# Generalization Bounds and Stopping Rules for Learning with Self-Selected Data

arXiv: https://arxiv.org/abs/2505.07367 · HTML: https://mlsanity.com/paper/2505.07367/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 110 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 30 of 37)

- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2101.06329/) (2021)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [Algorithms for multi-armed bandit problems](https://mlsanity.com/paper/1402.6028/) (2014)
- [Adaptive Second Order Coresets for Data-efficient Machine Learning](https://mlsanity.com/paper/2207.13887/) (2022)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [A Framework and Benchmark for Deep Batch Active Learning for Regression](https://mlsanity.com/paper/2203.09410/) (2022)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Credal Learning Theory](https://mlsanity.com/paper/2402.00957/) (2024)
- [Statistical Comparisons of Classifiers by Generalized Stochastic Dominance](https://mlsanity.com/paper/2209.01857/) (2022)
- [Training Subset Selection for Weak Supervision](https://mlsanity.com/paper/2206.02914/) (2022)
- [Local case-control sampling: Efficient subsampling in imbalanced data sets](https://mlsanity.com/paper/1306.3706/) (2013)
- [Training Data Subset Selection for Regression with Controlled Generalization Error](https://mlsanity.com/paper/2106.12491/) (2021)
- [Domain Generalisation via Imprecise Learning](https://mlsanity.com/paper/2404.04669/) (2024)
- [Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement](https://mlsanity.com/paper/2306.12803/) (2023)
- [Statistical Multicriteria Benchmarking via the GSD-Front](https://mlsanity.com/paper/2406.03924/) (2024)
- [Revisiting the Predictability of Performative, Social Events](https://mlsanity.com/paper/2503.11713/) (2025)
- [Approximately Bayes-Optimal Pseudo Label Selection](https://mlsanity.com/paper/2302.08883/) (2023)

## Built on by (most cited first, 5 of 5)

- [When Do Credal Sets Stabilize? Fixed-Point Theorems for Credal Set Updates](https://mlsanity.com/paper/2510.04769/) (2025)
- [Adversarial Bandit Optimization with Globally Bounded Perturbations to Linear Losses](https://mlsanity.com/paper/2603.26066/) (2026)
- [Efficient Generalization via Multimodal Co-Training under Data Scarcity and Distribution Shift](https://mlsanity.com/paper/2510.07509/) (2025)
- [Performative Learning Theory](https://mlsanity.com/paper/2602.04402/) (2026)
- [Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification](https://mlsanity.com/paper/2605.12208/) (2026)

## Abstract (arXiv)

Many learning paradigms self-select training data in light of previously learned parameters. Examples include active learning, semi-supervised learning, bandits, or boosting. Rodemann et al. (2024) unify them under the framework of "reciprocal learning". In this article, we address the question of how well these methods can generalize from their self-selected samples. In particular, we prove universal generalization bounds for reciprocal learning using covering numbers and Wasserstein ambiguity sets. Our results require no assumptions on the distribution of self-selected data, only verifiable conditions on the algorithms. We prove results for both convergent and finite iteration solutions. The latter are anytime valid, thereby giving rise to stopping rules for a practitioner seeking to guarantee the out-of-sample performance of their reciprocal learning algorithm. Finally, we illustrate our bounds and stopping rules for reciprocal learning's special case of semi-supervised learning.