We consider a class of a nested optimization problems involving inner and outer objectives. We observe that by taking into explicit account the optimization dynamics for the inner objective it is possible to derive a general framework that unifies gradient-based hyperparameter optimization and meta-learning (or learning-to-learn). Depending on the specific setting, the variables of the outer objective take either the meaning of hyperparameters in a supervised learning problem or parameters of a meta-learner. We show that some recently proposed methods in the latter setting can be instantiated in our framework and tackled with the same gradient-based algorithms. Finally, we discuss possible design patterns for learning-to-learn and present encouraging preliminary experiments for few-shot learning.
When hyperparameter optimization of a machine learning algorithm is repeated for multiple datasets it is possible to transfer knowledge to an optimization run on a new dataset. We develop a new hyperparameter-free ensemble model for Bayesian optimization that is a generalization of two existing transfer learning extensions to Bayesian optimization and establish a worst-case bound compared to vanilla Bayesian optimization. Using a large collection of hyperparameter optimization benchmark problems, we demonstrate that our contributions substantially reduce optimization time compared to standard Gaussian process-based Bayesian optimization and improve over the current state-of-the-art for transfer hyperparameter optimization.
One possible approach to tackle the class imbalance in classification tasks is to resample a training dataset, i.e., to drop some of its elements or to synthesize new ones. There exist several widely-used resampling methods. Recent research showed that the choice of resampling method significantly affects the quality of classification, which raises resampling selection problem. Exhaustive search for optimal resampling is time-consuming and hence it is of limited use. In this paper, we describe an alternative approach to the resampling selection. We follow the meta-learning concept to build resampling recommendation systems, i.e., algorithms recommending resampling for datasets on the basis of their properties.
Ability to continuously learn and adapt from limited experience in nonstationary environments is an important milestone on the path towards general intelligence. In this paper, we cast the problem of continuous adaptation into the learning-to-learn framework. We develop a simple gradient-based meta-learning algorithm suitable for adaptation in dynamically changing and adversarial scenarios. Additionally, we design a new multi-agent competitive environment, RoboSumo, and define iterated adaptation games for testing various aspects of continuous adaptation strategies. We demonstrate that meta-learning enables significantly more efficient adaptation than reactive baselines in the few-shot regime. Our experiments with a population of agents that learn and compete suggest that meta-learners are the fittest.
In few-shot classification, we are interested in learning algorithms that train a classifier from only a handful of labeled examples. Recent progress in few-shot classification has featured meta-learning, in which a parameterized model for a learning algorithm is defined and trained on episodes representing different classification problems, each with a small labeled training set and its corresponding test set. In this work, we advance this few-shot classification paradigm towards a scenario where unlabeled examples are also available within each episode. We consider two situations: one where all unlabeled examples are assumed to belong to the same set of classes as the labeled examples of the episode, as well as the more challenging situation where examples from other distractor classes are also provided. To address this paradigm, we propose novel extensions of Prototypical Networks (Snell et al., 2017) that are augmented with the ability to use unlabeled examples when producing prototypes. These models are trained in an end-to-end way on episodes, to learn to leverage the unlabeled examples successfully. We evaluate these methods on versions of the Omniglot and miniImageNet benchmarks, adapted to this new framework augmented with unlabeled examples. We also propose a new split of ImageNet, consisting of a large set of classes, with a hierarchical structure. Our experiments confirm that our Prototypical Networks can learn to improve their predictions due to unlabeled examples, much like a semi-supervised algorithm would.
This paper considers meta-learning problems, where there is a distribution of tasks, and we would like to obtain an agent that performs well (i.e., learns quickly) when presented with a previously unseen task sampled from this distribution. We analyze a family of algorithms for learning a parameter initialization that can be fine-tuned quickly on a new task, using only first-order derivatives for the meta-learning updates. This family includes and generalizes first-order MAML, an approximation to MAML obtained by ignoring second-order derivatives. It also includes Reptile, a new algorithm that we introduce here, which works by repeatedly sampling a task, training on it, and moving the initialization towards the trained weights on that task. We expand on the results from Finn et al. showing that first-order meta-learning algorithms perform well on some well-established benchmarks for few-shot classification, and we provide theoretical analysis aimed at understanding why these algorithms work.
How can we build agents that keep learning from experience, quickly and efficiently, after their initial training? Here we take inspiration from the main mechanism of learning in biological brains: synaptic plasticity, carefully tuned by evolution to produce efficient lifelong learning. We show that plasticity, just like connection weights, can be optimized by gradient descent in large (millions of parameters) recurrent networks with Hebbian plastic connections. First, recurrent plastic networks with more than two million parameters can be trained to memorize and reconstruct sets of novel, high-dimensional 1000+ pixels natural images not seen during training. Crucially, traditional non-plastic recurrent networks fail to solve this task. Furthermore, trained plastic networks can also solve generic meta-learning tasks such as the Omniglot task, with competitive results and little parameter overhead. Finally, in reinforcement learning settings, plastic networks outperform a non-plastic equivalent in a maze exploration task. We conclude that differentiable plasticity may provide a powerful novel approach to the learning-to-learn problem.
Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include data simulators that are widely used in engineering and scientific research, generative adversarial networks (GANs) for image synthesis, and hot-off-the-press approximate inference techniques relying on implicit distributions. The majority of existing approaches to learning implicit models rely on approximating the intractable distribution or optimisation objective for gradient-based optimisation, which is liable to produce inaccurate updates and thus poor models. This paper alleviates the need for such approximations by proposing the Stein gradient estimator, which directly estimates the score function of the implicitly defined distribution. The efficacy of the proposed estimator is empirically demonstrated by examples that include meta-learning for approximate inference, and entropy regularised GANs that provide improved sample diversity.
In order to achieve state-of-the-art performance, modern machine learning techniques require careful data pre-processing and hyperparameter tuning. Moreover, given the ever increasing number of machine learning models being developed, model selection is becoming increasingly important. Automating the selection and tuning of machine learning pipelines consisting of data pre-processing methods and machine learning models, has long been one of the goals of the machine learning community. In this paper, we tackle this meta-learning task by combining ideas from collaborative filtering and Bayesian optimization. Using probabilistic matrix factorization techniques and acquisition functions from Bayesian optimization, we exploit experiments performed in hundreds of different datasets to guide the exploration of the space of possible pipelines. In our experiments, we show that our approach quickly identifies high-performing pipelines across a wide range of datasets, significantly outperforming the current state-of-the-art.
We study few-shot learning in natural language domains. Compared to many existing works that apply either metric-based or optimization-based meta-learning to image domain with low inter-task variance, we consider a more realistic setting, where tasks are diverse. However, it imposes tremendous difficulties to existing state-of-the-art metric-based algorithms since a single metric is insufficient to capture complex task variations in natural language domain. To alleviate the problem, we propose an adaptive metric learning approach that automatically determines the best weighted combination from a set of metrics obtained from meta-training tasks for a newly seen few-shot task. Extensive quantitative evaluations on real-world sentiment analysis and dialog intent classification datasets demonstrate that the proposed method performs favorably against state-of-the-art few shot learning algorithms in terms of predictive accuracy. We make our code and data available for further study.
Meta-learning is a promising method to achieve efficient training method towards deep neural net and has been attracting increases interests in recent years. But most of the current methods are still not capable to train complex neuron net model with long-time training process. In this paper, a novel second-order meta-optimizer, named Meta-learning with Hessian-Free(MLHF) approach, is proposed based on the Hessian-Free approach. Two recurrent neural networks are established to generate the damping and the precondition matrix of this Hessian-Free framework. A series of techniques to meta-train the MLHF towards stable and reinforce the meta-training of this optimizer, including the gradient calculation of $H$. Numerical experiments on deep convolution neural nets, including CUDA-convnet and ResNet18(v2), with datasets of CIFAR10 and ILSVRC2012, indicate that the MLHF shows good and continuous training performance during the whole long-time training process, i.e., both the rapid-decreasing early stage and the steadily-deceasing later stage, and so is a promising meta-learning framework towards elevating the training efficiency in real-world deep neural nets.
Multi-task Inverse Reinforcement Learning (IRL) is the problem of inferring multiple reward functions from expert demonstrations. Prior work, built on Bayesian IRL, is unable to scale to complex environments due to computational constraints. This paper contributes a formulation of multi-task IRL in the more computationally efficient Maximum Causal Entropy (MCE) IRL framework. Experiments show our approach can perform one-shot imitation learning in a gridworld environment that single-task IRL algorithms need hundreds of demonstrations to solve. We outline preliminary work using meta-learning to extend our method to the function approximator setting of modern MCE IRL algorithms. Evaluating on multi-task variants of common simulated robotics benchmarks, we discover serious limitations of these IRL algorithms, and conclude with suggestions for further work.
A major goal of unsupervised learning is to discover data representations that are useful for subsequent tasks, without access to supervised labels during training. Typically, this involves minimizing a surrogate objective, such as the negative log likelihood of a generative model, with the hope that representations useful for subsequent tasks will arise as a side effect. In this work, we propose instead to directly target later desired tasks by meta-learning an unsupervised learning rule which leads to representations useful for those tasks. Specifically, we target semi-supervised classification performance, and we meta-learn an algorithm -- an unsupervised weight update rule -- that produces representations useful for this task. Additionally, we constrain our unsupervised update rule to a be a biologically-motivated, neuron-local function, which enables it to generalize to different neural network architectures, datasets, and data modalities. We show that the meta-learned update rule produces useful features and sometimes outperforms existing unsupervised learning techniques. We further show that the meta-learned unsupervised update rule generalizes to train networks with different widths, depths, and nonlinearities. It also generalizes to train on data with randomly permuted input dimensions and even generalizes from image datasets to a text task.
The goal of few-shot learning is to learn a classifier that generalizes well even when trained with a limited number of training instances per class. The recently introduced meta-learning approaches tackle this problem by learning a generic classifier across a large number of multiclass classification tasks and generalizing the model to a new task. Yet, even with such meta-learning, the low-data problem in the novel classification task still remains. In this paper, we propose Transductive Propagation Network (TPN), a novel meta-learning framework for transductive inference that classifies the entire test set at once to alleviate the low-data problem. Specifically, we propose to learn to propagate labels from labeled instances to unlabeled test instances, by learning a graph construction module that exploits the manifold structure in the data. TPN jointly learns both the parameters of feature embedding and the graph construction in an end-to-end manner. We validate TPN on multiple benchmark datasets, on which it largely outperforms existing few-shot learning approaches and achieves the state-of-the-art results.
We perform text normalization, i.e. the transformation of words from the written to the spoken form, using a memory augmented neural network. With the addition of dynamic memory access and storage mechanism, we present a neural architecture that will serve as a language-agnostic text normalization system while avoiding the kind of unacceptable errors made by the LSTM-based recurrent neural networks. By successfully reducing the frequency of such mistakes, we show that this novel architecture is indeed a better alternative. Our proposed system requires significantly lesser amounts of data, training time and compute resources. Additionally, we perform data up-sampling, circumventing the data sparsity problem in some semiotic classes, to show that sufficient examples in any particular class can improve the performance of our text normalization system. Although a few occurrences of these errors still remain in certain semiotic classes, we demonstrate that memory augmented networks with meta-learning capabilities can open many doors to a superior text normalization system.
This paper introduces a new framework for data efficient and versatile learning. Specifically: 1) We develop ML-PIP, a general framework for Meta-Learning approximate Probabilistic Inference for Prediction. ML-PIP extends existing probabilistic interpretations of meta-learning to cover a broad class of methods. 2) We introduce VERSA, an instance of the framework employing a flexible and versatile amortization network that takes few-shot learning datasets as inputs, with arbitrary numbers of shots, and outputs a distribution over task-specific parameters in a single forward pass. VERSA substitutes optimization at test time with forward passes through inference networks, amortizing the cost of inference and relieving the need for second derivatives during training. 3) We evaluate VERSA on benchmark datasets where the method sets new state-of-the-art results, handles arbitrary numbers of shots, and for classification, arbitrary numbers of classes at train and test time. The power of the approach is then demonstrated through a challenging few-shot ShapeNet view reconstruction task.
Deep neural networks have been shown to be very powerful modeling tools for many supervised learning tasks involving complex input patterns. However, they can also easily overfit to training set biases and label noises. In addition to various regularizers, example reweighting algorithms are popular solutions to these problems, but they require careful tuning of additional hyperparameters, such as example mining schedules and regularization hyperparameters. In contrast to past reweighting methods, which typically consist of functions of the cost value of each example, in this work we propose a novel meta-learning algorithm that learns to assign weights to training examples based on their gradient directions. To determine the example weights, our method performs a meta gradient descent step on the current mini-batch example weights (which are initialized from zero) to minimize the loss on a clean unbiased validation set. Our proposed method can be easily implemented on any type of deep network, does not require any additional hyperparameter tuning, and achieves impressive performance on class imbalance and corrupted label problems where only a small amount of clean validation data is available.
In meta-learning an agent extracts knowledge from observed tasks, aiming to facilitate learning of novel future tasks. Under the assumption that future tasks are 'related' to previous tasks, the accumulated knowledge should be learned in a way which captures the common structure across learned tasks, while allowing the learner sufficient flexibility to adapt to novel aspects of new tasks. We present a framework for meta-learning that is based on generalization error bounds, allowing us to extend various PAC-Bayes bounds to meta-learning. Learning takes place through the construction of a distribution over hypotheses based on the observed tasks, and its utilization for learning a new task. Thus, prior knowledge is incorporated through setting an experience-dependent prior for novel tasks. We develop a gradient-based algorithm which minimizes an objective function derived from the bounds and demonstrate its effectiveness numerically with deep neural networks. In addition to establishing the improved performance available through meta-learning, we demonstrate the intuitive way by which prior information is manifested at different levels of the network.
Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic model, even a simple modification of the underlying dynamical system requires significant physical intuition. This paper presents the first meta-learning algorithm that allows automated design for the underlying continuous dynamics of an SG-MCMC sampler. The learned sampler generalizes Hamiltonian dynamics with state-dependent drift and diffusion, enabling fast traversal and efficient exploration of neural network energy landscapes. Experiments validate the proposed approach on both Bayesian fully connected neural network and Bayesian recurrent neural network tasks, showing that the learned sampler out-performs generic, hand-designed SG-MCMC algorithms, and generalizes to different datasets and larger architectures.
In (Franceschi et al., 2018) we proposed a unified mathematical framework, grounded on bilevel programming, that encompasses gradient-based hyperparameter optimization and meta-learning. We formulated an approximate version of the problem where the inner objective is solved iteratively, and gave sufficient conditions ensuring convergence to the exact problem. In this work we show how to optimize learning rates, automatically weight the loss of single examples and learn hyper-representations with Far-HO, a software package based on the popular deep learning framework TensorFlow that allows to seamlessly tackle both HO and ML problems.