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A Comprehensive Overview and Survey of Recent Advances in Meta-Learning A PREPRINT
accounted, decoder network projects features to classifier. For generalization to unseen tasks, parameters in
all these modules are updated with MAML. Meta-learner provides initial values for these parameters in base
learner during generalization to unseen tasks. In the inner loop, base learner considers task training data and
updates these parameters from initial values supplied from meta-learner.
Bayesian meta-learning recasts meta-learning to be in the probabilistic framework and integrates Bayesian great minds
thoughts into meta-learning:
•
Bayesian program learning [
61
] generates hand-written characters indistinguishable from real hand writings
using visual checks. Joint distribution of character types, image-specific parameters and images are utilized to
simulate data indistinguishable from real data. Simulated data is augmentation to the original few-shot dataset
and contributes to improvement in predictive accuracy in few-shot learning. Joint posterior distribution of
image-specific parameters and character types is updated during model generalization to unseen tasks.
•
AI-GAs [
6
] consist of meta-learning architecture, learner algorithms and generation of more complex en-
vironment. AI-GAs consider coevolution between agents and environment. AI-GAs provide solutions for
complex environments which are otherwise unsolvable by training from scratch. AI-GAs contains important
interaction between agent and environment. Within evolution, as environment becomes more complex, so does
the solver agent. Each small change in environment corresponds to each small improvement in solver agent.
Evolution of environments guides solver agent to grow and to tackle complex tasks which cannot be solved by
tranining from scratch. AI-GAs are optimization techniques which use meta-learner to guide base learner to
find optimum closer to global optimum.
•
Neural Statistician [
100
] applies variational autoencoder (VAE) to approximate the posterior distribution of
task-specific context. Given posterior distribution, context corresponding to highest posterior probability
is the predicted label of input data. From posterior distribution, we can also obtain confidence interval of
unknow label on input data. VAE is an efficient Bayesian inference tool which not only provides estimation on
unknown quantity but also the uncertainty in predicted value.
•
LLAMA [
101
] recasts MAML as probabilistic inference in a hierarchical Bayesian model. It uses first-order
and second-order Laplace approximation to Gaussian distribution in log likelihood function. For other data
distributions such as multi-modal distribution, highly skewed distribution or fat-tailed distribution, Laplace
approximation does not work well. Laplace approximation shows best results for tightly distributed, symmetric
distributions such as Gaussian distrbution. All distributions in Bayesian framework are taken to be Gaussian so
that log likelihood function can be well approximated by Laplace approximation, which uses point estimation
at the mode to approximate integral of Gaussian distribution.
•
BMAML [
62
] replaces SGD (Stochastic gradient descent) in MAML with SVGD (Stein variational gradient
descent), where SVGD is an efficient Bayesian inference method combining MCMC and variational inference.
SVGD does not only work for all learners optimized with SGD. It uses chaser loss based upon SVGD to
estimate meta-parameter and Bayesian fast adaptation to update task-specific parameters.
•
VERSA [
18
] relies upon distributional Bayesian decision theory for amortized variational inference. Posterior
distribution of true label is approximated and updated during model generalization to unseen tasks.
•
Under Bayesian framework, not only task-specific parameters and meta-parameters are regarded as random
variables, task can also be viewed as a random variable. Task can be considered as countably infinitely many
and Chinese restaurant process is used as the prior distribution for task. Posterior distribution of task is
continually updated and maximum posterior estimate of task is provided in the model generalization process.
All task-specific parameters are taken to be functions of task. Estimation and uncertainty measure for task-
specific parameter are derived from posterior distribution of task. Meta-parameters should be updated using
aggregation of all task posterior distributions.
2.1 Black-Box Meta-Learning
Hyperparameter optimization can be achieved through random grid search or manual search [
48
]. Model search space
is usually indexed by hyperparameters [
22
]. In adaptation to novel tasks, hyperparameters are re-optimized using data
from the novel task. Optimizers can be approximated with neural networks or reinforcement learners [
88
]. Neural
networks can approximate any function with good convergence results. By using neural networks, the optimizer
search space represents a wide range of functions that guarantee better potential optima. For neural network with
varying architectures, hyperparameters include number of layers, number of block modules, number of neurons etc.
These hyperparameters are discrete and optimization techniques are different from continuous hyperparameters such
as learning rate, momentum etc. Bayesian optimization, reinforcement learning optimization, genetic programming
optimization may be employed to optimize both discrete and continuous hyperparameters in deep neural network model.
10