# An Adaptive Algorithm for Learning with Unknown Distribution Drift

arXiv: https://arxiv.org/abs/2305.02252 · HTML: https://mlsanity.com/paper/2305.02252/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 3 May 2023.

## Builds on (most cited first, 5 of 5)

- [On the Rademacher Complexity of Linear Hypothesis Sets](https://mlsanity.com/paper/2007.11045/) (2020)
- [The Sample Complexity of Learning Linear Predictors with the Squared Loss](https://mlsanity.com/paper/1406.5143/) (2014)
- [Statistical Learning under Nonstationary Mixing Processes](https://mlsanity.com/paper/1512.08064/) (2015)
- [Learning with a Drifting Target Concept](https://mlsanity.com/paper/1505.05215/) (2015)
- [Nonparametric Density Estimation under Distribution Drift](https://mlsanity.com/paper/2302.02460/) (2023)

## Built on by (most cited first, 16 of 16)

- [Model Assessment and Selection under Temporal Distribution Shift](https://mlsanity.com/paper/2402.08672/) (2024)
- [A Stability Principle for Learning under Non-Stationarity](https://mlsanity.com/paper/2310.18304/) (2023)
- [Adaptive Smooth Non-Stationary Bandits](https://mlsanity.com/paper/2407.08654/) (2024)
- [An Improved Algorithm for Learning Drifting Discrete Distributions](https://mlsanity.com/paper/2403.05446/) (2024)
- [Adapting to Online Distribution Shifts in Deep Learning: A Black-Box Approach](https://mlsanity.com/paper/2504.07261/) (2025)
- [Adaptive Estimation and Learning under Temporal Distribution Shift](https://mlsanity.com/paper/2505.15803/) (2025)
- [RCCDA: Adaptive Model Updates in the Presence of Concept Drift under a Constrained Resource Budget](https://mlsanity.com/paper/2505.24149/) (2025)
- [Optimal Empirical Risk Minimization under Temporal Distribution Shifts](https://mlsanity.com/paper/2507.13287/) (2025)
- [Online Learning in the Random Order Model](https://mlsanity.com/paper/2510.02820/) (2025)
- [An Adaptive Method for Weak Supervision with Drifting Data](https://mlsanity.com/paper/2306.01658/) (2023)
- [Fast Rates for Nonstationary Weighted Risk Minimization](https://mlsanity.com/paper/2602.05742/) (2026)
- [Distribution-Free Predictive Inference under Unknown Temporal Drift](https://mlsanity.com/paper/2406.06516/) (2024)
- [Efficiently Learning Drifting Halfspaces with Massart Noise](https://mlsanity.com/paper/2606.11149/) (2026)
- [When Can Old Evaluations Certify a New Model? Label-Efficient Release Decisions under Evaluator Drift](https://mlsanity.com/paper/2609.32267/) (2026)
- [Beyond Discrepancy: Oracle Drift in Nonstationary Weighted Risk Minimization](https://mlsanity.com/paper/2610.13598/) (2026)
- [Beyond Aggregate Drift: Optimal Client-Specific Windows in Federated Learning](https://mlsanity.com/paper/2610.15543/) (2026)

## Abstract (arXiv)

We develop and analyze a general technique for learning with an unknown distribution drift. Given a sequence of independent observations from the last T steps of a drifting distribution, our algorithm agnostically learns a family of functions with respect to the current distribution at time T. Unlike previous work, our technique does not require prior knowledge about the magnitude of the drift. Instead, the algorithm adapts to the sample data. Without explicitly estimating the drift, the algorithm learns a family of functions with almost the same error as a learning algorithm that knows the magnitude of the drift in advance. Furthermore, since our algorithm adapts to the data, it can guarantee a better learning error than an algorithm that relies on loose bounds on the drift. We demonstrate the application of our technique in two fundamental learning scenarios: binary classification and linear regression.