Implementing and exploring MAML, FOMAML, and direct pre-training on sinusoid regression tasks.
Model Agnostic Meta-Learning (Finn et al., 2017) is an algorithm that enables a model to leverage its prior experience in solving various tasks to then learn new tasks much more efficiently compared to otherwise learning from scratch. MAML does so by formulating meta-learning as a bi-level optimization problem, where the inner-level adapts to a new task and the outer-level performs a meta-update on the model's parameters. In this way, MAML learns a set of initial parameters for rapid finetuning:
The crux of MAML lies on Line 10; since the meta-gradient is computed with respect to the outer parameters θ, and not with respect to the inner adapted parameters θi(K), this entails backpropagating through the dynamics of the K steps of gradient descent. Since evaluating this term requires taking expensive higher-order derivatives, first-order MAML (Nichol et al., 2018) simplifies the computation by only considering first-order contributions.
MAML and FOMAML are evaluated on the sinusoid regression problem from Finn et al., 2017 and compared to a baseline of joint pre-training on all meta-training tasks. For consistency, model architectures and hyperparameter values are the same as those in Finn et al., 2017.
The figure below on the left shows the Frobenius norm of the initial adaptation gradient throughout meta-training. This metric quantifies the adaptability of the model parameters, and notably, its value increases over time in both MAML (blue) and FOMAML (green). These results support the claim that "[MAML] can be viewed as maximizing the sensitivity of the loss functions of new tasks with respect to the parameters" (Finn et al., 2017). As such, MAML and FOMAML are able to "learn how to learn" through meta-training and achieve low error using fewer than 10 adaptation steps when meta-testing. A direct pre-training approach (orange) fails because a given input corresponds to many different outputs across the meta-training tasks.
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The plot below qualitatively contrasts MAML and the pre-training baseline. Even when all inputs lie on the same half of the x-axis, MAML is still able to recover the ground truth function in 10 updates, whereas the pre-training approach struggles.
- Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks (Finn et al., 2017).
- On First-Order Meta-Learning Algorithms (Nichol et al., 2018).
- Code structure adapted from Stanford's CS330: Deep Multi-Task and Meta Learning, taught by Prof. Chelsea Finn.