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

2026-09-29

AI Summary

This study addresses the trade-off between annotation cost and information gain in multi-resolution supervised learning under unknown aggregation mechanisms. To tackle this challenge, we propose a cost-aware, adaptive two-resolution mixed decision framework. By revealing the information-geometric properties under unknown aggregation, we derive the break-even condition for coarse supervision. Integrating online learning with convex optimization techniques, the framework dynamically estimates and tracks the optimal strategy to achieve an optimal configuration of coarse- and fine-grained labels. Theoretically, we prove that the proposed online strategy attains the asymptotic minimax lower bound of the cumulative risk coefficient. Empirically, experiments demonstrate that under limited budgets, our framework significantly outperforms purely fine-grained annotation strategies while achieving performance closely approximating the oracle benchmark.

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.

Problem

• coarse supervision
• cost-aware learning
• unknown aggregation
• two-resolution learning
• annotation cost

Innovation

• Cost-Aware Learning
• Coarse Supervision
• Unknown Aggregation
• Estimate-and-Track Policy
• Information Geometry