When comparing metric-based and optimization-based meta-learning methods, one of the most significant differences lies in their speed of adaptation. Metric-based approaches, such as nearest neighbor or prototypical networks, are designed to rapidly adapt to new tasks by leveraging learned similarity measures in embedding spaces. These methods do not require iterative gradient updates when presented with a new task; instead, they classify new examples by comparing them to stored representations of previously seen data. This direct comparison enables metric-based methods to achieve fast adaptation, often requiring only a forward pass through the network to make predictions on new tasks. In contrast, optimization-based methods, such as Model-Agnostic Meta-Learning (MAML), involve performing several gradient steps during adaptation to a new task, which naturally introduces more computational overhead and latency during inference. The efficiency of metric-based methods makes them especially attractive in scenarios where rapid task adaptation is critical, such as real-time decision making or settings with tight computational constraints.

While metric-based methods excel in speed, optimization-based meta-learning approaches offer greater flexibility and expressiveness. Optimization-based methods are capable of modeling more complex forms of adaptation because they explicitly update model parameters for each new task, allowing the meta-learner to discover intricate dependencies and task-specific nuances. This flexibility enables these methods to handle a broader variety of tasks, especially those that cannot be easily captured by simple similarity measures.

On the other hand, metric-based methods are limited by the expressiveness of the embedding function and the underlying distance metric. If a task requires adaptation that goes beyond what the learned metric can capture, metric-based approaches may struggle. Therefore, when tasks are highly diverse or involve complex, non-linear transformations, optimization-based meta-learning can provide the necessary expressive power to achieve strong performance.

Stability is another key aspect to consider when choosing between these two families of meta-learning methods. Metric-based methods generally offer more stable adaptation, particularly in few-shot learning scenarios where data is scarce. Since these methods rely on fixed embedding spaces and simple comparison operations, they are less prone to overfitting or instability during adaptation. The absence of inner-loop optimization steps eliminates the risk of divergence or oscillations that can occur in optimization-based approaches, especially when task data is noisy or limited. However, the stability of metric-based methods comes at the cost of reduced adaptability to highly complex tasks, as discussed earlier. In summary, metric-based approaches provide a stable and efficient solution for rapid adaptation to tasks that are well-aligned with the learned metric, while optimization-based methods trade off some stability for increased flexibility and expressiveness.