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An increasingly popular machine learning paradigm is to pretrain a neural network (NN) on many tasks offline, then adapt it to downstream tasks, often by re-training only the last linear layer of the network. This approach yields strong downstream performance in a variety of contexts, demonstrating that multitask pretraining leads to effective feature learning. Although several recent theoretical studies have shown that shallow NNs learn meaningful features when either (i) they are trained on a single task or (ii) they are linear, very little is known about the closer-to-practice case of nonlinear NNs trained on multiple tasks. In this work, we present the first results proving that feature learning occurs during training with a nonlinear model on multiple tasks. Our key insight is that multi-task pretraining induces a pseudo-contrastive loss that favors representations that align points that typically have the same label across tasks. Using this observation, we show that when the tasks are binary classification tasks with labels depending on the projection of the data onto an r-dimensional subspace within the d k r-dimensional input space, a simple gradient-based multitask learning algorithm on a two-layer ReLU NN recovers this projection, allowing for generalization to downstream tasks with sample and neuron complexity independent of d. In contrast, we show that with high probability over the draw of a single task, training on this single task cannot guarantee to learn all r ground-truth features.
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Extracting Latent State Representations with Linear Dynamics from Rich Observations
Recently, many reinforcement learning techniques have been shown to have provable guarantees in the simple case of linear dynamics, especially in problems like linear quadratic regulators. However, in practice many tasks require learning a policy from rich, high-dimensional features such as images, which are unlikely to be linear. We consider a setting where there is a hidden linear subspace of the high-dimensional feature space in which the dynamics are linear. We design natural objectives based on forward and inverse dynamics models. We prove that these objectives can be efficiently optimized and their local optimizers extract the hidden linear subspace. We empirically verify our theoretical results with synthetic data and explore the effectiveness of our approach (generalized to nonlinear settings) in simple control tasks with rich observations.
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- PAR ID:
- 10346975
- Date Published:
- Journal Name:
- The Thirty-ninth International Conference on Machine Learning ICML
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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An increasingly popular machine learning paradigm is to pretrain a neural network (NN) on many tasks offline, then adapt it to downstream tasks, often by re-training only the last linear layer of the network. This approach yields strong downstream performance in a variety of contexts, demonstrating that multitask pretraining leads to effective feature learning. Although several recent theoretical studies have shown that shallow NNs learn meaningful features when either (i) they are trained on a single task or (ii) they are linear, very little is known about the closer-to-practice case of nonlinear NNs trained on multiple tasks. In this work, we present the first results proving that feature learning occurs during training with a nonlinear model on multiple tasks. Our key insight is that multi-task pretraining induces a pseudo-contrastive loss that favors representations that align points that typically have the same label across tasks. Using this observation, we show that when the tasks are binary classification tasks with labels depending on the projection of the data onto an 𝑟-dimensional subspace within the 𝑑 ≫𝑟-dimensional input space, a simple gradient-based multitask learning algorithm on a two-layer ReLU NN recovers this projection, allowing for generalization to downstream tasks with sample and neuron complexity independent of 𝑑. In contrast, we show that with high probability over the draw of a single task, training on this single task cannot guarantee to learn all 𝑟 ground-truth features.more » « less
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