mtybilly/Instruct2DS huggingface dataset:
Neuro-algorithmic Policies Enable Fast Combinatorial Generalization
Authors: Marin Vlastelica, Michal Rolinek, Georg Martius
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Although model-based and model-free approaches to learning the control of systems have achieved impressive results on standard benchmarks, generalization to task variations is still lacking. Recent results suggest that generalization for standard architectures improves only after obtaining exhaustive amounts of data. We give evidence that generalization capabilities are in many cases bottlenecked by the inability to generalize on the combinatorial aspects of the problem. We show that, for a certain subclass of the MDP framework, this can be alleviated by a neuro-algorithmic policy architecture that embeds a time-dependent shortest path solver in a deep neural network. Trained end-to-end via blackbox-differentiation, this method leads to considerable improvement in generalization capabilities in the low-data regime.
Efficient Training of Robust Decision Trees Against Adversarial Examples
Authors: Daniël Vos, Sicco Verwer
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Current state-of-the-art algorithms for training robust decision trees have high runtime costs and require hours to run. We present GROOT, an efficient algorithm for training robust decision trees and random forests that runs in a matter of seconds to minutes. Where before the worst-case Gini impurity was computed iteratively, we find that we can solve this function analytically to improve time complexity from O(n) to O(1) in terms of n samples. Our results on both single trees and ensembles on 14 structured datasets as well as on MNIST and Fashion-MNIST demonstrate that GROOT runs several orders of magnitude faster than the state-of-the-art works and also shows better performance in terms of adversarial accuracy on structured data.
Object Segmentation Without Labels with Large-Scale Generative Models
Authors: Andrey Voynov, Stanislav Morozov, Artem Babenko
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: The recent rise of unsupervised and self-supervised learning has dramatically reduced the dependency on labeled data, providing high-quality representations for transfer on downstream tasks. Furthermore, recent works also employed these representations in a fully unsupervised setup for image classification, reducing the need for human labels on the fine-tuning stage as well. This work demonstrates that large-scale unsupervised models can also perform a more challenging object segmentation task, requiring neither pixel-level nor image-level labeling. Namely, we show that recent unsupervised GANs allow to differentiate between foreground/background pixels, providing high-quality saliency masks. By extensive comparison on common benchmarks, we outperform existing unsupervised alternatives for object segmentation, achieving new state-of-the-art.
Principal Component Hierarchy for Sparse Quadratic Programs
Authors: Robbie Vreugdenhil, Viet Anh Nguyen, Armin Eftekhari, Peyman Mohajerin Esfahani
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose objective function can be optimized over the binary variables analytically, while preserving convexity in the continuous variables. Exploiting this property, we propose two scalable optimization algorithms, coined as the “best response" and the “dual program", that can efficiently screen the potential indices of the nonzero elements of the original program. We show that the proposed methods are competitive with the existing screening methods in the current sparse regression literature, and it is particularly fast on instances with high number of measurements in experiments with both synthetic and real datasets.
Whitening and Second Order Optimization Both Make Information in the Dataset Unusable During Training, and Can Reduce or Prevent Generalization
Authors: Neha Wadia, Daniel Duckworth, Samuel S Schoenholz, Ethan Dyer, Jascha Sohl-Dickstein
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Machine learning is predicated on the concept of generalization: a model achieving low error on a sufficiently large training set should also perform well on novel samples from the same distribution. We show that both data whitening and second order optimization can harm or entirely prevent generalization. In general, model training harnesses information contained in the sample-sample second moment matrix of a dataset. For a general class of models, namely models with a fully connected first layer, we prove that the information contained in this matrix is the only information which can be used to generalize. Models trained using whitened data, or with certain second order optimization schemes, have less access to this information, resulting in reduced or nonexistent generalization ability. We experimentally verify these predictions for several architectures, and further demonstrate that generalization continues to be harmed even when theoretical requirements are relaxed. However, we also show experimentally that regularized second order optimization can provide a practical tradeoff, where training is accelerated but less information is lost, and generalization can in some circumstances even improve.
Safe Reinforcement Learning Using Advantage-Based Intervention
Authors: Nolan C Wagener, Byron Boots, Ching-An Cheng
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Many sequential decision problems involve finding a policy that maximizes total reward while obeying safety constraints. Although much recent research has focused on the development of safe reinforcement learning (RL) algorithms that produce a safe policy after training, ensuring safety during training as well remains an open problem. A fundamental challenge is performing exploration while still satisfying constraints in an unknown Markov decision process (MDP). In this work, we address this problem for the chance-constrained setting.We propose a new algorithm, SAILR, that uses an intervention mechanism based on advantage functions to keep the agent safe throughout training and optimizes the agent’s policy using off-the-shelf RL algorithms designed for unconstrained MDPs. Our method comes with strong guarantees on safety during "both" training and deployment (i.e., after training and without the intervention mechanism) and policy performance compared to the optimal safety-constrained policy. In our experiments, we show that SAILR violates constraints far less during training than standard safe RL and constrained MDP approaches and converges to a well-performing policy that can be deployed safely without intervention. Our code is available at https://github.com/nolanwagener/safe_rl.
Task-Optimal Exploration in Linear Dynamical Systems
Authors: Andrew J Wagenmaker, Max Simchowitz, Kevin Jamieson
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Exploration in unknown environments is a fundamental problem in reinforcement learning and control. In this work, we study task-guided exploration and determine what precisely an agent must learn about their environment in order to complete a particular task. Formally, we study a broad class of decision-making problems in the setting of linear dynamical systems, a class that includes the linear quadratic regulator problem. We provide instance- and task-dependent lower bounds which explicitly quantify the difficulty of completing a task of interest. Motivated by our lower bound, we propose a computationally efficient experiment-design based exploration algorithm. We show that it optimally explores the environment, collecting precisely the information needed to complete the task, and provide finite-time bounds guaranteeing that it achieves the instance- and task-optimal sample complexity, up to constant factors. Through several examples of the linear quadratic regulator problem, we show that performing task-guided exploration provably improves on exploration schemes which do not take into account the task of interest. Along the way, we establish that certainty equivalence decision making is instance- and task-optimal, and obtain the first algorithm for the linear quadratic regulator problem which is instance-optimal. We conclude with several experiments illustrating the effectiveness of our approach in practice.
Learning and Planning in Average-Reward Markov Decision Processes
Authors: Yi Wan, Abhishek Naik, Richard S Sutton
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We introduce learning and planning algorithms for average-reward MDPs, including 1) the first general proven-convergent off-policy model-free control algorithm without reference states, 2) the first proven-convergent off-policy model-free prediction algorithm, and 3) the first off-policy learning algorithm that converges to the actual value function rather than to the value function plus an offset. All of our algorithms are based on using the temporal-difference error rather than the conventional error when updating the estimate of the average reward. Our proof techniques are a slight generalization of those by Abounadi, Bertsekas, and Borkar (2001). In experiments with an Access-Control Queuing Task, we show some of the difficulties that can arise when using methods that rely on reference states and argue that our new algorithms are significantly easier to use.
Think Global and Act Local: Bayesian Optimisation over High-Dimensional Categorical and Mixed Search Spaces
Authors: Xingchen Wan, Vu Nguyen, Huong Ha, Binxin Ru, Cong Lu, Michael A. Osborne
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: High-dimensional black-box optimisation remains an important yet notoriously challenging problem. Despite the success of Bayesian optimisation methods on continuous domains, domains that are categorical, or that mix continuous and categorical variables, remain challenging. We propose a novel solution—we combine local optimisation with a tailored kernel design, effectively handling high-dimensional categorical and mixed search spaces, whilst retaining sample efficiency. We further derive convergence guarantee for the proposed approach. Finally, we demonstrate empirically that our method outperforms the current baselines on a variety of synthetic and real-world tasks in terms of performance, computational costs, or both.
Zero-Shot Knowledge Distillation from a Decision-Based Black-Box Model
Authors: Zi Wang
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Knowledge distillation (KD) is a successful approach for deep neural network acceleration, with which a compact network (student) is trained by mimicking the softmax output of a pre-trained high-capacity network (teacher). In tradition, KD usually relies on access to the training samples and the parameters of the white-box teacher to acquire the transferred knowledge. However, these prerequisites are not always realistic due to storage costs or privacy issues in real-world applications. Here we propose the concept of decision-based black-box (DB3) knowledge distillation, with which the student is trained by distilling the knowledge from a black-box teacher (parameters are not accessible) that only returns classes rather than softmax outputs. We start with the scenario when the training set is accessible. We represent a sample’s robustness against other classes by computing its distances to the teacher’s decision boundaries and use it to construct the soft label for each training sample. After that, the student can be trained via standard KD. We then extend this approach to a more challenging scenario in which even accessing the training data is not feasible. We propose to generate pseudo samples that are distinguished by the decision boundaries of the DB3 teacher to the largest extent and construct soft labels for these samples, which are used as the transfer set. We evaluate our approaches on various benchmark networks and datasets and experiment results demonstrate their effectiveness.
Fairness of Exposure in Stochastic Bandits
Authors: Lequn Wang, Yiwei Bai, Wen Sun, Thorsten Joachims
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Contextual bandit algorithms have become widely used for recommendation in online systems (e.g. marketplaces, music streaming, news), where they now wield substantial influence on which items get shown to users. This raises questions of fairness to the items — and to the sellers, artists, and writers that benefit from this exposure. We argue that the conventional bandit formulation can lead to an undesirable and unfair winner-takes-all allocation of exposure. To remedy this problem, we propose a new bandit objective that guarantees merit-based fairness of exposure to the items while optimizing utility to the users. We formulate fairness regret and reward regret in this setting and present algorithms for both stochastic multi-armed bandits and stochastic linear bandits. We prove that the algorithms achieve sublinear fairness regret and reward regret. Beyond the theoretical analysis, we also provide empirical evidence that these algorithms can allocate exposure to different arms effectively.
A Proxy Variable View of Shared Confounding
Authors: Yixin Wang, David Blei
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Causal inference from observational data can be biased by unobserved confounders. Confounders—the variables that affect both the treatments and the outcome—induce spurious non-causal correlations between the two. Without additional conditions, unobserved confounders generally make causal quantities hard to identify. In this paper, we focus on the setting where there are many treatments with shared confounding, and we study under what conditions is causal identification possible. The key observation is that we can view subsets of treatments as proxies of the unobserved confounder and identify the intervention distributions of the rest. Moreover, while existing identification formulas for proxy variables involve solving integral equations, we show that one can circumvent the need for such solutions by directly modeling the data. Finally, we extend these results to an expanded class of causal graphs, those with other confounders and selection variables.
Fast Algorithms for Stackelberg Prediction Game with Least Squares Loss
Authors: Jiali Wang, He Chen, Rujun Jiang, Xudong Li, Zihao Li
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: The Stackelberg prediction game (SPG) has been extensively used to model the interactions between the learner and data provider in the training process of various machine learning algorithms. Particularly, SPGs played prominent roles in cybersecurity applications, such as intrusion detection, banking fraud detection, spam filtering, and malware detection. Often formulated as NP-hard bi-level optimization problems, it is generally computationally intractable to find global solutions to SPGs. As an interesting progress in this area, a special class of SPGs with the least squares loss (SPG-LS) have recently been shown polynomially solvable by a bisection method. However, in each iteration of this method, a semidefinite program (SDP) needs to be solved. The resulted high computational costs prevent its applications for large-scale problems. In contrast, we propose a novel approach that reformulates a SPG-LS as a single SDP of a similar form and the same dimension as those solved in the bisection method. Our SDP reformulation is, evidenced by our numerical experiments, orders of magnitude faster than the existing bisection method. We further show that the obtained SDP can be reduced to a second order cone program (SOCP). This allows us to provide real-time response to large-scale SPG-LS problems. Numerical results on both synthetic and real world datasets indicate that the proposed SOCP method is up to 20,000+ times faster than the state of the art.
Accelerate CNNs from Three Dimensions: A Comprehensive Pruning Framework
Authors: Wenxiao Wang, Minghao Chen, Shuai Zhao, Long Chen, Jinming Hu, Haifeng Liu, Deng Cai, Xiaofei He, Wei Liu
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Most neural network pruning methods, such as filter-level and layer-level prunings, prune the network model along one dimension (depth, width, or resolution) solely to meet a computational budget. However, such a pruning policy often leads to excessive reduction of that dimension, thus inducing a huge accuracy loss. To alleviate this issue, we argue that pruning should be conducted along three dimensions comprehensively. For this purpose, our pruning framework formulates pruning as an optimization problem. Specifically, it first casts the relationships between a certain model’s accuracy and depth/width/resolution into a polynomial regression and then maximizes the polynomial to acquire the optimal values for the three dimensions. Finally, the model is pruned along the three optimal dimensions accordingly. In this framework, since collecting too much data for training the regression is very time-costly, we propose two approaches to lower the cost: 1) specializing the polynomial to ensure an accurate regression even with less training data; 2) employing iterative pruning and fine-tuning to collect the data faster. Extensive experiments show that our proposed algorithm surpasses state-of-the-art pruning algorithms and even neural architecture search-based algorithms.
Explainable Automated Graph Representation Learning with Hyperparameter Importance
Authors: Xin Wang, Shuyi Fan, Kun Kuang, Wenwu Zhu
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Current graph representation (GR) algorithms require huge demand of human experts in hyperparameter tuning, which significantly limits their practical applications, leading to an urge for automated graph representation without human intervention. Although automated machine learning (AutoML) serves as a good candidate for automatic hyperparameter tuning, little literature has been reported on automated graph presentation learning and the only existing work employs a black-box strategy, lacking insights into explaining the relative importance of different hyperparameters. To address this issue, we study explainable automated graph representation with hyperparameter importance in this paper. We propose an explainable AutoML approach for graph representation (e-AutoGR) which utilizes explainable graph features during performance estimation and learns decorrelated importance weights for different hyperparameters in affecting the model performance through a non-linear decorrelated weighting regression. These learned importance weights can in turn help to provide more insights in hyperparameter search procedure. We theoretically prove the soundness of the decorrelated weighting algorithm. Extensive experiments on real-world datasets demonstrate the superiority of our proposed e-AutoGR model against state-of-the-art methods in terms of both model performance and hyperparameter importance explainability.
Self-Tuning for Data-Efficient Deep Learning
Authors: Ximei Wang, Jinghan Gao, Mingsheng Long, Jianmin Wang
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Deep learning has made revolutionary advances to diverse applications in the presence of large-scale labeled datasets. However, it is prohibitively time-costly and labor-expensive to collect sufficient labeled data in most realistic scenarios. To mitigate the requirement for labeled data, semi-supervised learning (SSL) focuses on simultaneously exploring both labeled and unlabeled data, while transfer learning (TL) popularizes a favorable practice of fine-tuning a pre-trained model to the target data. A dilemma is thus encountered: Without a decent pre-trained model to provide an implicit regularization, SSL through self-training from scratch will be easily misled by inaccurate pseudo-labels, especially in large-sized label space; Without exploring the intrinsic structure of unlabeled data, TL through fine-tuning from limited labeled data is at risk of under-transfer caused by model shift. To escape from this dilemma, we present Self-Tuning to enable data-efficient deep learning by unifying the exploration of labeled and unlabeled data and the transfer of a pre-trained model, as well as a Pseudo Group Contrast (PGC) mechanism to mitigate the reliance on pseudo-labels and boost the tolerance to false labels. Self-Tuning outperforms its SSL and TL counterparts on five tasks by sharp margins, e.g. it doubles the accuracy of fine-tuning on Cars with $15%$ labels.
Label Distribution Learning Machine
Authors: Jing Wang, Xin Geng
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Although Label Distribution Learning (LDL) has witnessed extensive classification applications, it faces the challenge of objective mismatch – the objective of LDL mismatches that of classification, which has seldom been noticed in existing studies. Our goal is to solve the objective mismatch and improve the classification performance of LDL. Specifically, we extend the margin theory to LDL and propose a new LDL method called \textbfLabel \textbfDistribution \textbfLearning \textbfMachine (LDLM). First, we define the label distribution margin and propose the \textbfSupport \textbfVector \textbfRegression \textbfMachine (SVRM) to learn the optimal label. Second, we propose the adaptive margin loss to learn label description degrees. In theoretical analysis, we develop a generalization theory for the SVRM and analyze the generalization of LDLM. Experimental results validate the better classification performance of LDLM.
AlphaNet: Improved Training of Supernets with Alpha-Divergence
Authors: Dilin Wang, Chengyue Gong, Meng Li, Qiang Liu, Vikas Chandra
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Weight-sharing neural architecture search (NAS) is an effective technique for automating efficient neural architecture design. Weight-sharing NAS builds a supernet that assembles all the architectures as its sub-networks and jointly trains the supernet with the sub-networks. The success of weight-sharing NAS heavily relies on distilling the knowledge of the supernet to the sub-networks. However, we find that the widely used distillation divergence, i.e., KL divergence, may lead to student sub-networks that over-estimate or under-estimate the uncertainty of the teacher supernet, leading to inferior performance of the sub-networks. In this work, we propose to improve the supernet training with a more generalized alpha-divergence. By adaptively selecting the alpha-divergence, we simultaneously prevent the over-estimation or under-estimation of the uncertainty of the teacher model. We apply the proposed alpha-divergence based supernets training to both slimmable neural networks and weight-sharing NAS, and demonstrate significant improvements. Specifically, our discovered model family, AlphaNet, outperforms prior-art models on a wide range of FLOPs regimes, including BigNAS, Once-for-All networks, and AttentiveNAS. We achieve ImageNet top-1 accuracy of 80.0% with only 444M FLOPs. Our code and pretrained models are available at https://github.com/facebookresearch/AlphaNet.
Global Convergence of Policy Gradient for Linear-Quadratic Mean-Field Control/Game in Continuous Time
Authors: Weichen Wang, Jiequn Han, Zhuoran Yang, Zhaoran Wang
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Recent years have witnessed the success of multi-agent reinforcement learning, which has motivated new research directions for mean-field control (MFC) and mean-field game (MFG), as the multi-agent system can be well approximated by a mean-field problem when the number of agents grows to be very large. In this paper, we study the policy gradient (PG) method for the linear-quadratic mean-field control and game, where we assume each agent has identical linear state transitions and quadratic cost functions. While most recent works on policy gradient for MFC and MFG are based on discrete-time models, we focus on a continuous-time model where some of our analyzing techniques could be valuable to the interested readers. For both the MFC and the MFG, we provide PG update and show that it converges to the optimal solution at a linear rate, which is verified by a synthetic simulation. For the MFG, we also provide sufficient conditions for the existence and uniqueness of the Nash equilibrium.
SG-PALM: a Fast Physically Interpretable Tensor Graphical Model
Authors: Yu Wang, Alfred Hero
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We propose a new graphical model inference procedure, called SG-PALM, for learning conditional dependency structure of high-dimensional tensor-variate data. Unlike most other tensor graphical models the proposed model is interpretable and computationally scalable to high dimension. Physical interpretability follows from the Sylvester generative (SG) model on which SG-PALM is based: the model is exact for any observation process that is a solution of a partial differential equation of Poisson type. Scalability follows from the fast proximal alternating linearized minimization (PALM) procedure that SG-PALM uses during training. We establish that SG-PALM converges linearly (i.e., geometric convergence rate) to a global optimum of its objective function. We demonstrate scalability and accuracy of SG-PALM for an important but challenging climate prediction problem: spatio-temporal forecasting of solar flares from multimodal imaging data.
Deep Generative Learning via Schrödinger Bridge
Authors: Gefei Wang, Yuling Jiao, Qian Xu, Yang Wang, Can Yang
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We propose to learn a generative model via entropy interpolation with a Schrödinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the Kullback-Leibler divergence. At the population level, this entropy interpolation is characterized via an SDE on [0,1] with a time-varying drift term. At the sample level, we derive our Schrödinger Bridge algorithm by plugging the drift term estimated by a deep score estimator and a deep density ratio estimator into the Euler-Maruyama method. Under some mild smoothness assumptions of the target distribution, we prove the consistency of both the score estimator and the density ratio estimator, and then establish the consistency of the proposed Schrödinger Bridge approach. Our theoretical results guarantee that the distribution learned by our approach converges to the target distribution. Experimental results on multimodal synthetic data and benchmark data support our theoretical findings and indicate that the generative model via Schrödinger Bridge is comparable with state-of-the-art GANs, suggesting a new formulation of generative learning. We demonstrate its usefulness in image interpolation and image inpainting.
Robust Inference for High-Dimensional Linear Models via Residual Randomization
Authors: Y. Samuel Wang, Si Kai Lee, Panos Toulis, Mladen Kolar
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We propose a residual randomization procedure designed for robust inference using Lasso estimates in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in settings that also include heavy-tailed covariates and errors. Moreover, our procedure can be valid under clustered errors, which is important in practice, but has been largely overlooked by earlier work. Through extensive simulations, we illustrate our method’s wider range of applicability as suggested by theory. In particular, we show that our method outperforms state-of-art methods in challenging, yet more realistic, settings where the distribution of covariates is heavy-tailed or the sample size is small, while it remains competitive in standard, “well behaved" settings previously studied in the literature.
A Modular Analysis of Provable Acceleration via Polyak’s Momentum: Training a Wide ReLU Network and a Deep Linear Network
Authors: Jun-Kun Wang, Chi-Heng Lin, Jacob D Abernethy
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Incorporating a so-called “momentum” dynamic in gradient descent methods is widely used in neural net training as it has been broadly observed that, at least empirically, it often leads to significantly faster convergence. At the same time, there are very few theoretical guarantees in the literature to explain this apparent acceleration effect. Even for the classical strongly convex quadratic problems, several existing results only show Polyak’s momentum has an accelerated linear rate asymptotically. In this paper, we first revisit the quadratic problems and show a non-asymptotic accelerated linear rate of Polyak’s momentum. Then, we provably show that Polyak’s momentum achieves acceleration for training a one-layer wide ReLU network and a deep linear network, which are perhaps the two most popular canonical models for studying optimization and deep learning in the literature. Prior works (Du et al. 2019) and (Wu et al. 2019) showed that using vanilla gradient descent, and with an use of over-parameterization, the error decays as $(1- Θ(\frac1 ąppa’))^t$ after $t$ iterations, where $\p̨pa’$ is the condition number of a Gram Matrix. Our result shows that with the appropriate choice of parameters Polyak’s momentum has a rate of $(1-Θ(\frac1\sqrt\kp̨a’))^t$. For the deep linear network, prior work (Hu et al. 2020) showed that vanilla gradient descent has a rate of $(1-Θ(\frac1\kaą))^t$, where $\kap$̨ is the condition number of a data matrix. Our result shows an acceleration rate $(1- Θ(\frac1\sqrt\kapp̨))^t$ is achievable by Polyak’s momentum. This work establishes that momentum does indeed speed up neural net training.
Optimal Non-Convex Exact Recovery in Stochastic Block Model via Projected Power Method
Authors: Peng Wang, Huikang Liu, Zirui Zhou, Anthony Man-Cho So
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: In this paper, we study the problem of exact community recovery in the symmetric stochastic block model, where a graph of $n$ vertices is randomly generated by partitioning the vertices into $K \ge 2$ equal-sized communities and then connecting each pair of vertices with probability that depends on their community memberships. Although the maximum-likelihood formulation of this problem is discrete and non-convex, we propose to tackle it directly using projected power iterations with an initialization that satisfies a partial recovery condition. Such an initialization can be obtained by a host of existing methods. We show that in the logarithmic degree regime of the considered problem, the proposed method can exactly recover the underlying communities at the information-theoretic limit. Moreover, with a qualified initialization, it runs in $\mO(nłog^2n/łogłog n)$ time, which is competitive with existing state-of-the-art methods. We also present numerical results of the proposed method to support and complement our theoretical development.
ConvexVST: A Convex Optimization Approach to Variance-stabilizing Transformation
Authors: Mengfan Wang, Boyu Lyu, Guoqiang Yu
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: The variance-stabilizing transformation (VST) problem is to transform heteroscedastic data to homoscedastic data so that they are more tractable for subsequent analysis. However, most of the existing approaches focus on finding an analytical solution for a certain parametric distribution, which severely limits the applications, because simple distributions cannot faithfully describe the real data while more complicated distributions cannot be analytically solved. In this paper, we converted the VST problem into a convex optimization problem, which can always be efficiently solved, identified the specific structure of the convex problem, which further improved the efficiency of the proposed algorithm, and showed that any finite discrete distributions and the discretized version of any continuous distributions from real data can be variance-stabilized in an easy and nonparametric way. We demonstrated the new approach on bioimaging data and achieved superior performance compared to peer algorithms in terms of not only the variance homoscedasticity but also the impact on subsequent analysis such as denoising. Source codes are available at https://github.com/yu-lab-vt/ConvexVST.
The Implicit Bias for Adaptive Optimization Algorithms on Homogeneous Neural Networks
Authors: Bohan Wang, Qi Meng, Wei Chen, Tie-Yan Liu
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Despite their overwhelming capacity to overfit, deep neural networks trained by specific optimization algorithms tend to generalize relatively well to unseen data. Recently, researchers explained it by investigating the implicit bias of optimization algorithms. A remarkable progress is the work (Lyu & Li, 2019), which proves gradient descent (GD) maximizes the margin of homogeneous deep neural networks. Except the first-order optimization algorithms like GD, adaptive algorithms such as AdaGrad, RMSProp and Adam are popular owing to their rapid training process. Mean-while, numerous works have provided empirical evidence that adaptive methods may suffer from poor generalization performance. However, theoretical explanation for the generalization of adaptive optimization algorithms is still lacking. In this paper, we study the implicit bias of adaptive optimization algorithms on homogeneous neural networks. In particular, we study the convergent direction of parameters when they are optimizing the logistic loss. We prove that the convergent direction of Adam and RMSProp is the same as GD, while for AdaGrad, the convergent direction depends on the adaptive conditioner. Technically, we provide a unified framework to analyze convergent direction of adaptive optimization algorithms by constructing novel and nontrivial adaptive gradient flow and surrogate margin. The theoretical findings explain the superiority on generalization of exponential moving average strategy that is adopted by RMSProp and Adam. To the best of knowledge, it is the first work to study the convergent direction of adaptive optimizations on non-linear deep neural networks
Robust Learning for Data Poisoning Attacks
Authors: Yunjuan Wang, Poorya Mianjy, Raman Arora
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: We investigate the robustness of stochastic approximation approaches against data poisoning attacks. We focus on two-layer neural networks with ReLU activation and show that under a specific notion of separability in the RKHS induced by the infinite-width network, training (finite-width) networks with stochastic gradient descent is robust against data poisoning attacks. Interestingly, we find that in addition to a lower bound on the width of the network, which is standard in the literature, we also require a distribution-dependent upper bound on the width for robust generalization. We provide extensive empirical evaluations that support and validate our theoretical results.
SketchEmbedNet: Learning Novel Concepts by Imitating Drawings
Authors: Alexander Wang, Mengye Ren, Richard Zemel
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Sketch drawings capture the salient information of visual concepts. Previous work has shown that neural networks are capable of producing sketches of natural objects drawn from a small number of classes. While earlier approaches focus on generation quality or retrieval, we explore properties of image representations learned by training a model to produce sketches of images. We show that this generative, class-agnostic model produces informative embeddings of images from novel examples, classes, and even novel datasets in a few-shot setting. Additionally, we find that these learned representations exhibit interesting structure and compositionality.
Directional Bias Amplification
Authors: Angelina Wang, Olga Russakovsky
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Mitigating bias in machine learning systems requires refining our understanding of bias propagation pathways: from societal structures to large-scale data to trained models to impact on society. In this work, we focus on one aspect of the problem, namely bias amplification: the tendency of models to amplify the biases present in the data they are trained on. A metric for measuring bias amplification was introduced in the seminal work by Zhao et al. (2017); however, as we demonstrate, this metric suffers from a number of shortcomings including conflating different types of bias amplification and failing to account for varying base rates of protected attributes. We introduce and analyze a new, decoupled metric for measuring bias amplification, $BiasAmp_i̊ghtarrow$ (Directional Bias Amplification). We thoroughly analyze and discuss both the technical assumptions and normative implications of this metric. We provide suggestions about its measurement by cautioning against predicting sensitive attributes, encouraging the use of confidence intervals due to fluctuations in the fairness of models across runs, and discussing the limitations of what this metric captures. Throughout this paper, we work to provide an interrogative look at the technical measurement of bias amplification, guided by our normative ideas of what we want it to encompass. Code is located at https://github.com/princetonvisualai/directional-bias-amp.
An exact solver for the Weston-Watkins SVM subproblem
Authors: Yutong Wang, Clayton Scott
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Recent empirical evidence suggests that the Weston-Watkins support vector machine is among the best performing multiclass extensions of the binary SVM. Current state-of-the-art solvers repeatedly solve a particular subproblem approximately using an iterative strategy. In this work, we propose an algorithm that solves the subproblem exactly using a novel reparametrization of the Weston-Watkins dual problem. For linear WW-SVMs, our solver shows significant speed-up over the state-of-the-art solver when the number of classes is large. Our exact subproblem solver also allows us to prove linear convergence of the overall solver.
SCC: an efficient deep reinforcement learning agent mastering the game of StarCraft II
Authors: Xiangjun Wang, Junxiao Song, Penghui Qi, Peng Peng, Zhenkun Tang, Wei Zhang, Weimin Li, Xiongjun Pi, Jujie He, Chao Gao, Haitao Long, Quan Yuan
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: AlphaStar, the AI that reaches GrandMaster level in StarCraft II, is a remarkable milestone demonstrating what deep reinforcement learning can achieve in complex Real-Time Strategy (RTS) games. However, the complexities of the game, algorithms and systems, and especially the tremendous amount of computation needed are big obstacles for the community to conduct further research in this direction. We propose a deep reinforcement learning agent, StarCraft Commander (SCC). With order of magnitude less computation, it demonstrates top human performance defeating GrandMaster players in test matches and top professional players in a live event. Moreover, it shows strong robustness to various human strategies and discovers novel strategies unseen from human plays. In this paper, we’ll share the key insights and optimizations on efficient imitation learning and reinforcement learning for StarCraft II full game.
Quantum algorithms for reinforcement learning with a generative model
Authors: Daochen Wang, Aarthi Sundaram, Robin Kothari, Ashish Kapoor, Martin Roetteler
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an optimal policy for a $γ$-discounted Markov decision process (MDP). For such an MDP, we design quantum algorithms that approximate an optimal policy ($π^*$), the optimal value function ($v^*$), and the optimal $Q$-function ($q^*$), assuming the algorithms can access samples from the environment in quantum superposition. This assumption is justified whenever there exists a simulator for the environment; for example, if the environment is a video game or some other program. Our quantum algorithms, inspired by value iteration, achieve quadratic speedups over the best-possible classical sample complexities in the approximation accuracy ($ε$) and two main parameters of the MDP: the effective time horizon ($\frac11-γ$) and the size of the action space ($A$). Moreover, we show that our quantum algorithm for computing $q^*$ is optimal by proving a matching quantum lower bound.
Matrix Completion with Model-free Weighting
Authors: Jiayi Wang, Raymond K. W. Wong, Xiaojun Mao, Kwun Chuen Gary Chan
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in the empirical risk without explicitly modeling the observation probabilities, and can be computed efficiently via convex optimization. The recovered matrix based on the proposed weighted empirical risk enjoys appealing theoretical guarantees. In particular, the proposed method achieves stronger guarantee than existing work in terms of the scaling with respect to the observation probabilities, under asymptotically heterogeneous missing settings (where entry-wise observation probabilities can be of different orders). These settings can be regarded as a better theoretical model of missing patterns with highly varying probabilities. We also provide a new minimax lower bound under a class of heterogeneous settings. Numerical experiments are also provided to demonstrate the effectiveness of the proposed method.
UniSpeech: Unified Speech Representation Learning with Labeled and Unlabeled Data
Authors: Chengyi Wang, Yu Wu, Yao Qian, Kenichi Kumatani, Shujie Liu, Furu Wei, Michael Zeng, Xuedong Huang
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: In this paper, we propose a unified pre-training approach called UniSpeech to learn speech representations with both labeled and unlabeled data, in which supervised phonetic CTC learning and phonetically-aware contrastive self-supervised learning are conducted in a multi-task learning manner. The resultant representations can capture information more correlated with phonetic structures and improve the generalization across languages and domains. We evaluate the effectiveness of UniSpeech for cross-lingual representation learning on public CommonVoice corpus. The results show that UniSpeech outperforms self-supervised pretraining and supervised transfer learning for speech recognition by a maximum of 13.4% and 26.9% relative phone error rate reductions respectively (averaged over all testing languages). The transferability of UniSpeech is also verified on a domain-shift speech recognition task, i.e., a relative word error rate reduction of 6% against the previous approach.
Instabilities of Offline RL with Pre-Trained Neural Representation
Authors: Ruosong Wang, Yifan Wu, Ruslan Salakhutdinov, Sham Kakade
Published in: Proceedings of the 38th International Conference on Machine Learning (Main Conference Track), 2021

Abstract: In offline reinforcement learning (RL), we seek to utilize offline data to evaluate (or learn) policies in scenarios where the data are collected from a distribution that substantially differs from that of the target policy to be evaluated. Recent theoretical advances have shown that such sample-efficient offline RL is indeed possible provided certain strong representational conditions hold, else there are lower bounds exhibiting exponential error amplification (in the problem horizon) unless the data collection distribution has only a mild distribution shift relative to the target policy. This work studies these issues from an empirical perspective to gauge how stable offline RL methods are. In particular, our methodology explores these ideas when using features from pre-trained neural networks, in the hope that these representations are powerful enough to permit sample efficient offline RL. Through extensive experiments on a range of tasks, we see that substantial error amplification does occur even when using such pre-trained representations (trained on the same task itself); we find offline RL is stable only under extremely mild distribution shift. The implications of these results, both from a theoretical and an empirical perspective, are that successful offline RL (where we seek to go beyond the low distribution shift regime) requires substantially stronger conditions beyond those which suffice for successful supervised learning.