MetaLearning-Standford-Lecture4

MetaLearning Learning Note - 4

• optimization based on meta learning
• non-parametric few-shot learning
• properties of meta learning algorithms.

Recap Optimization based meta learning

1. Fine-tuning => MAML our pre-trained parameters will be fine tuned in the test process. $\theta \rightarrow \phi$. In this way, these two varaibles are the same value.

2. Probabilistic Interpretation of Optimization-Based Interference

meta-parameter $\theta$ serve as prior;

$$max_{\theta} log \prod_i p (D_i|\theta)$$

And if we use $\theta$ to initalize $\phi$, we can have this formula:

$$log \prod \int p(D_i| \phi_i)p(\phi_i,\theta) d \theta_i$$

$$log \prod p(D_i | \overline{\phi_i})$$

as the empirical bayes.

3. Optimizaton-Based Inference

Acquire $\phi_i$ through optimization

initialization for fine-tuning

gradient decent + early stopping == MAML

Challenges:

• NAS is also important.
• Bi level optimization can exhibit instabilities - metaRL learn inner vector learning rate - MetaSGD, AlphaMAML
• Backpropagating through many inner GD is compute & memory intensive

we can compute the gradient of $d \frac{\phi}{\theta}$ call the meta gradient implicit function theory.

Can we compute the meta-gradient without differentiating through the optimization path?

Idea: Derive meta-gradient using the implicit function theorem.

Allows for second order optimizers in inenr loop.

Non parametric few shot learning

In low data regimes, non-parametric methods are simple work well.

Learn how to compare using your meta-learning traning for your new tasks

• Siamese network to predict whether or not two images are the same class

but this way, in meta-training: binary classification, but in the metatest, we need to do N-binary classification which means N-way classification.

we do not need to use meta-learner to learn a meta parameter. And do not need to use meta parameter to generate parameter for meta test.

• idea: learn non-linear relation module on embeddings.
• idea: learn infinite mxitre of prototypes
• idea: Perform relationships like nodes in the graph

Properties of meta learning algorithms

• Comparison of approaches

1. computation graph perspective We can mix & match complonents, e.g. embedding + meta-training or MAML + Prototypes
2. Algorithmic Properties Perspective
   • Expresive power the ability for f to represnet a range of learning procedures
   • Consistency learned learning procedure will solve task with enough data. Reduce reliance Black box - no inductive bias at the initialization
3. Uncertainty awareness ability to reason about ambiguity during learning. principled Bayesian approaches.