Notes

Optimization-Based ML Deep Learning models learn through backpropagation of gradients. However, the gradient-based optimization is neither designed to cope with a small number of training sample, nor to converge within a small number of optimization steps. Is there a way to adjust the optimization algorithm so that the model can be good at learning with a few examples? This is what optimization-based approach meta-learning algorithms intend for. Look at Model-Agnostic Meta-Learning (MAML) and LSTM Meta-Learner, Reptile for further information (Not covered in this class).

Model-Agnostic Meta-Learning (MAML) This is a fairly general optimization algorithm, compatible with any model that learns through gradient descent. Let's say our model is $f_{\theta}$ with parameters $\theta$. Given a task $\tau_{i}$ and its associated dataset ($\mathcal{D}^{(i)}$ train, $\mathcal{D}^{(i)}$ test), we can update the model parameters by one or more gradient descent steps (the following example only contains one step):

where $\mathcal{L}^{(0)}$ is the loss computed using the mini data batch with id (0). The above formula only optimizes for one task. To achieve a good generalization across a variety of tasks, we would like to find the optimal $\theta^{*}$ so that the task-specific fine-tuning is more efficient. Now, we sample a new data batch with id (1) for updating the meta-objective. The loss, denoted as $\mathcal{L}^{(1)}$, depends on the mini batch (1). The superscripts in $\mathcal{L}^{(0)}$ and $\mathcal{L}^{(1)}$ only indicate different data batches, and they refer to the same loss objective for the same task.