Online learning methods, like the online gradient algorithm (OGA) and exponentially weighted aggregation (EWA), often depend on tuning parameters that are difficult to set in practice. We consider an online meta-learning scenario, and we propose a meta-strategy to learn these parameters from past tasks. Our strategy is based on the minimization of a regret bound. It allows to learn the initialization and the step size in OGA with guarantees. It also allows to learn the prior or the learning rate in EWA. We provide a regret analysis of the strategy. It allows to identify settings where meta-learning indeed improves on learning each task in isolation.
Choosing the right parameters for optimization algorithms is often the key to their success in practice. Solving this problem using a learning-to-learn approach -- using meta-gradient descent on a meta-objective based on the trajectory that the optimizer generates -- was recently shown to be effective. However, the meta-optimization problem is difficult. In particular, the meta-gradient can often explode/vanish, and the learned optimizer may not have good generalization performance if the meta-objective is not chosen carefully. In this paper we give meta-optimization guarantees for the learnin…
Tandon School of Engineering（坦登工程学院）；New York University（纽约大学）
This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We consider the problem of finding the best interpolant from a class of kernels with unknown hyperparameters, assuming only that the noise is square-integrable. We provide finite-sample guarantees for the problem, characterizing how increasing the complexity of the kernel class increases the complexity of learning kernel hyperparameters. For common kernel classes (e.g. squared-exponential kernels with unknown lengthscale), our results show that hyperparamet…
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…
Generative priors have been shown to provide improved results over sparsity priors in linear inverse problems. However, current state of the art methods suffer from one or more of the following drawbacks: (a) speed of recovery is slow; (b) reconstruction quality is deficient; (c) reconstruction quality is contingent on a computationally expensive process of tuning hyperparameters. In this work, we address these issues by utilizing Denoising Auto Encoders (DAEs) as priors and a projected gradient descent algorithm for recovering the original signal. We provide rigorous theoretical guarantees fo…
We are motivated by the problem of providing strong generalization guarantees in the context of meta-learning. Existing generalization bounds are either challenging to evaluate or provide vacuous guarantees in even relatively simple settings. We derive a probably approximately correct (PAC) bound for gradient-based meta-learning using two different generalization frameworks in order to deal with the qualitatively different challenges of generalization at the "base" and "meta" levels. We employ bounds for uniformly stable algorithms at the base level and bounds from the PAC-Bayes framework at t…
Johns Hopkins University Applied Physics Laboratory（约翰斯·霍普金斯大学应用物理实验室）；Defense Nuclear Facilities Safety Board（美国国防核设施安全委员会）
There is great interest in using formal methods to guarantee the reliability of deep neural networks. However, these techniques may also be used to implant carefully selected input-output pairs. We present initial results on a novel technique for using SMT solvers to fine tune the weights of a ReLU neural network to guarantee outcomes on a finite set of particular examples. This procedure can be used to ensure performance on key examples, but it could also be used to insert difficult-to-find incorrect examples that trigger unexpected performance. We demonstrate this approach by fine tuning an …
Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing calibration schemes in the logistic regression framework lack any finite sample guarantees. In this paper, we introduce a novel calibration scheme for $\ell_1$-penalized logistic regression. It is based on simple tests along the tuning parameter path and is equipped with optimal guarantees for feature selection. It is also amenable to easy and efficient implement…
Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function
Université Grenoble Alpes, LJK, CNRS, Grenoble INP（格拉诺布尔大学，LJK，CNRS，格拉诺布尔INP）；Carnegie Mellon University, Machine Learning Department（卡内基梅隆大学，机器学习系）；Chinese University of Hong Kong, Department of Systems Engineering and Engineering Management（香港中文大学，系统工程与工程管理系）
Nonlinear Meta-Learning Can Guarantee Faster Rates
Gatsby Computational Neuroscience Unit, University College London（伦敦大学学院盖茨比计算神经科学单元）；Department of Mathematics, Imperial College London（伦敦帝国理工学院数学系）；Department of Statistics, Columbia University（哥伦比亚大学统计系）
Federal Technology University（联邦技术大学）；University of São Paulo（圣保罗大学）；Universidade Estadual Paulista（保利斯塔州立大学）；Eindhoven University of Technology（埃因霍温理工大学）
For many machine learning algorithms, predictive performance is critically affected by the hyperparameter values used to train them. However, tuning these hyperparameters can come at a high computational cost, especially on larger datasets, while the tuned settings do not always significantly outperform the default values. This paper proposes a recommender system based on meta-learning to identify exactly when it is better to use default values and when to tune hyperparameters for each new dataset. Besides, an in-depth analysis is performed to understand what they take into account for their d…
Biased regularization and fine-tuning are two recent meta-learning approaches. They have been shown to be effective to tackle distributions of tasks, in which the tasks' target vectors are all close to a common meta-parameter vector. However, these methods may perform poorly on heterogeneous environments of tasks, where the complexity of the tasks' distribution cannot be captured by a single meta-parameter vector. We address this limitation by conditional meta-learning, inferring a conditioning function mapping task's side information into a meta-parameter vector that is appropriate for that t…
University of Texas at Austin（得克萨斯大学奥斯汀分校）；University of Sydney（悉尼大学）
Selecting hyperparameters for unsupervised learning problems is challenging in general due to the lack of ground truth for validation. Despite the prevalence of this issue in statistics and machine learning, especially in clustering problems, there are not many methods for tuning these hyperparameters with theoretical guarantees. In this paper, we provide a framework with provable guarantees for selecting hyperparameters in a number of distinct models. We consider both the subgaussian mixture model and network models to serve as examples of i.i.d. and non-i.i.d. data. We demonstrate that the s…
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…
Reinforcement learning (RL) has had many successes in both "deep" and "shallow" settings. In both cases, significant hyperparameter tuning is often required to achieve good performance. Furthermore, when nonlinear function approximation is used, non-stationarity in the state representation can lead to learning instability. A variety of techniques exist to combat this --- most notably large experience replay buffers or the use of multiple parallel actors. These techniques come at the cost of moving away from the online RL problem as it is traditionally formulated (i.e., a single agent learning …
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…
Representation learning has been widely studied in the context of meta-learning, enabling rapid learning of new tasks through shared representations. Recent works such as MAML have explored using fine-tuning-based metrics, which measure the ease by which fine-tuning can achieve good performance, as proxies for obtaining representations. We present a theoretical framework for analyzing representations derived from a MAML-like algorithm, assuming the available tasks use approximately the same underlying representation. We then provide risk bounds on the best predictor found by fine-tuning via gr…
Notre Dame（圣母大学）；California Polytechnic State University（加州州立理工大学）
Recent studies have shown that tuning prediction models increases prediction accuracy and that Random Forest can be used to construct prediction intervals. However, to our best knowledge, no study has investigated the need to, and the manner in which one can, tune Random Forest for optimizing prediction intervals { this paper aims to fill this gap. We explore a tuning approach that combines an effectively exhaustive search with a validation technique on a single Random Forest parameter. This paper investigates which, out of eight validation techniques, are beneficial for tuning, i.e., which au…
Conventional frequentist learning is known to yield poorly calibrated models that fail to reliably quantify the uncertainty of their decisions. Bayesian learning can improve calibration, but formal guarantees apply only under restrictive assumptions about correct model specification. Conformal prediction (CP) offers a general framework for the design of set predictors with calibration guarantees that hold regardless of the underlying data generation mechanism. However, when training data are limited, CP tends to produce large, and hence uninformative, predicted sets. This paper introduces a no…
Georgia Institute of Technology（佐治亚理工学院）；University of Pennsylvania（宾夕法尼亚大学）
Uncertainty quantification is a key component of machine learning models targeted at safety-critical systems such as in healthcare or autonomous vehicles. We study this problem in the context of meta learning, where the goal is to quickly adapt a predictor to new tasks. In particular, we propose a novel algorithm to construct \emph{PAC prediction sets}, which capture uncertainty via sets of labels, that can be adapted to new tasks with only a few training examples. These prediction sets satisfy an extension of the typical PAC guarantee to the meta learning setting; in particular, the PAC guara…
Ridge estimators regularize the squared Euclidean lengths of parameters. Such estimators are mathematically and computationally attractive but involve tuning parameters that can be difficult to calibrate. In this paper, we show that ridge estimators can be modified such that tuning parameters can be avoided altogether. We also show that these modified versions can improve on the empirical prediction accuracies of standard ridge estimators combined with cross-validation, and we provide first theoretical guarantees.
Central Research Laboratories, NEC Corporation（日本电气公司中央研究所）；Artificial Intelligence Research Center, National Institute of Advanced Industrial Science and Technology（独立行政法人产业技术综合研究所人工智能研究中心）；Center for Advanced Intelligence Project, RIKEN（理化学研究所先进智能项目中心）；Department of Human Intelligence Systems, Kyushu Institute of Technology（九州工业大学人类智能系统系）；Department of Information and Communication Engineering, The University of Tokyo（东京大学信息与通信工程系）
Model-based meta-reinforcement learning (RL) methods have recently been shown to be a promising approach to improving the sample efficiency of RL in multi-task settings. However, the theoretical understanding of those methods is yet to be established, and there is currently no theoretical guarantee of their performance in a real-world environment. In this paper, we analyze the performance guarantee of model-based meta-RL methods by extending the theorems proposed by Janner et al. (2019). On the basis of our theoretical results, we propose Meta-Model-Based Meta-Policy Optimization (M3PO), a mod…
