# Online control of the false discovery rate with decaying memory

arXiv: https://arxiv.org/abs/1710.00499 · HTML: https://mlsanity.com/paper/1710.00499/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2017.

## Built on by (most cited first, 11 of 11)

- [Online false discovery rate control for anomaly detection in time series](https://mlsanity.com/paper/2112.03196/) (2021)
- [PACE: Anytime-Valid Acceptance Tests for Self-Evolving Agents](https://mlsanity.com/paper/2606.08106/) (2026)
- [Conformal Anomaly Detection on Spatio-Temporal Observations with Missing Data](https://mlsanity.com/paper/2105.11886/) (2021)
- [Online multiple testing with e-values](https://mlsanity.com/paper/2311.06412/) (2023)
- [QuTE: decentralized multiple testing on sensor networks with false discovery rate control](https://mlsanity.com/paper/2210.04334/) (2022)
- [Online Control of the False Discovery Rate under "Decision Deadlines"](https://mlsanity.com/paper/2110.01583/) (2021)
- [Online False Discovery Rate Control for LORD & SAFFRON Under Positive, Local Dependence](https://mlsanity.com/paper/2110.08161/) (2021)
- [Structural Enforcement of Statistical Rigor in AI-Driven Discovery: A Functional Architecture](https://mlsanity.com/paper/2511.06701/) (2025)
- [Cost-aware Generalized α-investing for Multiple Hypothesis Testing](https://mlsanity.com/paper/2210.17514/) (2022)
- [Online Conformal Anomaly Detection with Prediction-Powered Data Acquisition](https://mlsanity.com/paper/2505.01783/) (2025)
- [A Regret Perspective on Online Multiple Testing](https://mlsanity.com/paper/2605.13916/) (2026)

## Abstract (arXiv)

In the online multiple testing problem, p-values corresponding to different null hypotheses are observed one by one, and the decision of whether or not to reject the current hypothesis must be made immediately, after which the next p-value is observed. Alpha-investing algorithms to control the false discovery rate (FDR), formulated by Foster and Stine, have been generalized and applied to many settings, including quality-preserving databases in science and multiple A/B or multi-armed bandit tests for internet commerce. This paper improves the class of generalized alpha-investing algorithms (GAI) in four ways: (a) we show how to uniformly improve the power of the entire class of monotone GAI procedures by awarding more alpha-wealth for each rejection, giving a win-win resolution to a recent dilemma raised by Javanmard and Montanari, (b) we demonstrate how to incorporate prior weights to indicate domain knowledge of which hypotheses are likely to be non-null, (c) we allow for differing penalties for false discoveries to indicate that some hypotheses may be more important than others, (d) we define a new quantity called the decaying memory false discovery rate (mem-FDR) that may be more meaningful for truly temporal applications, and which alleviates problems that we describe and refer to as "piggybacking" and "alpha-death". Our GAI++ algorithms incorporate all four generalizations simultaneously, and reduce to more powerful variants of earlier algorithms when the weights and decay are all set to unity. Finally, we also describe a simple method to derive new online FDR rules based on an estimated false discovery proportion.