  3. 2021High-probability Bounds for Non-Convex Stochastic Optimization with Heavy Tailscited by 80
  4. 2022Making SGD Parameter-Freecited by 50
  5. 2021Tight Concentrations and Confidence Sequences from the Regret of Universal Portfoliocited by 42
  6. 2021Tracking the risk of a deployed model and detecting harmful distribution shiftscited by 38
  7. 2022Anytime-valid off-policy inference for contextual banditscited by 37
  8. 2021On the Theory of Reinforcement Learning with Once-per-Episode Feedbackcited by 32
  9. 2023SGD with AdaGrad Stepsizes: Full Adaptivity with High Probability to Unknown Parameters, Unbounded Gradients and Affine Variancecited by 30
  10. 2021Time-uniform central limit theory and asymptotic confidence sequencescited by 29
  11. 2022Guarantees for Epsilon-Greedy Reinforcement Learning with Function Approximationcited by 29
  12. 2022E-detectors: a nonparametric framework for sequential change detectioncited by 27
38 more
  1. 2022Parameter-free Regret in High Probability with Heavy Tailscited by 26
  2. 2022Proximal Point Imitation Learningcited by 25
  3. 2023A unified recipe for deriving (time-uniform) PAC-Bayes boundscited by 25
  4. 2023On the Sublinear Regret of GP-UCBcited by 25
  5. 2023Semiparametric Efficient Inference in Adaptive Experimentscited by 23
  6. 2025E-Values Expand the Scope of Conformal Predictioncited by 23
  7. 2021Neural Active Learning with Performance Guaranteescited by 22
  8. 2022Fully Adaptive Composition in Differential Privacycited by 22
  9. 2024Protected Test-Time Adaptation via Online Entropy Matching: A Betting Approachcited by 22
  10. 2021Near-optimal inference in adaptive linear regressioncited by 20
  11. 2023More PAC-Bayes bounds: From bounded losses, to losses with general tail behaviors, to anytime validitycited by 17
  12. 2022Almost Optimal Variance-Constrained Best Arm Identificationcited by 16
  13. 2025Prediction-Powered E-Valuescited by 16
  14. 2021Off-policy Confidence Sequencescited by 15
  15. 2022Sequential Kernelized Independence Testingcited by 15
  16. 2025Is Your Imitation Learning Policy Better than Mine? Policy Comparison with Near-Optimal Stoppingcited by 14
  17. 2021Weak Signal Asymptotics for Sequentially Randomized Experimentscited by 13
  18. 2022Bregman Deviations of Generic Exponential Familiescited by 13
  19. 2023Online multiple testing with e-valuescited by 12
  20. 2024How Free is Parameter-Free Stochastic Optimization?cited by 12
  21. 2024Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choicescited by 12
  22. 2025Certified Self-Consistency: Statistical Guarantees and Test-Time Training for Reliable Reasoning in LLMscited by 12
  23. 2025Monitoring Risks in Test-Time Adaptationcited by 10
  24. 2023On the near-optimality of betting confidence sets for bounded meanscited by 9
  25. 2024Peeking with PEAK: Sequential, Nonparametric Composite Hypothesis Tests for Means of Multiple Data Streamscited by 9
  26. 2024Second Order Bounds for Contextual Bandits with Function Approximationcited by 9
  27. 2024Sequential Harmful Shift Detection Without Labelscited by 9
  28. 2021A unified framework for bandit multiple testingcited by 8
  29. 2021Best-Arm Identification in Correlated Multi-Armed Banditscited by 8
  30. 2021Comparing Sequential Forecasterscited by 8
  31. 2021Online Selective Classification with Limited Feedbackcited by 8
  32. 2022Multi-disciplinary fairness considerations in machine learning for clinical trialscited by 8
  33. 2022Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observationscited by 8
  34. 2023An Experimental Design for Anytime-Valid Causal Inference on Multi-Armed Banditscited by 8
  35. 2024An Auditing Test To Detect Behavioral Shift in Language Modelscited by 8
  36. 2026Who Drifted: the System or the Judge? Anytime-Valid Attribution in LLM Evaluation Pipelinescited by 8
  37. 2021A Non-asymptotic Approach to Best-Arm Identification for Gaussian Banditscited by 7
  38. 2022Leveraging Initial Hints for Free in Stochastic Linear Banditscited by 7

50 most cited of 220 All 220 (JSON)