# One Knob to Rule Them All: A Unified Optimal Transport View of Cold-Start Active Learning

arXiv: https://arxiv.org/abs/2608.03249 · HTML: https://mlsanity.com/paper/2608.03249/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 54 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 18 of 18)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Selection via Proxy: Efficient Data Selection for Deep Learning](https://mlsanity.com/paper/1906.11829/) (2019)
- [Learning Loss for Active Learning](https://mlsanity.com/paper/1905.03677/) (2019)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Active Learning on a Budget: Opposite Strategies Suit High and Low Budgets](https://mlsanity.com/paper/2202.02794/) (2022)
- [Cold-start Active Learning through Self-supervised Language Modeling](https://mlsanity.com/paper/2010.09535/) (2020)
- [Gone Fishing: Neural Active Learning with Fisher Embeddings](https://mlsanity.com/paper/2106.09675/) (2021)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [Reducing Label Effort: Self-Supervised meets Active Learning](https://mlsanity.com/paper/2108.11458/) (2021)
- [Parting with Illusions about Deep Active Learning](https://mlsanity.com/paper/1912.05361/) (2019)
- [Active Finetuning: Exploiting Annotation Budget in the Pretraining-Finetuning Paradigm](https://mlsanity.com/paper/2303.14382/) (2023)
- [Generalized Coverage for More Robust Low-Budget Active Learning](https://mlsanity.com/paper/2407.12212/) (2024)
- [Uncertainty Herding: One Active Learning Method for All Label Budgets](https://mlsanity.com/paper/2412.20644/) (2024)
- [DCoM: Active Learning for All Learners](https://mlsanity.com/paper/2407.01804/) (2024)

## Abstract (arXiv)

Cold-Start Active Learning (CSAL) aims to select a valuable subset from an unlabeled pool without any prior knowledge or human assistance. Existing methods take diverse routes based on typicality, coverage, or diversity. Each rests on its own inductive bias and therefore performs well on some tasks yet poorly on others. We argue that the real challenge is not to design yet another selection heuristic, but to make CSAL adapt automatically to the data and task at hand. To this end, we revisit CSAL through the lens of optimal transport. First, we propose a generalized transport selection framework that reveals the shared allocation structure of existing methods and exactly subsumes representative formulations. Second, we introduce a theoretical analysis that characterizes the trade-off controlled by entropic regularization and establishes a task-agnostic minimax bound for cold-start selection. These results provide a principled foundation for adapting the regularization strength to the unlabeled data. Third, we derive a data-adaptive regularization rule and present a novel Sinkhorn-based CSAL algorithm, termed ε-Adaptive Selection (ε-AS). Extensive experiments on six public datasets and multiple annotation budgets show that ε-AS consistently achieves state-of-the-art performance. On ImageNet-1k, it improves the average accuracy over ActiveFT by 1.29% while reducing selection time by 56.2%. Code will be released at https://github.com/Z-yiwei/OT-CSAL