Wasserstein Task Embedding for Measuring Task Similarities
This addresses a critical need in transfer, multi-task, continual, and meta-learning by providing a faster and more efficient way to compare tasks, though it is incremental as it builds on existing optimal transport methods.
The paper tackles the problem of measuring task similarities in machine learning by proposing a model-agnostic, training-free task embedding based on optimal transport theory, which significantly speeds up comparisons and shows statistically significant correlations with transfer metrics.
Measuring similarities between different tasks is critical in a broad spectrum of machine learning problems, including transfer, multi-task, continual, and meta-learning. Most current approaches to measuring task similarities are architecture-dependent: 1) relying on pre-trained models, or 2) training networks on tasks and using forward transfer as a proxy for task similarity. In this paper, we leverage the optimal transport theory and define a novel task embedding for supervised classification that is model-agnostic, training-free, and capable of handling (partially) disjoint label sets. In short, given a dataset with ground-truth labels, we perform a label embedding through multi-dimensional scaling and concatenate dataset samples with their corresponding label embeddings. Then, we define the distance between two datasets as the 2-Wasserstein distance between their updated samples. Lastly, we leverage the 2-Wasserstein embedding framework to embed tasks into a vector space in which the Euclidean distance between the embedded points approximates the proposed 2-Wasserstein distance between tasks. We show that the proposed embedding leads to a significantly faster comparison of tasks compared to related approaches like the Optimal Transport Dataset Distance (OTDD). Furthermore, we demonstrate the effectiveness of our proposed embedding through various numerical experiments and show statistically significant correlations between our proposed distance and the forward and backward transfer between tasks.