Meta-learning allows an intelligent agent to leverage prior learning episodes as a basis for quickly improving performance on a novel task. Bayesian hierarchical modeling provides a theoretical framework for formalizing meta-learning as inference for a set of parameters that are shared across tasks. Here, we reformulate the model-agnostic meta-learning algorithm (MAML) of Finn et al. (2017) as a method for probabilistic inference in a hierarchical Bayesian model. In contrast to prior methods for meta-learning via hierarchical Bayes, MAML is naturally applicable to complex function approximators through its use of a scalable gradient descent procedure for posterior inference. Furthermore, the identification of MAML as hierarchical Bayes provides a way to understand the algorithm's operation as a meta-learning procedure, as well as an opportunity to make use of computational strategies for efficient inference. We use this opportunity to propose an improvement to the MAML algorithm that makes use of techniques from approximate inference and curvature estimation.
The University of Melbourne（墨尔本大学）；Monash University（莫纳什大学）
Inspired by the concept of preconditioning, we propose a novel method to increase adaptation speed for gradient-based meta-learning methods without incurring extra parameters. We demonstrate that recasting the optimization problem to a non-linear least-squares formulation provides a principled way to actively enforce a $\textit{well-conditioned}$ parameter space for meta-learning models based on the concepts of the condition number and local curvature. Our comprehensive evaluations show that the proposed method significantly outperforms its unconstrained counterpart especially during initial a…
Meta-learning or few-shot learning, has been successfully applied in a wide range of domains from computer vision to reinforcement learning. Among the many frameworks proposed for meta-learning, bayesian methods are particularly favoured when accurate and calibrated uncertainty estimate is required. In this paper, we investigate the similarities and disparities among two recently published bayesian meta-learning methods: ALPaCA (Harrison et al. [2018]) and PACOH (Rothfuss et al. [2020]). We provide theoretical analysis as well as empirical benchmarks across synthetic and real-world dataset. Wh…
University of Edinburgh（爱丁堡大学）；Samsung AI Centre（三星人工智能中心）；University of Chinese Academy of Sciences（中国科学院大学）
Current state-of-the-art few-shot learners focus on developing effective training procedures for feature representations, before using simple, e.g. nearest centroid, classifiers. In this paper, we take an orthogonal approach that is agnostic to the features used and focus exclusively on meta-learning the actual classifier layer. Specifically, we introduce MetaQDA, a Bayesian meta-learning generalization of the classic quadratic discriminant analysis. This setup has several benefits of interest to practitioners: meta-learning is fast and memory-efficient, without the need to fine-tune features.…
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 tes…
Bayesian Meta-Learning with Expert Feedback for Task-Shift Adaptation through Causal Embeddings
Department of Computer Science, Aalto University, Espoo, Finland（Aalto大学计算机科学系）；ELLIS Institute Finland, Espoo, Finland（芬兰ELLIS研究所）；Department of Computer Science, University of Manchester, United Kingdom（曼彻斯特大学计算机科学系）
Didi AI Labs（滴滴人工智能实验室）；Columbia University（哥伦比亚大学）
Bayesian meta-learning enables robust and fast adaptation to new tasks with uncertainty assessment. The key idea behind Bayesian meta-learning is empirical Bayes inference of hierarchical model. In this work, we extend this framework to include a variety of existing methods, before proposing our variant based on gradient-EM algorithm. Our method improves computational efficiency by avoiding back-propagation computation in the meta-update step, which is exhausting for deep neural networks. Furthermore, it provides flexibility to the inner-update optimization procedure by decoupling it from meta…
Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a…
Element AI（Element AI公司）；Kakao Brain（Kakao Brain公司）；MILA Université de Montréal（蒙特利尔大学MILA研究所）；Rutgers University（罗格斯大学）
Learning to infer Bayesian posterior from a few-shot dataset is an important step towards robust meta-learning due to the model uncertainty inherent in the problem. In this paper, we propose a novel Bayesian model-agnostic meta-learning method. The proposed method combines scalable gradient-based meta-learning with nonparametric variational inference in a principled probabilistic framework. During fast adaptation, the method is capable of learning complex uncertainty structure beyond a point estimate or a simple Gaussian approximation. In addition, a robust Bayesian meta-update mechanism with …
University of Oxford（牛津大学）；Latent Logic（潜在逻辑公司）；Microsoft Research（微软研究院）
Trading off exploration and exploitation in an unknown environment is key to maximising expected return during learning. A Bayes-optimal policy, which does so optimally, conditions its actions not only on the environment state but on the agent's uncertainty about the environment. Computing a Bayes-optimal policy is however intractable for all but the smallest tasks. In this paper, we introduce variational Bayes-Adaptive Deep RL (variBAD), a way to meta-learn to perform approximate inference in an unknown environment, and incorporate task uncertainty directly during action selection. In a grid-…
Despite recent advances in its theoretical understanding, there still remains a significant gap in the ability of existing PAC-Bayesian theories on meta-learning to explain performance improvements in the few-shot learning setting, where the number of training examples in the target tasks is severely limited. This gap originates from an assumption in the existing theories which supposes that the number of training examples in the observed tasks and the number of training examples in the target tasks follow the same distribution, an assumption that rarely holds in practice. By relaxing this ass…
Australian Institute for Machine Learning, University of Adelaide（阿德莱德大学机器学习研究所）；Monash University（莫纳什大学）
We introduce a new and rigorously-formulated PAC-Bayes meta-learning algorithm that solves few-shot learning. Our proposed method extends the PAC-Bayes framework from a single task setting to the meta-learning multiple task setting to upper-bound the error evaluated on any, even unseen, tasks and samples. We also propose a generative-based approach to estimate the posterior of task-specific model parameters more expressively compared to the usual assumption based on a multivariate normal distribution with a diagonal covariance matrix. We show that the models trained with our proposed meta-lear…
Meta-learning optimizes the hyperparameters of a training procedure, such as its initialization, kernel, or learning rate, based on data sampled from a number of auxiliary tasks. A key underlying assumption is that the auxiliary tasks, known as meta-training tasks, share the same generating distribution as the tasks to be encountered at deployment time, known as meta-test tasks. This may, however, not be the case when the test environment differ from the meta-training conditions. To address shifts in task generating distribution between meta-training and meta-testing phases, this paper introdu…
Memory-based meta-learning is a powerful technique to build agents that adapt fast to any task within a target distribution. A previous theoretical study has argued that this remarkable performance is because the meta-training protocol incentivises agents to behave Bayes-optimally. We empirically investigate this claim on a number of prediction and bandit tasks. Inspired by ideas from theoretical computer science, we show that meta-learned and Bayes-optimal agents not only behave alike, but they even share a similar computational structure, in the sense that one agent system can approximately …
Near-term noisy intermediate-scale quantum circuits can efficiently implement implicit probabilistic models in discrete spaces, supporting distributions that are practically infeasible to sample from using classical means. One of the possible applications of such models, also known as Born machines, is probabilistic inference, which is at the core of Bayesian methods. This paper studies the use of Born machines for the problem of training binary Bayesian neural networks. In the proposed approach, a Born machine is used to model the variational distribution of the binary weights of the neural n…
Meta-training agents with memory has been shown to culminate in Bayes-optimal agents, which casts Bayes-optimality as the implicit solution to a numerical optimization problem rather than an explicit modeling assumption. Bayes-optimal agents are risk-neutral, since they solely attune to the expected return, and ambiguity-neutral, since they act in new situations as if the uncertainty were known. This is in contrast to risk-sensitive agents, which additionally exploit the higher-order moments of the return, and ambiguity-sensitive agents, which act differently when recognizing situations in whi…
University of Edinburgh（爱丁堡大学）；School of Informatics（信息学院）；School of Engineering（工程学院）
Recently, different machine learning methods have been introduced to tackle the challenging few-shot learning scenario that is, learning from a small labeled dataset related to a specific task. Common approaches have taken the form of meta-learning: learning to learn on the new problem given the old. Following the recognition that meta-learning is implementing learning in a multi-level model, we present a Bayesian treatment for the meta-learning inner loop through the use of deep kernels. As a result we can learn a kernel that transfers to new tasks; we call this Deep Kernel Transfer (DKT). Th…
Two of the main principles underlying the life cycle of an artificial intelligence (AI) module in communication networks are adaptation and monitoring. Adaptation refers to the need to adjust the operation of an AI module depending on the current conditions; while monitoring requires measures of the reliability of an AI module's decisions. Classical frequentist learning methods for the design of AI modules fall short on both counts of adaptation and monitoring, catering to one-off training and providing overconfident decisions. This paper proposes a solution to address both challenges by integ…
Meta-learning for sample-efficient Bayesian optimisation of fed-batch processes
Department of Computing, Imperial College London, United Kingdom（帝国理工学院伦敦分校计算机系）；BASF SE, Ludwigshafen, Germany（巴斯夫股份有限公司，德国路德维希沙芬）；School of Mathematical Sciences, Lancaster University, United Kingdom（兰卡斯特大学数学科学学院）；Department of Computer Science, University of Oxford, United Kingdom（牛津大学计算机科学系）
The University of Queensland（昆士兰大学）；Harbin Institute of Technology（哈尔滨工业大学）；Pengcheng Laboratory（鹏城实验室）；University of Electronic Science and Technology of China（电子科技大学）
Meta-learning for few-shot learning allows a machine to leverage previously acquired knowledge as a prior, thus improving the performance on novel tasks with only small amounts of data. However, most mainstream models suffer from catastrophic forgetting and insufficient robustness issues, thereby failing to fully retain or exploit long-term knowledge while being prone to cause severe error accumulation. In this paper, we propose a novel Continual Meta-Learning approach with Bayesian Graph Neural Networks (CML-BGNN) that mathematically formulates meta-learning as continual learning of a sequenc…
The field of meta-learning seeks to improve the ability of today's machine learning systems to adapt efficiently to small amounts of data. Typically this is accomplished by training a system with a parametrized update rule to improve a task-relevant objective based on supervision or a reward function. However, in many domains of practical interest, task data is unlabeled, or reward functions are unavailable. In this paper we introduce a new approach to address the more general problem of generative meta-learning, which we argue is an important prerequisite for obtaining human-level cognitive f…
École des Ponts ParisTech（巴黎桥路学院）；Amazon（亚马逊）；Swiss Data Science Center（瑞士数据科学中心）；University of Cambridge（剑桥大学）
We propose a meta-learning approach that learns from multiple tasks in a transductive setting, by leveraging the unlabeled query set in addition to the support set to generate a more powerful model for each task. To develop our framework, we revisit the empirical Bayes formulation for multi-task learning. The evidence lower bound of the marginal log-likelihood of empirical Bayes decomposes as a sum of local KL divergences between the variational posterior and the true posterior on the query set of each task. We derive a novel amortized variational inference that couples all the variational pos…
Meta-Learning is a family of methods that use a set of interrelated tasks to learn a model that can quickly learn a new query task from a possibly small contextual dataset. In this study, we use a probabilistic framework to formalize what it means for two tasks to be related and reframe the meta-learning problem into the problem of Bayesian risk minimization (BRM). In our formulation, the BRM optimal solution is given by the predictive distribution computed from the posterior distribution of the task-specific latent variable conditioned on the contextual dataset, and this justifies the philoso…
The overall predictive uncertainty of a trained predictor can be decomposed into separate contributions due to epistemic and aleatoric uncertainty. Under a Bayesian formulation, assuming a well-specified model, the two contributions can be exactly expressed (for the log-loss) or bounded (for more general losses) in terms of information-theoretic quantities (Xu and Raginsky, 2020). This paper addresses the study of epistemic uncertainty within an information-theoretic framework in the broader setting of Bayesian meta-learning. A general hierarchical Bayesian model is assumed in which hyperparam…
UBMF: Uncertainty-Aware Bayesian Meta-Learning Framework for Fault Diagnosis with Imbalanced Industrial Data
Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州国际创新研究院）；Institute of Reliability Engineering, Beihang University（北京航空航天大学可靠性工程研究所）；Science & Technology on Reliability & Environmental Engineering Laboratory（可靠性与环境工程技术重点实验室）；School of Reliability and Systems Engineering, Beihang University（北京航空航天大学可靠性与系统工程学院）
Amortising Inference and Meta-Learning Priors in Neural Networks
Helmholtz AI（海德堡人工智能研究所）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Technical University of Munich（慕尼黑技术大学）；University of Technology Nuremberg（纽伦堡技术大学）
Data-efficient learning algorithms are essential in many practical applications for which data collection is expensive, e.g., for the optimal deployment of wireless systems in unknown propagation scenarios. Meta-learning can address this problem by leveraging data from a set of related learning tasks, e.g., from similar deployment settings. In practice, one may have available only unlabeled data sets from the related tasks, requiring a costly labeling procedure to be carried out before use in meta-learning. For instance, one may know the possible positions of base stations in a given area, but…
Gaussian Process (GP) regression has seen widespread use in robotics due to its generality, simplicity of use, and the utility of Bayesian predictions. The predominant implementation of GP regression is a nonparameteric kernel-based approach, as it enables fitting of arbitrary nonlinear functions. However, this approach suffers from two main drawbacks: (1) it is computationally inefficient, as computation scales poorly with the number of samples; and (2) it can be data inefficient, as encoding prior knowledge that can aid the model through the choice of kernel and associated hyperparameters is…
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；University of Montréal（蒙特利尔大学）；Tsinghua University（清华大学）；HEC Montréal（蒙特利尔高等商学院）
This paper studies few-shot relation extraction, which aims at predicting the relation for a pair of entities in a sentence by training with a few labeled examples in each relation. To more effectively generalize to new relations, in this paper we study the relationships between different relations and propose to leverage a global relation graph. We propose a novel Bayesian meta-learning approach to effectively learn the posterior distribution of the prototype vectors of relations, where the initial prior of the prototype vectors is parameterized with a graph neural network on the global relat…
Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning
University of Electronic Science and Technology of China（电子科技大学）；University of Exeter（埃克塞特大学）；Texas A & M University at Qatar（德州农工大学卡塔尔分校）；University of Technology Sydney（悉尼科技大学）；Hamad Bin Khalifa University（哈马德·本·哈利法大学）
Virginia Tech（弗吉尼亚理工大学）；US Army Research Laboratory（美国陆军研究实验室）
A key component of cognitive radar is the ability to generalize, or achieve consistent performance across a range of sensing environments, since aspects of the physical scene may vary over time. This presents a challenge for learning-based waveform selection approaches, since transmission policies which are effective in one scene may be highly suboptimal in another. We address this problem by strategically biasing a learning algorithm by exploiting high-level structure across tracking instances, referred to as meta-learning. In this work, we develop an online meta-learning approach for wavefor…
UC Berkeley（加州大学伯克利分校）；Columbia University（哥伦比亚大学）；Microsoft Research NYC（微软研究院纽约）；Massachusetts Institute of Technology（麻省理工学院）
Thompson sampling and other Bayesian sequential decision-making algorithms are among the most popular approaches to tackle explore/exploit trade-offs in (contextual) bandits. The choice of prior in these algorithms offers flexibility to encode domain knowledge but can also lead to poor performance when misspecified. In this paper, we demonstrate that performance degrades gracefully with misspecification. We prove that the expected reward accrued by Thompson sampling (TS) with a misspecified prior differs by at most $\tilde{\mathcal{O}}(H^2 ε)$ from TS with a well specified prior, where $ε$ is …
Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points via an acquisition function and a prior over functions, such as a Gaussian process. Recently, however, a reformulation of BO via density-ratio estimation (BORE) allowed reinterpreting the acquisition function as a probabilistic binary classifier, removing the need for an explicit prior over functions and increasing scalability. In this paper, we present a the…
By leveraging experience from previous tasks, meta-learning algorithms can achieve effective fast adaptation ability when encountering new tasks. However it is unclear how the generalization property applies to new tasks. Probably approximately correct (PAC) Bayes bound theory provides a theoretical framework to analyze the generalization performance for meta-learning. We derive three novel generalisation error bounds for meta-learning based on PAC-Bayes relative entropy bound. Furthermore, using the empirical risk minimization (ERM) method, a PAC-Bayes bound for meta-learning with data-depend…
Meta learning automatically infers an inductive bias, that includes the hyperparameter of the base-learning algorithm, by observing data from a finite number of related tasks. This paper studies PAC-Bayes bounds on meta generalization gap. The meta-generalization gap comprises two sources of generalization gaps: the environment-level and task-level gaps resulting from observation of a finite number of tasks and data samples per task, respectively. In this paper, by upper bounding arbitrary convex functions, which link the expected and empirical losses at the environment and also per-task level…
Recent advances in the field of meta-learning have tackled domains consisting of large numbers of small ("few-shot") supervised learning tasks. Meta-learning algorithms must be able to rapidly adapt to any individual few-shot task, fitting to a small support set within a task and using it to predict the labels of the task's query set. This problem setting can be extended to the Bayesian context, wherein rather than predicting a single label for each query data point, a model predicts a distribution of labels capturing its uncertainty. Successful methods in this domain include Bayesian ensembli…
While tasks could come with varying the number of instances and classes in realistic settings, the existing meta-learning approaches for few-shot classification assume that the number of instances per task and class is fixed. Due to such restriction, they learn to equally utilize the meta-knowledge across all the tasks, even when the number of instances per task and class largely varies. Moreover, they do not consider distributional difference in unseen tasks, on which the meta-knowledge may have less usefulness depending on the task relatedness. To overcome these limitations, we propose a nov…
How to explore efficiently is a central problem in multi-armed bandits. In this paper, we introduce the metadata-based multi-task bandit problem, where the agent needs to solve a large number of related multi-armed bandit tasks and can leverage some task-specific features (i.e., metadata) to share knowledge across tasks. As a general framework, we propose to capture task relations through the lens of Bayesian hierarchical models, upon which a Thompson sampling algorithm is designed to efficiently learn task relations, share information, and minimize the cumulative regrets. Two concrete example…
BayMOTH: Bayesian optiMizatiOn with meTa-lookahead -- a simple approacH
Laboratory for Laser Energetics（激光能实验室）；Department of Mechanical Engineering（机械工程系）；Hewlett Packard Labs（惠普实验室）；Department of Computer Science（计算机科学系）；Department of Physics（物理系）
University of Stuttgart（斯图加特大学）；Heidelberg University（海德堡大学）
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed data of interest. These posterior model probabilities (PMPs) are measures of uncertainty, but -- when derived from a finite number of observations -- are also uncertain themselves. In this paper, we conceptualize distinct levels of uncertainty which arise in BMC. We explore a fully probabilistic framework for quantifying meta-uncertainty, resulting in an appli…
