# When Is Coarse Supervision Worth It? Cost-Aware Learning under Unknown Aggregation

arXiv: https://arxiv.org/abs/2609.36704 · HTML: https://mlsanity.com/paper/2609.36704/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 14 of 14)

- [Active Learning with Partial Feedback](https://mlsanity.com/paper/1802.07427/) (2018)
- [Efficient Algorithms for Learning from Coarse Labels](https://mlsanity.com/paper/2108.09805/) (2021)
- [Multi-task Active Learning for Pre-trained Transformer-based Models](https://mlsanity.com/paper/2208.05379/) (2022)
- [Full or Weak annotations? An adaptive strategy for budget-constrained annotation campaigns](https://mlsanity.com/paper/2303.11678/) (2023)
- [Instance-wise Supervision-level Optimization in Active Learning](https://mlsanity.com/paper/2503.06517/) (2025)
- [Online Decision Making with Generative Action Sets](https://mlsanity.com/paper/2509.25777/) (2025)
- [Computing exact D-optimal designs by mixed integer second-order cone programming](https://mlsanity.com/paper/1307.4953/) (2013)
- [A bandit-learning approach to multifidelity approximation](https://mlsanity.com/paper/2103.15342/) (2021)
- [Developing and evaluating a chatbot to support maternal health care](https://mlsanity.com/paper/2603.13168/) (2026)
- [Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand](https://mlsanity.com/paper/2605.05609/) (2026)
- [A Randomized Exchange Algorithm for Optimal Design of Multi-Response Experiments](https://mlsanity.com/paper/2407.16283/) (2024)
- [Optimal Exact Designs of Multiresponse Experiments under Linear and Sparsity Constraints](https://mlsanity.com/paper/2507.04713/) (2025)
- [Cost-Aware Optimized Front-Door Experimental Design](https://mlsanity.com/paper/2603.22024/) (2026)
- [Leveraging Vision-Language Models as Weak Annotators in Active Learning](https://mlsanity.com/paper/2605.00480/) (2026)

## Abstract (arXiv)

Modern learning systems often acquire supervision at multiple resolutions, trading annotation cost against information content. We study cost-aware two-resolution learning, where expensive fine labels reveal a vector response and cheaper coarse labels reveal a scalar aggregate formed with unknown weights, while the target remains the full response. The challenge is that unknown aggregation changes which directions coarse data can identify, so the value of coarse supervision depends jointly on cost, noise, and identification. We characterize this information geometry and develop an estimate-and-track policy that learns the aggregation rule and tracks the optimal resolution mix. We derive a closed-form break-even condition for coarse supervision and prove that the online policy attains the optimal leading cumulative-risk coefficient, with a matching local asymptotic minimax lower bound. Synthetic experiments support the predicted all-fine/mixed transition, show the online learner approaching the oracle-share benchmark, and demonstrate a finite-budget gain over all-fine acquisition when coarse supervision is sufficiently favorable. Our results provide a principled way to balance information and annotation cost across supervision resolutions.