# Game-theoretic statistics and safe anytime-valid inference

arXiv: https://arxiv.org/abs/2210.01948 · HTML: https://mlsanity.com/paper/2210.01948/

## Key facts

- Cited by 155 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2022.

## Built on by (most cited first, 30 of 155)

- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Anytime-valid off-policy inference for contextual bandits](https://mlsanity.com/paper/2210.10768/) (2022)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [A unified recipe for deriving (time-uniform) PAC-Bayes bounds](https://mlsanity.com/paper/2302.03421/) (2023)
- [Auditing Fairness by Betting](https://mlsanity.com/paper/2305.17570/) (2023)
- [Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion](https://mlsanity.com/paper/2310.18554/) (2023)
- [Semiparametric Efficient Inference in Adaptive Experiments](https://mlsanity.com/paper/2311.18274/) (2023)
- [Protected Test-Time Adaptation via Online Entropy Matching: A Betting Approach](https://mlsanity.com/paper/2408.07511/) (2024)
- [E-valuator: Reliable Agent Verifiers with Sequential Hypothesis Testing](https://mlsanity.com/paper/2512.03109/) (2025)
- [Prediction-Powered E-Values](https://mlsanity.com/paper/2502.04294/) (2025)
- [WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingales](https://mlsanity.com/paper/2505.04608/) (2025)
- [Adaptive Learn-then-Test: Statistically Valid and Efficient Hyperparameter Selection](https://mlsanity.com/paper/2409.15844/) (2024)
- [Active, anytime-valid risk controlling prediction sets](https://mlsanity.com/paper/2406.10490/) (2024)
- [Is Your Imitation Learning Policy Better than Mine? Policy Comparison with Near-Optimal Stopping](https://mlsanity.com/paper/2503.10966/) (2025)
- [PACE: Anytime-Valid Acceptance Tests for Self-Evolving Agents](https://mlsanity.com/paper/2606.08106/) (2026)
- [Online multiple testing with e-values](https://mlsanity.com/paper/2311.06412/) (2023)
- [Online Detection of LLM-Generated Texts via Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2410.22318/) (2024)
- [Adaptive Prediction-Powered AutoEval with Reliability and Efficiency Guarantees](https://mlsanity.com/paper/2505.18659/) (2025)
- [Monitoring Risks in Test-Time Adaptation](https://mlsanity.com/paper/2507.08721/) (2025)
- [E-Valuating Classifier Two-Sample Tests](https://mlsanity.com/paper/2210.13027/) (2022)
- [Likelihood Ratio Confidence Sets for Sequential Decision Making](https://mlsanity.com/paper/2311.04402/) (2023)
- [On Continuous Monitoring of Risk Violations under Unknown Shift](https://mlsanity.com/paper/2506.16416/) (2025)
- [Near-Optimal Non-Parametric Sequential Tests and Confidence Sequences with Possibly Dependent Observations](https://mlsanity.com/paper/2212.14411/) (2022)
- [Peeking with PEAK: Sequential, Nonparametric Composite Hypothesis Tests for Means of Multiple Data Streams](https://mlsanity.com/paper/2402.06122/) (2024)
- [An Auditing Test To Detect Behavioral Shift in Language Models](https://mlsanity.com/paper/2410.19406/) (2024)
- [Huber-Robust Confidence Sequences](https://mlsanity.com/paper/2301.09573/) (2023)
- [Deep anytime-valid hypothesis testing](https://mlsanity.com/paper/2310.19384/) (2023)
- [Anytime-valid, Bayes-assisted, Prediction-Powered Inference](https://mlsanity.com/paper/2505.18000/) (2025)
- [Detecting Multi-Agent Collusion Through Multi-Agent Interpretability](https://mlsanity.com/paper/2604.01151/) (2026)
- [Resolution Diagnostics for Paired LLM Evaluation](https://mlsanity.com/paper/2605.30315/) (2026)

## Abstract (arXiv)

Safe anytime-valid inference (SAVI) provides measures of statistical evidence and certainty -- e-processes for testing and confidence sequences for estimation -- that remain valid at all stopping times, accommodating continuous monitoring and analysis of accumulating data and optional stopping or continuation for any reason. These measures crucially rely on test martingales, which are nonnegative martingales starting at one. Since a test martingale is the wealth process of a player in a betting game, SAVI centrally employs game-theoretic intuition, language and mathematics. We summarize the SAVI goals and philosophy, and report recent advances in testing composite hypotheses and estimating functionals in nonparametric settings.