Bilevel Online Deep Learning in Non-stationary Environment
China University of Petroleum, Beijing Campus (CUP)（中国石油大学（北京）校区）；Department of Automation, College of Information Science and Engineering, China University of Petroleum, Beijing Campus (CUP)（中国石油大学（北京）校区信息科学与工程学院自动化系）
Ya-nan Han, Jian-wei Liu, Bing-biao Xiao, Xin-Tan Wang, Xiong-lin Luo
Recent years have witnessed enormous progress of online learning. However, a major challenge on the road to artificial agents is concept drift, that is, the data probability distribution would change where the data instance arrives sequentially in a stream fashion, which would lead to catastrophic forgetting and degrade the performance of the model. In this paper, we proposed a new Bilevel Online Deep Learning (BODL) framework, which combine bilevel optimization strategy and online ensemble classifier. In BODL algorithm, we use an ensemble classifier, which use the output of different hidden layers in deep neural network to build multiple base classifiers, the important weights of the base classifiers are updated according to exponential gradient descent method in an online manner. Besides, we apply the similar constraint to overcome the convergence problem of online ensemble framework. Then an effective concept drift detection mechanism utilizing the error rate of classifier is designed to monitor the change of the data probability distribution. When the concept drift is detected, our BODL algorithm can adaptively update the model parameters via bilevel optimization and then circumvent the large drift and encourage positive transfer. Finally, the extensive experiments and ablation studies are conducted on various datasets and the competitive numerical results illustrate that our BODL algorithm is a promising approach.
On the Complexity of Finding Stationary Points in Nonconvex Simple Bilevel Optimization
Department of Electrical and Computer Engineering, The University of Texas at Austin（电气与计算机工程系，德克萨斯大学奥斯汀分校）；Department of Systems and Industrial Engineering, The University of Arizona（系统与工业工程系，亚利桑那大学）
Rensselaer Polytechnic Institute（伦斯勒理工学院）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Stochastic bilevel optimization generalizes the classic stochastic optimization from the minimization of a single objective to the minimization of an objective function that depends the solution of another optimization problem. Recently, stochastic bilevel optimization is regaining popularity in emerging machine learning applications such as hyper-parameter optimization and model-agnostic meta learning. To solve this class of stochastic optimization problems, existing methods require either double-loop or two-timescale updates, which are sometimes less efficient. This paper develops a new opti…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
Bilevel optimization is a popular hierarchical model in machine learning, and has been widely applied to many machine learning tasks such as meta learning, hyperparameter learning and policy optimization. Although many bilevel optimization algorithms recently have been developed, few adaptive algorithm focuses on the bilevel optimization under the distributed setting. It is well known that the adaptive gradient methods show superior performances on both distributed and non-distributed optimization. In the paper, thus, we propose a novel adaptive federated bilevel optimization algorithm (i.e.,A…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；University of Pittsburgh（匹兹堡大学）
Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods do not consider using adaptive learning rates. It is well known that adaptive learning rates can accelerate optimization algorithms. To fill this gap, in the paper, we propose a novel fast adaptive bilevel framework to solve stochastic bilevel optimization problems that the outer problem is possibly nonconvex and the inner problem is strongly convex. Our fr…
Fully First-Order Methods for Decentralized Bilevel Optimization
The Hong Kong University of Science and Technology（香港科技大学）；University of California Davis（加州大学戴维斯分校）；Rice University（莱斯大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Sequential QCQP for Bilevel Optimization with Line Search
Department of Electrical and Computer Engineering at Johns Hopkins University（约翰霍普金斯大学电气与计算机工程系）；Department of Systems and Industrial Engineering, The University of Arizona（亚利桑那大学系统与工业工程系）
Texas A&M University（得克萨斯农工大学）；University of Iowa（爱荷华大学）
In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual variables and lower level problems. Due to the intertwined multi-block min-max bilevel structure, the computational cost at each iteration could be prohibitively high, especially with a large number of blocks. To tackle this challenge, we present a single-loop randomized stochastic algorithm, which requires updates for only a constant number of blocks at each it…
The University of Iowa（爱荷华大学）；Nanjing University（南京大学）
In this paper, we consider non-convex stochastic bilevel optimization (SBO) problems that have many applications in machine learning. Although numerous studies have proposed stochastic algorithms for solving these problems, they are limited in two perspectives: (i) their sample complexities are high, which do not match the state-of-the-art result for non-convex stochastic optimization; (ii) their algorithms are tailored to problems with only one lower-level problem. When there are many lower-level problems, it could be prohibitive to process all these lower-level problems at each iteration. To…
Online convex optimization is a sequential prediction framework with the goal to track and adapt to the environment through evaluating proper convex loss functions. We study efficient particle filtering methods from the perspective of such a framework. We formulate an efficient particle filtering methods for the non-stationary environment by making connections with the online mirror descent algorithm which is known to be a universal online convex optimization algorithm. As a result of this connection, our proposed particle filtering algorithm proves to achieve optimal particle efficiency.
Forecasting of time series in continuous systems becomes an increasingly relevant task due to recent developments in IoT and 5G. The popular forecasting model ARIMA is applied to a large variety of applications for decades. An online variant of ARIMA applies the Online Newton Step in order to learn the underlying process of the time series. This optimization method has pitfalls concerning the computational complexity and convergence. Thus, this work focuses on the computational less expensive Online Gradient Descent optimization method, which became popular for learning of neural networks in r…
University of Waterloo（滑铁卢大学）；University of Victoria（维多利亚大学）；Southern University of Science and Technology（南方科技大学）；National Center for Applied Mathematics Shenzhen（深圳国家应用数学中心）
Gradient-based optimization methods for hyperparameter tuning guarantee theoretical convergence to stationary solutions when for fixed upper-level variable values, the lower level of the bilevel program is strongly convex (LLSC) and smooth (LLS). This condition is not satisfied for bilevel programs arising from tuning hyperparameters in many machine learning algorithms. In this work, we develop a sequentially convergent Value Function based Difference-of-Convex Algorithm with inexactness (VF-iDCA). We show that this algorithm achieves stationary solutions without LLSC and LLS assumptions for b…
Stochastic Regret Guarantees for Online Zeroth- and First-Order Bilevel Optimization
Amirkabir University of Technology（阿姆斯泰尔大学）；University of Pennsylvania（宾夕法尼亚大学）；Samsung SDS Research America（三星SDS美国研究部）；University of California, Los Angeles（加州大学洛杉矶分校）
Coresets are small data summaries that are sufficient for model training. They can be maintained online, enabling efficient handling of large data streams under resource constraints. However, existing constructions are limited to simple models such as k-means and logistic regression. In this work, we propose a novel coreset construction via cardinality-constrained bilevel optimization. We show how our framework can efficiently generate coresets for deep neural networks, and demonstrate its empirical benefits in continual learning and in streaming settings.
Tongji University（同济大学）；University of Connecticut（康涅狄格大学）
Bilevel optimization plays an essential role in many machine learning tasks, ranging from hyperparameter optimization to meta-learning. Existing studies on bilevel optimization, however, focus on either centralized or synchronous distributed setting. The centralized bilevel optimization approaches require collecting massive amount of data to a single server, which inevitably incur significant communication expenses and may give rise to data privacy risks. Synchronous distributed bilevel optimization algorithms, on the other hand, often face the straggler problem and will immediately stop worki…
Singapore Management University（新加坡管理大学）；Salesforce Research Asia（Salesforce亚洲研究院）
Continual learning aims to learn continuously from a stream of tasks and data in an online-learning fashion, being capable of exploiting what was learned previously to improve current and future tasks while still being able to perform well on the previous tasks. One common limitation of many existing continual learning methods is that they often train a model directly on all available training data without validation due to the nature of continual learning, thus suffering poor generalization at test time. In this work, we present a novel framework of continual learning named "Bilevel Continual…
Your Offline Policy is Not Trustworthy: Bilevel Reinforcement Learning for Sequential Portfolio Optimization
MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University, China（人工智能教育部重点实验室、人工智能研究院、上海交通大学）；Department of Computer Science, University of Illinois Chicago, USA（计算机科学系、伊利诺伊大学芝加哥分校）
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact be…
The increasing availability of massive data sets poses a series of challenges for machine learning. Prominent among these is the need to learn models under hardware or human resource constraints. In such resource-constrained settings, a simple yet powerful approach is to operate on small subsets of the data. Coresets are weighted subsets of the data that provide approximation guarantees for the optimization objective. However, existing coreset constructions are highly model-specific and are limited to simple models such as linear regression, logistic regression, and $k$-means. In this work, we…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
Bilevel optimization (BO) is useful for solving a variety of important machine learning problems including but not limited to hyperparameter optimization, meta-learning, continual learning, and reinforcement learning. Conventional BO methods need to differentiate through the low-level optimization process with implicit differentiation, which requires expensive calculations related to the Hessian matrix. There has been a recent quest for first-order methods for BO, but the methods proposed to date tend to be complicated and impractical for large-scale deep learning applications. In this work, w…
Google Brain（谷歌大脑）；DeepMind（深度思维）；University of Cambridge（剑桥大学）；Alan Turing Institute（艾伦·图灵研究所）
Bilevel optimization (BLO) is a popular approach with many applications including hyperparameter optimization, neural architecture search, adversarial robustness and model-agnostic meta-learning. However, the approach suffers from time and memory complexity proportional to the length $r$ of its inner optimization loop, which has led to several modifications being proposed. One such modification is \textit{first-order} BLO (FO-BLO) which approximates outer-level gradients by zeroing out second derivative terms, yielding significant speed gains and requiring only constant memory as $r$ varies. D…
University of Texas, Austin（得克萨斯大学奥斯汀分校）；Facebook Inc.（脸书公司）
Large scale deep learning provides a tremendous opportunity to improve the quality of content recommendation systems by employing both wider and deeper models, but this comes at great infrastructural cost and carbon footprint in modern data centers. Pruning is an effective technique that reduces both memory and compute demand for model inference. However, pruning for online recommendation systems is challenging due to the continuous data distribution shift (a.k.a non-stationary data). Although incremental training on the full model is able to adapt to the non-stationary data, directly applying…
Non-stationarity appears in many online applications such as web search and advertising. In this paper, we study the online learning to rank problem in a non-stationary environment where user preferences change abruptly at an unknown moment in time. We consider the problem of identifying the K most attractive items and propose cascading non-stationary bandits, an online learning variant of the cascading model, where a user browses a ranked list from top to bottom and clicks on the first attractive item. We propose two algorithms for solving this non-stationary problem: CascadeDUCB and CascadeS…
Online Adaptive Reinforcement Learning with Echo State Networks for Non-Stationary Dynamics
Department of Computer Science, Nagoya Institute of Technology（名古屋技术大学计算机科学系）；Nagoya Institute of Technology（名古屋技术大学）；International Research Center for Neurointelligence, The University of Tokyo（神经智能国际研究中心，东京大学）
