Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning -- a key tool for performing meta-learning -- learns a data representation that can transfer knowledge across multiple tasks, which is essential in regimes where data is scarce. Despite a recent surge of interest in the practice of meta-learning, the theoretical underpinnings of meta-learning algorithms are lacking, especially in the context of learning transferable representations. In this paper, we focus on the problem of multi-task linear regression -- in which multiple linear regression models share a common, low-dimensional linear representation. Here, we provide provably fast, sample-efficient algorithms to address the dual challenges of (1) learning a common set of features from multiple, related tasks, and (2) transferring this knowledge to new, unseen tasks. Both are central to the general problem of meta-learning. Finally, we complement these results by providing information-theoretic lower bounds on the sample complexity of learning these linear features.
We study the problem of meta-learning through the lens of online convex optimization, developing a meta-algorithm bridging the gap between popular gradient-based meta-learning and classical regularization-based multi-task transfer methods. Our method is the first to simultaneously satisfy good sample efficiency guarantees in the convex setting, with generalization bounds that improve with task-similarity, while also being computationally scalable to modern deep learning architectures and the many-task setting. Despite its simplicity, the algorithm matches, up to a constant factor, a lower boun…
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）；University of Washington（华盛顿大学）
A common strategy in modern learning systems is to learn a representation that is useful for many tasks, a.k.a. representation learning. We study this strategy in the imitation learning setting for Markov decision processes (MDPs) where multiple experts' trajectories are available. We formulate representation learning as a bi-level optimization problem where the "outer" optimization tries to learn the joint representation and the "inner" optimization encodes the imitation learning setup and tries to learn task-specific parameters. We instantiate this framework for the imitation learning settin…
UT Austin（德克萨斯大学奥斯汀分校）；Google Research（谷歌研究院）；UC Berkeley（加州大学伯克利分校）；DeepMind（深度思维）；University of Alberta（阿尔伯塔大学）
Representation learning lies at the heart of the empirical success of deep learning for dealing with the curse of dimensionality. However, the power of representation learning has not been fully exploited yet in reinforcement learning (RL), due to i), the trade-off between expressiveness and tractability; and ii), the coupling between exploration and representation learning. In this paper, we first reveal the fact that under some noise assumption in the stochastic control model, we can obtain the linear spectral feature of its corresponding Markov transition operator in closed-form for free. B…
Provable Data Scaling Law for Meta Learning via Complexity Minimization
University of Tsukuba（筑波大学）；RIKEN AIP（理化学研究所人工智能研究中心）；SB Intuitions Corp.（SB Intuitions公司）；Kyoto University（京都大学）；Shiga University（滋贺大学）；Institute of Science Tokyo（东京科学研究所）
In this work we provide provable regret guarantees for an online meta-learning control algorithm in an iterative control setting, where in each iteration the system to be controlled is a linear deterministic system that is different and unknown, the cost for the controller in an iteration is a general additive cost function and the control input is required to be constrained, which if violated incurs an additional cost. We prove (i) that the algorithm achieves a regret for the controller cost and constraint violation that are $O(T^{3/4})$ for an episode of duration $T$ with respect to the best…
Georgia Tech（佐治亚理工学院）；University of Cambridge（剑桥大学）；MPI-IS（马克斯·普朗克智能系统研究所）
In lifelong learning, tasks (or classes) to be learned arrive sequentially over time in arbitrary order. During training, knowledge from previous tasks can be captured and transferred to subsequent ones to improve sample efficiency. We consider the setting where all target tasks can be represented in the span of a small number of unknown linear or nonlinear features of the input data. We propose a lifelong learning algorithm that maintains and refines the internal feature representation. We prove that for any desired accuracy on all tasks, the dimension of the representation remains close to t…
In imitation learning, it is common to learn a behavior policy to match an unknown target policy via max-likelihood training on a collected set of target demonstrations. In this work, we consider using offline experience datasets - potentially far from the target distribution - to learn low-dimensional state representations that provably accelerate the sample-efficiency of downstream imitation learning. A central challenge in this setting is that the unknown target policy itself may not exhibit low-dimensional behavior, and so there is a potential for the representation learning objective to a…
Chandra Family Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX, USA（Chandra Family 电子与计算机工程系，德克萨斯大学奥斯汀分校）；Snap, Inc.（Snap公司）；Google Research（Google研究）
Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical) changes in the data-generating process, whether due to natural reasons or by the action of an adversary. We consider causal Bayesian networks and formally define the interventional robustness problem, a novel model-based notion of robustness for decision functions that measures worst-case performance with respect to a set of interventions that denote changes t…
Yahoo Research（雅虎研究院）；JP Morgan & Co（摩根大通公司）；U.S. Bancorp（美国合众银行）；Xiaohongshu（小红书）
Accurate understanding of users in terms of predicative segments play an essential role in the day to day operation of modern internet enterprises. Nevertheless, there are significant challenges that limit the quality of data, especially on long tail predictive tasks. In this work, we present MetaCon, our unified predicative segments system with scalable, trillion concepts meta learning that addresses these challenges. It builds on top of a flat concept representation that summarizes entities' heterogeneous digital footprint, jointly considers the entire spectrum of predicative tasks as a sing…
Hierarchical reinforcement learning (HRL) has seen widespread interest as an approach to tractable learning of complex modular behaviors. However, existing work either assume access to expert-constructed hierarchies, or use hierarchy-learning heuristics with no provable guarantees. To address this gap, we analyze HRL in the meta-RL setting, where a learner learns latent hierarchical structure during meta-training for use in a downstream task. We consider a tabular setting where natural hierarchical structure is embedded in the transition dynamics. Analogous to supervised meta-learning theory, …
Parameter-transfer is a well-known and versatile approach for meta-learning, with applications including few-shot learning, federated learning, and reinforcement learning. However, parameter-transfer algorithms often require sharing models that have been trained on the samples from specific tasks, thus leaving the task-owners susceptible to breaches of privacy. We conduct the first formal study of privacy in this setting and formalize the notion of task-global differential privacy as a practical relaxation of more commonly studied threat models. We then propose a new differentially private alg…
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）；Carnegie Mellon University（卡内基梅隆大学）
Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzi…
Princeton University（普林斯顿大学）；Google Research NYC（谷歌纽约研究院）；EPFL（洛桑联邦理工学院）；Microsoft Research, New England（微软新英格兰研究院）
We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an $n$ node multilayer neural net that has degree at most $n^γ$ for some $γ<1$ and each edge has a random edge weight in $[-1,1]$. Our algorithm learns {\em almost all} networks in this class with polynomial running time. The sample complexity is quadratic or cubic depending upon the details of the model. The algorithm uses layerwise learning. It is based upon a novel idea of observing correlations among features and using these to i…
Provable Representation with Efficient Planning for Partial Observable Reinforcement Learning
University of Alberta（阿尔伯塔大学）；UT Austin（德克萨斯大学奥斯汀分校）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Google DeepMind（谷歌DeepMind）；Georgia Tech（佐治亚理工学院）
Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works have focused on fairness with respect to a specific metric, modeled the corresponding fair classification problem as a constrained optimization problem, and developed tailored algorithms to solve them. Despite this, there still remain important metrics for which we do not have fair classifiers and many of the aforementioned algorithms do not come with theore…
Safety is a crucial necessity in many applications of reinforcement learning (RL), whether robotic, automotive, or medical. Many existing approaches to safe RL rely on receiving numeric safety feedback, but in many cases this feedback can only take binary values; that is, whether an action in a given state is safe or unsafe. This is particularly true when feedback comes from human experts. We therefore consider the problem of provable safe RL when given access to an offline oracle providing binary feedback on the safety of state, action pairs. We provide a novel meta algorithm, SABRE, which ca…
In this paper we provide provable regret guarantees for an online meta-learning receding horizon control algorithm in an iterative control setting. We consider the setting where, in each iteration the system to be controlled is a linear deterministic system that is different and unknown, the cost for the controller in an iteration is a general additive cost function and there are affine control input constraints. By analysing conditions under which sub-linear regret is achievable, we prove that the meta-learning online receding horizon controller achieves an average of the dynamic regret for t…
There is general consensus that learning representations is useful for a variety of reasons, e.g. efficient use of labeled data (semi-supervised learning), transfer learning and understanding hidden structure of data. Popular techniques for representation learning include clustering, manifold learning, kernel-learning, autoencoders, Boltzmann machines, etc. To study the relative merits of these techniques, it's essential to formalize the definition and goals of representation learning, so that they are all become instances of the same definition. This paper introduces such a formal framework t…
Tsinghua University（清华大学）；University of Washington（华盛顿大学）
While multitask representation learning has become a popular approach in reinforcement learning (RL) to boost the sample efficiency, the theoretical understanding of why and how it works is still limited. Most previous analytical works could only assume that the representation function is already known to the agent or from linear function class, since analyzing general function class representation encounters non-trivial technical obstacles such as generalization guarantee, formulation of confidence bound in abstract function space, etc. However, linear-case analysis heavily relies on the part…
Google Research（谷歌研究院）；Carnegie Mellon University（卡内基梅隆大学）；Cornell University（康奈尔大学）；Princeton University（普林斯顿大学）
We study the problem of representational transfer in RL, where an agent first pretrains in a number of source tasks to discover a shared representation, which is subsequently used to learn a good policy in a \emph{target task}. We propose a new notion of task relatedness between source and target tasks, and develop a novel approach for representational transfer under this assumption. Concretely, we show that given generative access to source tasks, we can discover a representation, using which subsequent linear RL techniques quickly converge to a near-optimal policy in the target task. The sam…
Columbia University（哥伦比亚大学）；MPI-SWS（马克斯·普朗克软件系统研究所）
We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different tasks, and do not consider the additional task-specific observable side information. In this work, we model the meta-parameter through an order-$3$ tensor, which can adapt to the observed task features of the task. We propose two methods to estimate the underlying tensor. The first method solves a tensor regression problem and works under natural assumptions…
Tsinghua University（清华大学）；The Ohio State University（俄亥俄州立大学）
Despite the superior empirical success of deep meta-learning, theoretical understanding of overparameterized meta-learning is still limited. This paper studies the generalization of a widely used meta-learning approach, Model-Agnostic Meta-Learning (MAML), which aims to find a good initialization for fast adaptation to new tasks. Under a mixed linear regression model, we analyze the generalization properties of MAML trained with SGD in the overparameterized regime. We provide both upper and lower bounds for the excess risk of MAML, which captures how SGD dynamics affect these generalization bo…
Advances in next-generation metagenome sequencing have the potential to revolutionize the point-of-care diagnosis of novel pathogen infections, which could help prevent potential widespread transmission of diseases. Given the high volume of metagenome sequences, there is a need for scalable frameworks to analyze and segment metagenome sequences from clinical samples, which can be highly imbalanced. There is an increased need for learning robust representations from metagenome reads since pathogens within a family can have highly similar genome structures (some more than 90%) and hence enable t…
Princeton University（普林斯顿大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Self-supervised representation learning solves auxiliary prediction tasks (known as pretext tasks) without requiring labeled data to learn useful semantic representations. These pretext tasks are created solely using the input features, such as predicting a missing image patch, recovering the color channels of an image from context, or predicting missing words in text; yet predicting this \textit{known} information helps in learning representations effective for downstream prediction tasks. We posit a mechanism exploiting the statistical connections between certain {\em reconstruction-based} p…
University of California, Riverside（加州大学河滨分校）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）
Constructing useful representations across a large number of tasks is a key requirement for sample-efficient intelligent systems. A traditional idea in multitask learning (MTL) is building a shared representation across tasks which can then be adapted to new tasks by tuning last layers. A desirable refinement of using a shared one-fits-all representation is to construct task-specific representations. To this end, recent PathNet/muNet architectures represent individual tasks as pathways within a larger supernet. The subnetworks induced by pathways can be viewed as task-specific representations …
Consider the problem: given the data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network model and run gradient flow on the weights over time until reaching any stationarity. How does $f_t$, the function computed by the neural network at time $t$, relate to $f_*$, in terms of approximation and representation? What are the provable benefits of the adaptive representation by neural networks compared to the pre-specified fixed basis representation in the classical nonparametric literature? We answer the above qu…
Carnegie Mellon University（卡内基梅隆大学）；NEC Laboratories America, Inc.（美国NEC实验室）；University of Washington（华盛顿大学）
This paper studies zero-shot domain adaptation where each domain is indexed on a multi-dimensional array, and we only have data from a small subset of domains. Our goal is to produce predictors that perform well on \emph{unseen} domains. We propose a model which consists of a domain-invariant latent representation layer and a domain-specific linear prediction layer with a low-rank tensor structure. Theoretically, we present explicit sample complexity bounds to characterize the prediction error on unseen domains in terms of the number of domains with training data and the number of data per dom…
University of Chicago（芝加哥大学）；Princeton University（普林斯顿大学）；Northwestern University（西北大学）；Booth School of Business（布斯商学院）
Graph representation learning is a ubiquitous task in machine learning where the goal is to embed each vertex into a low-dimensional vector space. We consider the bipartite graph and formalize its representation learning problem as a statistical estimation problem of parameters in a semiparametric exponential family distribution. The bipartite graph is assumed to be generated by a semiparametric exponential family distribution, whose parametric component is given by the proximity of outputs of two one-layer neural networks, while nonparametric (nuisance) component is the base measure. Neural n…
University of Science and Technology of China（中国科学技术大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；The Ohio State University（俄亥俄州立大学）
As representation learning becomes a powerful technique to reduce sample complexity in reinforcement learning (RL) in practice, theoretical understanding of its advantage is still limited. In this paper, we theoretically characterize the benefit of representation learning under the low-rank Markov decision process (MDP) model. We first study multitask low-rank RL (as upstream training), where all tasks share a common representation, and propose a new multitask reward-free algorithm called REFUEL. REFUEL learns both the transition kernel and the near-optimal policy for each task, and outputs a …
University College of London（伦敦大学学院）；Istituto Italiano di Tecnologia（意大利理工学院）
Standard meta-learning for representation learning aims to find a common representation to be shared across multiple tasks. The effectiveness of these methods is often limited when the nuances of the tasks' distribution cannot be captured by a single representation. In this work we overcome this issue by inferring a conditioning function, mapping the tasks' side information (such as the tasks' training dataset itself) into a representation tailored to the task at hand. We study environments in which our conditional strategy outperforms standard meta-learning, such as those in which tasks can b…
Provable Sample-Efficient Transfer Learning Conditional Diffusion Models via Representation Learning
Department of Industrial Engineering and Operations Research, University of California, Berkeley（加州大学伯克利分校工业工程与运筹学系）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Center for Statistical Science, Peking University（北京大学统计科学中心）
Microsoft Research（微软研究院）；Carnegie Mellon University（卡内基梅隆大学）
The combination of multilingual pre-trained representations and cross-lingual transfer learning is one of the most effective methods for building functional NLP systems for low-resource languages. However, for extremely low-resource languages without large-scale monolingual corpora for pre-training or sufficient annotated data for fine-tuning, transfer learning remains an under-studied and challenging task. Moreover, recent work shows that multilingual representations are surprisingly disjoint across languages, bringing additional challenges for transfer onto extremely low-resource languages. …
Federated learning (FL) is a popular distributed learning framework that can reduce privacy risks by not explicitly sharing private data. However, recent works demonstrated that sharing model updates makes FL vulnerable to inference attacks. In this work, we show our key observation that the data representation leakage from gradients is the essential cause of privacy leakage in FL. We also provide an analysis of this observation to explain how the data presentation is leaked. Based on this observation, we propose a defense against model inversion attack in FL. The key idea of our defense is le…
Provable Compositional Generalization for Object-Centric Learning
University of Tübingen（蒂宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Tübingen AI Center（蒂宾根人工智能中心）；ELLIS Institute Tübingen（ELLIS蒂宾根研究所）
Provable Low-Frequency Bias of In-Context Learning of Representations
Computer Science and Engineering, University of Michigan（密歇根大学计算机科学与工程系）；CBS-NTT Physics of Intelligence Program, Harvard University（哈佛大学CBS-NTT智能物理计划）；Physics of Artificial Intelligence Group, NTT Research, Inc.（NTT研究公司人工智能物理小组）
In continual learning (CL), the goal is to design models that can learn a sequence of tasks without catastrophic forgetting. While there is a rich set of techniques for CL, relatively little understanding exists on how representations built by previous tasks benefit new tasks that are added to the network. To address this, we study the problem of continual representation learning (CRL) where we learn an evolving representation as new tasks arrive. Focusing on zero-forgetting methods where tasks are embedded in subnetworks (e.g., PackNet), we first provide experiments demonstrating CRL can sign…
Booth School of Business, University of Chicago（芝加哥大学布斯商学院）；Princeton University（普林斯顿大学）；Georgia Institute of Technology（佐治亚理工学院）；Northwestern University（西北大学）
The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural information about data. However, recently there has been a surge in approaches that learn how to encode the data automatically in a low dimensional space. Exponential family embedding provides a probabilistic framework for learning low-dimensional representation for various types of high-dimensional data. Though successful in practice, theoretical underpinnings for ex…
This paper studies the subspace clustering problem in which data points collected from high-dimensional ambient space lie in a union of linear subspaces. Subspace clustering becomes challenging when the dimension of intersection between subspaces is large and most of the self-representation based methods are sensitive to the intersection between the span of clusters. In sharp contrast to the self-representation based methods, a recently proposed clustering method termed Innovation Pursuit, computed a set of optimal directions (directions of innovation) to build the adjacency matrix. This paper…
Deep learning provides a promising way to extract effective representations from raw data in an end-to-end fashion and has proven its effectiveness in various domains such as computer vision, natural language processing, etc. However, in domains such as content/product recommendation and risk management, where sequence of event data is the most used raw data form and experts derived features are more commonly used, deep learning models struggle to dominate the game. In this paper, we propose a symbolic testing framework that helps to answer the question of what kinds of expert-derived features…
University of Minnesota – Twin Cities（明尼苏达大学双城分校）；Princeton University（普林斯顿大学）
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as coefficients. Since the dictionary and coefficients, parameterizing the linear model are unknown, the corresponding optimization is inherently non-convex. This was a major challenge until recently, when provable algorithms for dictionary learning were proposed. Yet, these provide guarantees only on the recovery of the dictionary, without explicit recovery guarantees …
