Curriculum Learning as Transport: Understanding Curricula with Wasserstein Geodesics

Curriculum learning couples two design choices, how samples are scored by difficulty and how harder samples are paced into training, making it difficult to attribute observed gains to either component. We disentangle these factors with two evaluation protocols: stage-wise test subsets that validate scoring functions independently of curriculum training, and a baseline that applies the same pacing schedule to randomly ordered data. Within the Transfer Teacher framework (TTF), we use these protocols to evaluate a confusion-aware difficulty score that considers both correct-class confidence and the probability distribution over incorrect classes. On CIFAR-10 with ResNet-18 and VGG-16, the proposed score produces model-interpretable difficulty rankings that align with human intuition. However, at full data, neither curriculum nor anti-curriculum ordering improves accuracy over standard training, indicating that improving the scoring function alone is insufficient to overcome the known failure modes of curriculum learning in TTF. In contrast, We find that confusion-aware curriculum ordering result in consistent data-efficiency benefits, outperforming random ordering by up to 8.7% points at the 20% data regime, suggesting the potential of TTF as a data-efficient training method.

Despite more than a decade of curriculum learning (CL) research in NLP, the field lacks a principled account of which difficulty function or scheduler to use for a given problem. To understand what has hindered progress towards this account, we propose a fine-grained taxonomy separating difficulty evaluation from training scheduling to enable systematic analysis of CL strategies. For difficulty evaluation, we distinguish attribution source and task dependence, revealing difficulty as a perspectival concept encoding different assumptions about what makes an instance hard to learn. For scheduling, we provide the first formalisation of CL schedulers in terms of expected training contribution, enabling comparison across implementations by introducing retention regimes and monotonicity properties. Applied in a dedicated analysis of CL works in NLP, our taxonomy reveals a systematic incomparability problem: prior works conflate distinct notions of difficulty and scheduling, often pursuing different objectives under the same CL label -- hindering comparison and the accumulation of a coherent evidence base. Beyond diagnosis, the taxonomy supports the design, analysis, and comparison of CL strategies, and motivates evaluation practices that disentangle the sources of observed improvement.

In curriculum reinforcement learning (CRL), an agent incrementally accumulates knowledge over a sequence of tasks (i.e., a curriculum), and the learning process is aimed at using the accumulated knowledge to finally solve a challenging target task. While early CRL works focus on sequencing candidate tasks, recent research explores automatic curriculum generation. Among the rich CRL literature, the interpolation-based CRL paradigm is a main body, which automatically generates intermediate tasks by interpolating between the initial task distribution and the target task distribution in task space with meaningful distance metrics (i.e., can measure the task similarity). However, in challenging navigation tasks, the non-Euclidean context (task) space invalidates this assumption. To achieve automatic curriculum generation in complex task, we propose a novel automatic curriculum generation approach based on measurable task representation learning. To better measure the similarity, we propose to transform the task space to a latent space. Through a variational autoencoder structure that encodes the reward and the state transitions, we achieve a latent task representation with a task similarity measurement property, and two close task embeddings correspond to two similar tasks in terms of rewards and state transitions. Based on the learned task representation, we further develop an automatic curriculum generation scheme, which can effectively generate new tasks more and more similar to the target task. We evaluate our method in a variety of challenging navigation tasks, and the experiment results indicate that the proposed approach surpasses state-of-the-art CRL approaches based on interpolation and generative adversarial networks.