Understanding the practical application of Model-Agnostic Meta-Learning (MAML) requires examining its computational demands and the ways researchers have sought to make it more efficient. One significant innovation is the use of first-order approximations. In standard MAML, the meta-gradient is computed by backpropagating through the inner adaptation steps, which requires calculating higher-order derivatives. First-order approximations, such as First-Order MAML (FOMAML) and Reptile, simplify this process by ignoring or approximating these second-order terms. This means that, instead of differentiating through the entire adaptation process, you update the meta-parameters using only the gradients from the adapted parameters, effectively treating the adaptation as a constant with respect to the meta-parameters. This simplification dramatically reduces the complexity of the meta-gradient computation while often retaining much of the benefit of full MAML.

The computational cost of MAML can be substantial, especially when dealing with deep neural networks or a large number of adaptation steps. Each meta-update involves running several forward and backward passes for every task in the meta-batch, and then differentiating through these steps, leading to high memory usage and increased computation time. First-order approximations help mitigate this by reducing the need to store intermediate computations required for second-order derivatives, resulting in faster training and lower memory requirements. However, this comes at the potential cost of slightly reduced accuracy or slower convergence, since the update is no longer fully aligned with the true meta-gradient.

Despite its strengths, MAML is not without limitations. Theoretical analysis reveals that MAML assumes the existence of a shared initialization that can be quickly adapted to all tasks, which may not hold if tasks are highly diverse or non-stationary. In such cases, the meta-learned initialization may not provide a significant advantage, and adaptation may fail to generalize.

MAML can also be sensitive to hyperparameters such as the number of inner adaptation steps, the choice of optimizer, and the size of the meta-batch. Furthermore, when the tasks are not sufficiently similar, MAML may converge to an initialization that is suboptimal for all tasks, or even fail to converge at all.

These limitations highlight the importance of understanding the assumptions underlying MAML and carefully evaluating its applicability to a given problem domain.