# Protected Test-Time Adaptation via Online Entropy Matching: A Betting Approach

arXiv: https://arxiv.org/abs/2408.07511 · HTML: https://mlsanity.com/paper/2408.07511/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 73 of its 110 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 30 of 73)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Improving robustness against common corruptions by covariate shift adaptation](https://mlsanity.com/paper/2006.16971/) (2020)
- [Towards Stable Test-Time Adaptation in Dynamic Wild World](https://mlsanity.com/paper/2302.12400/) (2023)
- [MEMO: Test Time Robustness via Adaptation and Augmentation](https://mlsanity.com/paper/2110.09506/) (2021)
- [A Survey of Unsupervised Deep Domain Adaptation](https://mlsanity.com/paper/1812.02849/) (2018)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [Contrastive Test-Time Adaptation](https://mlsanity.com/paper/2204.10377/) (2022)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [A DIRT-T Approach to Unsupervised Domain Adaptation](https://mlsanity.com/paper/1802.08735/) (2018)
- [Simultaneous Deep Transfer Across Domains and Tasks](https://mlsanity.com/paper/1510.02192/) (2015)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Robust Test-Time Adaptation in Dynamic Scenarios](https://mlsanity.com/paper/2303.13899/) (2023)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Asymmetric Tri-training for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1702.08400/) (2017)
- [NOTE: Robust Continual Test-time Adaptation Against Temporal Correlation](https://mlsanity.com/paper/2208.05117/) (2022)
- [Coin Betting and Parameter-Free Online Learning](https://mlsanity.com/paper/1602.04128/) (2016)
- [Cycle Self-Training for Domain Adaptation](https://mlsanity.com/paper/2103.03571/) (2021)
- [An introduction to domain adaptation and transfer learning](https://mlsanity.com/paper/1812.11806/) (2018)
- [Test-Time Adaptable Neural Networks for Robust Medical Image Segmentation](https://mlsanity.com/paper/2004.04668/) (2020)

## Built on by (most cited first, 23 of 23)

- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (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)
- [Online Detection of LLM-Generated Texts via Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2410.22318/) (2024)
- [Monitoring Risks in Test-Time Adaptation](https://mlsanity.com/paper/2507.08721/) (2025)
- [On Continuous Monitoring of Risk Violations under Unknown Shift](https://mlsanity.com/paper/2506.16416/) (2025)
- [You only need 4 extra tokens: Synergistic Test-time Adaptation for LLMs](https://mlsanity.com/paper/2510.10223/) (2025)
- [Optimistic Interior Point Methods for Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2502.07774/) (2025)
- [Testing For Distribution Shifts with Conditional Conformal Test Martingales](https://mlsanity.com/paper/2602.13848/) (2026)
- [ASAP: Unsupervised Post-training with Label Distribution Shift Adaptive Learning Rate](https://mlsanity.com/paper/2508.13445/) (2025)
- [Class-aware Domain Knowledge Fusion and Fission for Continual Test-Time Adaptation](https://mlsanity.com/paper/2510.12150/) (2025)
- [Prediction-Powered Risk Monitoring of Deployed Models for Detecting Harmful Distribution Shifts](https://mlsanity.com/paper/2602.02229/) (2026)
- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [On the Learnability of Test-Time Adaptation: A Recovery Complexity Perspective](https://mlsanity.com/paper/2605.28057/) (2026)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [ProtoDCS: Towards Robust and Efficient Open-Set Test-Time Adaptation for Vision-Language Models](https://mlsanity.com/paper/2602.23653/) (2026)
- [Fairness-Aware Test-Time Prompt Tuning](https://mlsanity.com/paper/2608.25707/) (2026)
- [Detecting Object Tracking Failure via Sequential Hypothesis Testing](https://mlsanity.com/paper/2602.12983/) (2026)
- [Toward Robust Open-set Adaptation: Synapse Consolidation Inspired by Rac1/MAPK Pathways](https://mlsanity.com/paper/2604.00533/) (2026)
- [Entropy Minimization without Model Collapse: Mitigating Prediction Bias in Medical Imaging](https://mlsanity.com/paper/2606.02339/) (2026)
- [Online Safety Monitoring for LLMs](https://mlsanity.com/paper/2607.02510/) (2026)
- [Online Test-Time Adaptation for Generalizable Dynamic Graph Anomaly Detection](https://mlsanity.com/paper/2608.19858/) (2026)
- [The Premise Is the Problem: Exchangeability Failure in Self-Monitored Test-Time Adaptation](https://mlsanity.com/paper/2610.07038/) (2026)

## Abstract (arXiv)

We present a novel approach for test-time adaptation via online self-training, consisting of two components. First, we introduce a statistical framework that detects distribution shifts in the classifier's entropy values obtained on a stream of unlabeled samples. Second, we devise an online adaptation mechanism that utilizes the evidence of distribution shifts captured by the detection tool to dynamically update the classifier's parameters. The resulting adaptation process drives the distribution of test entropy values obtained from the self-trained classifier to match those of the source domain, building invariance to distribution shifts. This approach departs from the conventional self-training method, which focuses on minimizing the classifier's entropy. Our approach combines concepts in betting martingales and online learning to form a detection tool capable of quickly reacting to distribution shifts. We then reveal a tight relation between our adaptation scheme and optimal transport, which forms the basis of our novel self-supervised loss. Experimental results demonstrate that our approach improves test-time accuracy under distribution shifts while maintaining accuracy and calibration in their absence, outperforming leading entropy minimization methods across various scenarios.