Towards Understanding Generalization in Gradient-Based Meta-Learning

Dans ce mémoire, nous étudions la généralisation des réseaux de neurones dans le contexte du méta-apprentissage, en analysant divers propriétés des surface leurs fonctions objectifs. La recherche en apprentissage automatique portant sur les surfaces de fonctions objectifs des réseaux de neurones ayant aidé à comprendre leur généralisation en apprentissage supervisé standard, nous proposons l'étude de telles surfaces dans le but d'approfondir nos connaissances sur la généralisation en méta-apprentissage. Nous introduisons d'abord la littérature sur les fonctions objectifs des réseaux de neurones à la Section \ref{sec:intro:objective_landscapes}, puis celle portant sur le méta-apprentissage à la Section \ref{sec:intro:meta-learning}, pour enfin terminer notre introduction avec le méta-apprentissage par descente de gradient, très similaire à l'entraînement des réseaux de neurones par descente de gradient stochastique et pour une tâche unique. Nous présentons par la suite notre travail sur les fonctions objectifs en méta-apprentissage au Chapitre \ref{chap:prof_forcing}, lequel nous avons soumis à la conférence NeurIPS 2019 en tant qu'article scientifique. Au moment d'écrire ce mémoire, et au meilleur de notre connaissance, ce travail est le premier à étudier empiriquement les surfaces des fonctions objectifs en méta-apprentissage, particulièrement dans le contexte de l'apprentissage profond, et nous mettons notamment en lumière certaines propriétés de ces surfaces qui apparaissent liées à la généralisation des réseaux de neurones à de nouvelles tâches. Nous démontrons empiriquement qu'alors que progresse la phase de méta-entraînement, pour les solutions aux nouvelles tâches obtenues via quelques itérations de descente de gradient, la courbure de la fonction objective décroit monotoniquement, la valeur de la fonction objective diminue, tandis que la distance euclidienne avec la solution ``méta-entraînement" augmente. Cependant, nous observons que la courbure des minima continue de décroître même lorsque le sur-apprentissage devient apparent et que la généralisation commence à se dégrader, indiquant que la courbure des minima semble peu corrélée à la généralisation en méta-apprentissage par descente de gradient. De plus, nous montrons empiriquement que la généralisation aux nouvelles tâches semble plutôt liée à la cohérence de leurs trajectoires d'adaptation dans l'espace des paramètres, mesurée par la similarité cosinus moyenne entre les trajectoires. Nous montrons également que la cohérence des gradients ''meta-test", mesurée par le produit scalaire moyen entre les vecteurs de gradients spécifiques aux nouvelles tâches, évalué à solution meta-entraînement, est également corrélée à la généralisation. Nous basant sur ces observations, nous proposons un nouveau terme de régularisation pour l'algorithme de méta-apprentissage Model Agnostic Meta-Learning (MAML).In this master's thesis, we study the generalization of neural networks in gradient-based meta-learning by analyzing various properties of the objective landscapes. Meta-learning, a challenging paradigm where models not only have to learn a task but beyond that, are trained for ``learning to learn" as they must adapt to new tasks and environments with very limited data about them. With research on the objective landscapes of neural networks in classical supervised having provided some answers regarding their ability to generalize for new data points, we propose similar analyses aimed at understanding generalization in meta-learning. We first introduce the literature on objective landscapes of neural networks in Section \ref{sec:intro:objective_landscapes}. We then introduce the literature of meta-learning in Section \ref{chap:prof_forcing}, concluding our introduction with the approach of gradient-based meta-learning, a meta-learning setup that bears strong similarities to the traditional supervised learning setup through stochastic gradient-based optimization. At the time of writing of this thesis, and to the best of our knowledge, this is the first work to empirically study the objective landscapes in gradient-based meta-learning, especially in the context of deep learning. We notably provide some insights on some properties of those landscapes that appear correlated to the generalization to new tasks. We experimentally demonstrate that as meta-training progresses, the meta-test solutions, obtained after adapting the meta-train solution of the model, to new tasks via few steps of gradient-based fine-tuning, become flatter, lower in loss, and further away from the meta-train solution. We also show that those meta-test solutions become flatter even as generalization starts to degrade, thus providing experimental evidence against the correlation between generalization and flat minima in the paradigm of gradient-based meta-leaning. Furthermore, we provide empirical evidence that generalization to new tasks is correlated with the coherence between their adaptation trajectories in parameter space, measured by the average cosine similarity between task-specific trajectory directions, starting from a same meta-train solution. We also show that coherence of meta-test gradients, measured by the average inner product between the task-specific gradient vectors evaluated at meta-train solution, is also correlated with generalization. Based on these observations, we propose a novel regularizer for the Model Agnostic Meta-Learning (MAML) algorithm and provide experimental evidence for its effectiveness

How to Retrain Recommender System? A Sequential Meta-Learning Method

Practical recommender systems need be periodically retrained to refresh the model with new interaction data. To pursue high model fidelity, it is usually desirable to retrain the model on both historical and new data, since it can account for both long-term and short-term user preference. However, a full model retraining could be very time-consuming and memory-costly, especially when the scale of historical data is large. In this work, we study the model retraining mechanism for recommender systems, a topic of high practical values but has been relatively little explored in the research community. Our first belief is that retraining the model on historical data is unnecessary, since the model has been trained on it before. Nevertheless, normal training on new data only may easily cause overfitting and forgetting issues, since the new data is of a smaller scale and contains fewer information on long-term user preference. To address this dilemma, we propose a new training method, aiming to abandon the historical data during retraining through learning to transfer the past training experience. Specifically, we design a neural network-based transfer component, which transforms the old model to a new model that is tailored for future recommendations. To learn the transfer component well, we optimize the "future performance" -- i.e., the recommendation accuracy evaluated in the next time period. Our Sequential Meta-Learning(SML) method offers a general training paradigm that is applicable to any differentiable model. We demonstrate SML on matrix factorization and conduct experiments on two real-world datasets. Empirical results show that SML not only achieves significant speed-up, but also outperforms the full model retraining in recommendation accuracy, validating the effectiveness of our proposals. We release our codes at: https://github.com/zyang1580/SML.Comment: Appear in SIGIR 202