Isabeau Prémont-Schwarz, Jaroslav Vítků, Jan Feyereisl
备注：
8 pages main article, 19 figures total, 2 pages of references, 7 pages of appendix. ICML 2022. Added Appendix Section H with extra experiments about stability
发表信息：
In Proc. 39th International Conference on Machine Learning (ICML 2022)
If the trend of learned components eventually outperforming their hand-crafted version continues, learned optimizers will eventually outperform hand-crafted optimizers like SGD or Adam. Even if learned optimizers (L2Os) eventually outpace hand-crafted ones in practice however, they are still not provably convergent and might fail out of distribution. These are the questions addressed here. Currently, learned optimizers frequently outperform generic hand-crafted optimizers (such as gradient descent) at the beginning of learning but they generally plateau after some time while the generic algorithms continue to make progress and often overtake the learned algorithm as Aesop's tortoise which overtakes the hare. L2Os also still have a difficult time generalizing out of distribution. Heaton et al. proposed Safeguarded L2O (GL2O) which can take a learned optimizer and safeguard it with a generic learning algorithm so that by conditionally switching between the two, the resulting algorithm is provably convergent. We propose a new class of Safeguarded L2O, called Loss-Guarded L2O (LGL2O), which is both conceptually simpler and computationally less expensive. The guarding mechanism decides solely based on the expected future loss value of both optimizers. Furthermore, we show theoretical proof of LGL2O's convergence guarantee and empirical results comparing to GL2O and other baselines showing that it combines the best of both L2O and SGD and that in practice converges much better than GL2O.
Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers capable of training a wide variety of problems with no user-specified hyperparameters. We introduce a new, neural network parameterized, hierarchical optimizer with access to additional features such as validation loss to enable automatic regularization. Most learned optimizers have been trained on only a single task, or a small number of tasks. We train our…
Adversarial attack has recently become a tremendous threat to deep learning models. To improve the robustness of machine learning models, adversarial training, formulated as a minimax optimization problem, has been recognized as one of the most effective defense mechanisms. However, the non-convex and non-concave property poses a great challenge to the minimax training. In this paper, we empirically demonstrate that the commonly used PGD attack may not be optimal for inner maximization, and improved inner optimizer can lead to a more robust model. Then we leverage a learning-to-learn (L2L) fra…
Learned optimizers are increasingly effective, with performance exceeding that of hand designed optimizers such as Adam~\citep{kingma2014adam} on specific tasks \citep{metz2019understanding}. Despite the potential gains available, in current work the meta-training (or `outer-training') of the learned optimizer is performed by a hand-designed optimizer, or by an optimizer trained by a hand-designed optimizer \citep{metz2020tasks}. We show that a population of randomly initialized learned optimizers can be used to train themselves from scratch in an online fashion, without resorting to a hand de…
Optimization plays a costly and crucial role in developing machine learning systems. In learned optimizers, the few hyperparameters of commonly used hand-designed optimizers, e.g. Adam or SGD, are replaced with flexible parametric functions. The parameters of these functions are then optimized so that the resulting learned optimizer minimizes a target loss on a chosen class of models. Learned optimizers can both reduce the number of required training steps and improve the final test loss. However, they can be expensive to train, and once trained can be expensive to use due to computational and…
Google Research, Brain Team（谷歌研究院大脑团队）；Meta Reality Labs（Meta现实实验室）
Learned optimizers are algorithms that can themselves be trained to solve optimization problems. In contrast to baseline optimizers (such as momentum or Adam) that use simple update rules derived from theoretical principles, learned optimizers use flexible, high-dimensional, nonlinear parameterizations. Although this can lead to better performance in certain settings, their inner workings remain a mystery. How is a learned optimizer able to outperform a well tuned baseline? Has it learned a sophisticated combination of existing optimization techniques, or is it implementing completely new beha…
When Muon Optimizer Meets Adversarial Training: A Theoretical and Empirical Study
IT College, Shanghai Ocean University（上海海洋大学信息学院）；School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）；SEIE, Suzhou University of Science and Technology（苏州科技大学SEIE学院）；DP Tech（DP科技）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）
Learned optimizers -- neural networks that are trained to act as optimizers -- have the potential to dramatically accelerate training of machine learning models. However, even when meta-trained across thousands of tasks at huge computational expense, blackbox learned optimizers often struggle with stability and generalization when applied to tasks unlike those in their meta-training set. In this paper, we use tools from dynamical systems to investigate the inductive biases and stability properties of optimization algorithms, and apply the resulting insights to designing inductive biases for bl…
While deep learning models have replaced hand-designed features across many domains, these models are still trained with hand-designed optimizers. In this work, we leverage the same scaling approach behind the success of deep learning to learn versatile optimizers. We train an optimizer for deep learning which is itself a small neural network that ingests gradients and outputs parameter updates. Meta-trained with approximately four thousand TPU-months of compute on a wide variety of optimization tasks, our optimizer not only exhibits compelling performance, but optimizes in interesting and une…
The Ohio State University（俄亥俄州立大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Learning to Optimize (L2O) has drawn increasing attention as it often remarkably accelerates the optimization procedure of complex tasks by ``overfitting" specific task type, leading to enhanced performance compared to analytical optimizers. Generally, L2O develops a parameterized optimization method (i.e., ``optimizer") by learning from solving sample problems. This data-driven procedure yields L2O that can efficiently solve problems similar to those seen in training, that is, drawn from the same ``task distribution". However, such learned optimizers often struggle when new test problems come…
State-of-the art vision models can achieve superhuman performance on image classification tasks when testing and training data come from the same distribution. However, when models are tested on corrupted images (e.g. due to scale changes, translations, or shifts in brightness or contrast), performance degrades significantly. Here, we explore the possibility of meta-training a learned optimizer that can train image classification models such that they are robust to common image corruptions. Specifically, we are interested training models that are more robust to noise distributions not present …
Google Brain（谷歌大脑）；Stanford University（斯坦福大学）；DeepMind（深度思维）
Learning to learn has emerged as an important direction for achieving artificial intelligence. Two of the primary barriers to its adoption are an inability to scale to larger problems and a limited ability to generalize to new tasks. We introduce a learned gradient descent optimizer that generalizes well to new tasks, and which has significantly reduced memory and computation overhead. We achieve this by introducing a novel hierarchical RNN architecture, with minimal per-parameter overhead, augmented with additional architectural features that mirror the known structure of optimization tasks. …
$μ$LO: Compute-Efficient Meta-Generalization of Learned Optimizers
Université de Montréal（蒙特利尔大学）；Mila – Quebec AI Institute（魁北克人工智能研究所）；Concordia University（康科迪亚大学）；Samsung AI Lab（三星AI实验室）；ISIR, Sorbonne University, CNRS, Paris, France（巴黎法国索邦大学ISIR研究所、法国国家科学研究中心）
We show that the error achievable using physics-informed neural networks for solving systems of differential equations can be substantially reduced when these networks are trained using meta-learned optimization methods rather than to using fixed, hand-crafted optimizers as traditionally done. We choose a learnable optimization method based on a shallow multi-layer perceptron that is meta-trained for specific classes of differential equations. We illustrate meta-trained optimizers for several equations of practical relevance in mathematical physics, including the linear advection equation, Poi…
How the Optimizer Shapes Learned Solutions in Equivariant Neural Networks
University of Stuttgart, Germany（斯图加特大学）；International Max Planck Research School for Intelligent Systems, Germany（国际马克斯·普朗克智能系统研究学校）；Tudor Vianu High School of Computer Science, Romania（托尔德·维安乌计算机科学高中）
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所及凝聚态物理国家实验室（北京））；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Songshan Lake Materials Laboratory（松山湖材料实验室）
Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex optimization and replace the ill-posed inverse problem by a sequence of well-conditioned surrogate problems. After training, the learned optimizers are able to give a solution of high quality with low time cost and achieve higher parameter efficiency than heuristic fully-connected networks. The output can also be used as a neural default model to improve the…
Meta-learning Optimizers for Communication-Efficient Learning
Department of Computer Science and Operation Research, Université de Montréal（计算机科学与运筹学系，蒙特利尔大学）；Department of Computer Science and Software Engineering, Concordia University（计算机科学与软件工程系，康科迪亚大学）；Mila, Montréal, Canada（Mila，蒙特利尔，加拿大）；Samsung - SAIT AI Lab, Montréal, Canada（三星-SAIT AI实验室，蒙特利尔，加拿大）
The no free lunch theorem states that no model is better suited to every problem. A question that arises from this is how to design methods that propose optimizers tailored to specific problems achieving state-of-the-art performance. This paper addresses this issue by proposing the use of meta-learning to infer population-based black-box optimizers that can automatically adapt to specific classes of problems. We suggest a general modeling of population-based algorithms that result in Learning-to-Optimize POMDP (LTO-POMDP), a meta-learning framework based on a specific partially observable Mark…
TU Darmstadt（达姆施塔特工业大学）；Fraunhofer IAIS（弗劳恩霍夫智能分析与信息系统研究所）
The move from hand-designed to learned optimizers in machine learning has been quite successful for gradient-based and -free optimizers. When facing a constrained problem, however, maintaining feasibility typically requires a projection step, which might be computationally expensive and not differentiable. We show how the design of projection-free convex optimization algorithms can be cast as a learning problem based on Frank-Wolfe Networks: recurrent networks implementing the Frank-Wolfe algorithm aka. conditional gradients. This allows them to learn to exploit structure when, e.g., optimizin…
We learn recurrent neural network optimizers trained on simple synthetic functions by gradient descent. We show that these learned optimizers exhibit a remarkable degree of transfer in that they can be used to efficiently optimize a broad range of derivative-free black-box functions, including Gaussian process bandits, simple control objectives, global optimization benchmarks and hyper-parameter tuning tasks. Up to the training horizon, the learned optimizers learn to trade-off exploration and exploitation, and compare favourably with heavily engineered Bayesian optimization packages for hyper…
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…
The advancement of artificial intelligence has cast a new light on the development of optimization algorithm. This paper proposes to learn a two-phase (including a minimization phase and an escaping phase) global optimization algorithm for smooth non-convex functions. For the minimization phase, a model-driven deep learning method is developed to learn the update rule of descent direction, which is formalized as a nonlinear combination of historical information, for convex functions. We prove that the resultant algorithm with the proposed adaptive direction guarantees convergence for convex fu…
The Ohio State University（俄亥俄州立大学）；UT Austin（德克萨斯大学奥斯汀分校）；JD Explore Academy（京东探索研究院）
Learning to optimize (L2O) has gained increasing popularity, which automates the design of optimizers by data-driven approaches. However, current L2O methods often suffer from poor generalization performance in at least two folds: (i) applying the L2O-learned optimizer to unseen optimizees, in terms of lowering their loss function values (optimizer generalization, or ``generalizable learning of optimizers"); and (ii) the test performance of an optimizee (itself as a machine learning model), trained by the optimizer, in terms of the accuracy over unseen data (optimizee generalization, or ``lear…
Do language models have beliefs about the world? Dennett (1995) famously argues that even thermostats have beliefs, on the view that a belief is simply an informational state decoupled from any motivational state. In this paper, we discuss approaches to detecting when models have beliefs about the world, and we improve on methods for updating model beliefs to be more truthful, with a focus on methods based on learned optimizers or hypernetworks. Our main contributions include: (1) new metrics for evaluating belief-updating methods that focus on the logical consistency of beliefs, (2) a trainin…
In the learning to learn (L2L) framework, we cast the design of optimization algorithms as a machine learning problem and use deep neural networks to learn the update rules. In this paper, we extend the L2L framework to zeroth-order (ZO) optimization setting, where no explicit gradient information is available. Our learned optimizer, modeled as recurrent neural network (RNN), first approximates gradient by ZO gradient estimator and then produces parameter update utilizing the knowledge of previous iterations. To reduce high variance effect due to ZO gradient estimator, we further introduce ano…
Boosting Offline Optimizers with Surrogate Sensitivity
Hanoi University of Science and Technology（河内科学技术大学）；National Institute of Advanced Industrial Science and Technology（日本产业技术综合研究所）；Washington State University（华盛顿州立大学）
Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict the acoustic field passing through the skull (e.g., to account for subject-specific dose and targeting variations). As a step towards real-time predictions, in the current work, a fast iterative solver for the heterogeneous Helmholtz equation in 2D is developed using a fully-learned optimizer. The lightweight network architecture is based on a modified UNet …
University of Science and Technology of China（中国科学技术大学）；MIT-IBM Watson AI Lab, IBM Research（麻省理工学院-IBM Watson人工智能实验室，IBM研究）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Shanghai Jiao Tong University（上海交通大学）
Learning to optimize (L2O) has gained increasing attention since classical optimizers require laborious problem-specific design and hyperparameter tuning. However, there is a gap between the practical demand and the achievable performance of existing L2O models. Specifically, those learned optimizers are applicable to only a limited class of problems, and often exhibit instability. With many efforts devoted to designing more sophisticated L2O models, we argue for another orthogonal, under-explored theme: the training techniques for those L2O models. We show that even the simplest L2O model cou…
