Conditions for optimality of easy-to-hard curricula

Determine the conditions under which an easy-to-hard curriculum—i.e., training protocols that present examples in increasing order of difficulty—achieves optimal final generalization performance, and characterize alternative difficulty schedules that outperform the easy-to-hard ordering when those conditions are not met.

Background

The paper studies curriculum learning within a teacher–student setting and develops an optimal-control framework to design training schedules. Prior analytical works have largely evaluated fixed curricula and heuristic strategies, leaving open when an easy-to-hard ordering is provably optimal and when other schedules are better. The authors apply their framework to a prototypical binary classification model and find non-monotonic optimal schedules, motivating a formal characterization of the conditions that favor easy-to-hard curricula versus alternatives.

This problem seeks a principled delineation of regimes—across data heterogeneity, model class, and training dynamics—in which an easy-to-hard curriculum is optimal, and identification of schedules that strictly dominate it otherwise.

References

In particular, it remains unclear under what conditions an easy-to-hard curriculum is truly optimal and what alternative strategies might outperform it when it is not.

— A statistical physics framework for optimal learning  (2507.07907 - Mignacco et al., 10 Jul 2025) in Section 4.1 (Curriculum learning)

We intentionally constrain most of the study to from-scratch training and newly constructed tasks, reducing confounding from pretrained knowledge but leaving open how the results transfer to pretrained settings, natural data, and tasks whose difficulty structure interacts with prior knowledge.

— Curriculum Learning as Transport: Understanding Curricula with Wasserstein Geodesics  (2609.09099 - Shin et al., 8 Sep 2026) in Section ‘Limitations and Future Work’ in the Conclusion

Whether it had also stopped improving is not established here.

— CORAL: Curriculum-Optimized Reward Adaptation for LiDAR-Based Goal-Directed Urban Driving  (2608.14332 - Saleem et al., 14 Aug 2026) in Section 4.3, 'Ablation: Reward and Distance Schedules'