When Is Coarse Supervision Worth It? Cost-Aware Learning under Unknown Aggregation
Abstract
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.
Related
- Structure-preserving Fourier Neural Operators for Long-time Cahn-Hilliard Dynamics under Coarse Temporal Supervision
- ELIPPS: Exact Learning for Inverse Problems from Partial Self-supervision
- Fast covariance-free spatiotemporal modeling via coarse-to-fine learning
- Learning to Solve Stochastic Controls with Unknown Drifts and Running Rewards: Theory, Algorithms and Convergence
- A Fully Dual Domain Decomposition Method for Extreme Learning Machines Using GenEO Spectral Coarse Spaces
BibTeX
@misc{xu2026when,
title = {{When Is Coarse Supervision Worth It? Cost-Aware Learning under Unknown Aggregation}},
author = {Jianyu Xu and Smriti Jha and Aarti Singh and Bryan Wilder},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36704},
eprint = {2609.36704},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36704},
}
RIS
TY - UNPB
TI - When Is Coarse Supervision Worth It? Cost-Aware Learning under Unknown Aggregation
AU - Jianyu Xu
AU - Smriti Jha
AU - Aarti Singh
AU - Bryan Wilder
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36704
UR - https://arxiv.org/abs/2609.36704
AB - 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.
ER -