Learning to Extrapolate: A Transductive Approach
This addresses the challenge of poor performance on out-of-support data for machine learning practitioners, though it appears incremental as it builds on existing transductive and combinatorial generalization ideas.
The paper tackles the problem of enabling overparameterized machine learning systems to extrapolate to out-of-support test points by proposing a transductive reparameterization that converts it into a within-support combinatorial generalization problem, resulting in a simple algorithm applicable to supervised and imitation learning tasks.
Machine learning systems, especially with overparameterized deep neural networks, can generalize to novel test instances drawn from the same distribution as the training data. However, they fare poorly when evaluated on out-of-support test points. In this work, we tackle the problem of developing machine learning systems that retain the power of overparameterized function approximators while enabling extrapolation to out-of-support test points when possible. This is accomplished by noting that under certain conditions, a "transductive" reparameterization can convert an out-of-support extrapolation problem into a problem of within-support combinatorial generalization. We propose a simple strategy based on bilinear embeddings to enable this type of combinatorial generalization, thereby addressing the out-of-support extrapolation problem under certain conditions. We instantiate a simple, practical algorithm applicable to various supervised learning and imitation learning tasks.