Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance

Multi-objective learning (MOL) problems often arise in emerging machine learning problems when there are multiple learning criteria or multiple learning tasks. Recent works have developed various dynamic weighting algorithms for MOL such as MGDA and its variants, where the central idea is to find an update direction that avoids conflicts among objectives. Albeit its appealing intuition, empirical studies show that dynamic weighting methods may not always outperform static ones. To understand this theory-practical gap, we focus on a new stochastic variant of MGDA - the Multi-objective gradient with Double sampling (MoDo) algorithm, and study the generalization performance of the dynamic weighting-based MoDo and its interplay with optimization through the lens of algorithm stability. Perhaps surprisingly, we find that the key rationale behind MGDA -- updating along conflict-avoidant direction - may hinder dynamic weighting algorithms from achieving the optimal ${\cal O}(1/\sqrt{n})$ population risk, where $n$ is the number of training samples. We further demonstrate the variability of dynamic weights on the three-way trade-off among optimization, generalization, and conflict avoidance that is unique in MOL.

Learning with Limited Samples -- Meta-Learning and Applications to Communication Systems

Deep learning has achieved remarkable success in many machine learning tasks such as image classification, speech recognition, and game playing. However, these breakthroughs are often difficult to translate into real-world engineering systems because deep learning models require a massive number of training samples, which are costly to obtain in practice. To address labeled data scarcity, few-shot meta-learning optimizes learning algorithms that can efficiently adapt to new tasks quickly. While meta-learning is gaining significant interest in the machine learning literature, its working principles and theoretic fundamentals are not as well understood in the engineering community. This review monograph provides an introduction to meta-learning by covering principles, algorithms, theory, and engineering applications. After introducing meta-learning in comparison with conventional and joint learning, we describe the main meta-learning algorithms, as well as a general bilevel optimization framework for the definition of meta-learning techniques. Then, we summarize known results on the generalization capabilities of meta-learning from a statistical learning viewpoint. Applications to communication systems, including decoding and power allocation, are discussed next, followed by an introduction to aspects related to the integration of meta-learning with emerging computing technologies, namely neuromorphic and quantum computing. The monograph is concluded with an overview of open research challenges.

Understanding Benign Overfitting in Nested Meta Learning

Meta learning has demonstrated tremendous success in few-shot learning with limited supervised data. In those settings, the meta model is usually overparameterized. While the conventional statistical learning theory suggests that overparameterized models tend to overfit, empirical evidence reveals that overparameterized meta learning methods still work well -- a phenomenon often called ``benign overfitting.'' To understand this phenomenon, we focus on the meta learning settings with a challenging nested structure that we term the nested meta learning, and analyze its generalization performance under an overparameterized meta learning model. While our analysis uses the relatively tractable linear models, our theory contributes to understanding the delicate interplay among data heterogeneity, model adaptation and benign overfitting in nested meta learning tasks. We corroborate our theoretical claims through numerical simulations.

Sharp-MAML: Sharpness-Aware Model-Agnostic Meta Learning

Model-agnostic meta learning (MAML) is currently one of the dominating approaches for few-shot meta-learning. Albeit its effectiveness, the optimization of MAML can be challenging due to the innate bilevel problem structure. Specifically, the loss landscape of MAML is much more complex with possibly more saddle points and local minimizers than its empirical risk minimization counterpart. To address this challenge, we leverage the recently invented sharpness-aware minimization and develop a sharpness-aware MAML approach that we term Sharp-MAML. We empirically demonstrate that Sharp-MAML and its computation-efficient variant can outperform popular existing MAML baselines (e.g., $+12\%$ accuracy on Mini-Imagenet). We complement the empirical study with the convergence rate analysis and the generalization bound of Sharp-MAML. To the best of our knowledge, this is the first empirical and theoretical study on sharpness-aware minimization in the context of bilevel learning. The code is available at https://github.com/mominabbass/Sharp-MAML.

Is Bayesian Model-Agnostic Meta Learning Better than Model-Agnostic Meta Learning, Provably?

Meta learning aims at learning a model that can quickly adapt to unseen tasks. Widely used meta learning methods include model agnostic meta learning (MAML), implicit MAML, Bayesian MAML. Thanks to its ability of modeling uncertainty, Bayesian MAML often has advantageous empirical performance. However, the theoretical understanding of Bayesian MAML is still limited, especially on questions such as if and when Bayesian MAML has provably better performance than MAML. In this paper, we aim to provide theoretical justifications for Bayesian MAML's advantageous performance by comparing the meta test risks of MAML and Bayesian MAML. In the meta linear regression, under both the distribution agnostic and linear centroid cases, we have established that Bayesian MAML indeed has provably lower meta test risks than MAML. We verify our theoretical results through experiments.

Deep Structured Prediction for Facial Landmark Detection

Existing deep learning based facial landmark detection methods have achieved excellent performance. These methods, however, do not explicitly embed the structural dependencies among landmark points. They hence cannot preserve the geometric relationships between landmark points or generalize well to challenging conditions or unseen data. This paper proposes a method for deep structured facial landmark detection based on combining a deep Convolutional Network with a Conditional Random Field. We demonstrate its superior performance to existing state-of-the-art techniques in facial landmark detection, especially a better generalization ability on challenging datasets that include large pose and occlusion.