OpenRaiser/Intern-Atlas huggingface dataset:
Striving for Simplicity and Performance in Off-Policy DRL: Output Normalization and Non-Uniform Sampling
Venue: Conference ICML 2020
Year: 2020

We aim to develop off-policy DRL algorithms that not only exceed state-of-the-art performance but are also simple and minimalistic. For standard continuous control benchmarks, Soft Actor-Critic (SAC), which employs entropy maximization, currently provides state-of-the-art performance. We first demonstrate that the entropy term in SAC addresses action saturation due to the bounded nature of the action spaces, with this insight, we propose a streamlined algorithm with a simple normalization scheme or with inverted gradients. We show that both approaches can match SAC's sample efficiency performance without the need of entropy maximization, we then propose a simple non-uniform sampling method for selecting transitions from the replay buffer during training. Extensive experimental results demonstrate that our proposed sampling scheme leads to state of the art sample efficiency on challenging continuous control tasks. We combine all of our findings into one simple algorithm, which we call Streamlined Off Policy with Emphasizing Recent Experience, for which we provide robust public-domain code.
Breaking the Curse of Many Agents: Provable Mean Embedding Q-Iteration for Mean-Field Reinforcement Learning
Venue: Conference ICML 2020
Year: 2020

Multi-agent reinforcement learning (MARL) achieves significant empirical successes. However, MARL suffers from the curse of many agents. In this paper, we exploit the symmetry of agents in MARL. In the most generic form, we study a mean-field MARL problem. Such a mean-field MARL is defined on mean-field states, which are distributions that are supported on continuous space. Based on the mean embedding of the distributions, we propose MF-FQI algorithm that solves the mean-field MARL and establishes a non-asymptotic analysis for MF-FQI algorithm. We highlight that MF-FQI algorithm enjoys a "blessing of many agents" property in the sense that a larger number of observed agents improves the performance of MF-FQI algorithm.
Model-free Reinforcement Learning in Infinite-horizon Average-reward Markov Decision Processes
Venue: Conference ICML 2020
Year: 2020

Model-free reinforcement learning is known to be memory and computation efficient and more amendable to large scale problems. In this paper, two model-free algorithms are introduced for learning infinite-horizon average-reward Markov Decision Processes (MDPs). The first algorithm reduces the problem to the discounted-reward version and achieves $\mathcal{O}(T^{2/3})$ regret after $T$ steps, under the minimal assumption of weakly communicating MDPs. To our knowledge, this is the first model-free algorithm for general MDPs in this setting. The second algorithm makes use of recent advances in adaptive algorithms for adversarial multi-armed bandits and improves the regret to $\mathcal{O}(\sqrt{T})$, albeit with a stronger ergodic assumption. This result significantly improves over the $\mathcal{O}(T^{3/4})$ regret achieved by the only existing model-free algorithm by Abbasi-Yadkori et al. (2019a) for ergodic MDPs in the infinite-horizon average-reward setting.
The Implicit and Explicit Regularization Effects of Dropout
Venue: Conference ICML 2020
Year: 2020

Dropout is a widely-used regularization technique, often required to obtain state-of-the-art for a number of architectures. This work demonstrates that dropout introduces two distinct but entangled regularization effects: an explicit effect (also studied in prior work) which occurs since dropout modifies the expected training objective, and, perhaps surprisingly, an additional implicit effect from the stochasticity in the dropout training update. This implicit regularization effect is analogous to the effect of stochasticity in small mini-batch stochastic gradient descent. We disentangle these two effects through controlled experiments. We then derive analytic simplifications which characterize each effect in terms of the derivatives of the model and the loss, for deep neural networks. We demonstrate these simplified, analytic regularizers accurately capture the important aspects of dropout, showing they faithfully replace dropout in practice.
Batch Stationary Distribution Estimation
Venue: Conference ICML 2020
Year: 2020

We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of sufficient length can be gathered to approximate stationary sampling. Instead, we consider an alternative setting where a fixed set of transitions has been collected beforehand, by a separate, possibly unknown procedure. The goal is still to estimate properties of the stationary distribution, but without additional access to the underlying system. We propose a consistent estimator that is based on recovering a correction ratio function over the given data. In particular, we develop a variational power method (VPM) that provides provably consistent estimates under general conditions. In addition to unifying a number of existing approaches from different subfields, we also find that VPM yields significantly better estimates across a range of problems, including queueing, stochastic differential equations, post-processing MCMC, and off-policy evaluation.
Towards Understanding the Regularization of Adversarial Robustness on Neural Networks
Venue: Conference ICML 2020
Year: 2020

The problem of adversarial examples has shown that modern Neural Network (NN) models could be rather fragile. Among the more established techniques to solve the problem, one is to require the model to be {\it $ε$-adversarially robust} (AR); that is, to require the model not to change predicted labels when any given input examples are perturbed within a certain range. However, it is observed that such methods would lead to standard performance degradation, i.e., the degradation on natural examples. In this work, we study the degradation through the regularization perspective. We identify quantities from generalization analysis of NNs; with the identified quantities we empirically find that AR is achieved by regularizing/biasing NNs towards less confident solutions by making the changes in the feature space (induced by changes in the instance space) of most layers smoother uniformly in all directions; so to a certain extent, it prevents sudden change in prediction w.r.t. perturbations. However, the end result of such smoothing concentrates samples around decision boundaries, resulting in less confident solutions, and leads to worse standard performance. Our studies suggest that one might consider ways that build AR into NNs in a gentler way to avoid the problematic regularization.
Predictive Sampling with Forecasting Autoregressive Models
Venue: Conference ICML 2020
Year: 2020

Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is impractically slow. In this paper, we introduce the predictive sampling algorithm: a procedure that exploits the fast inference property of ARMs in order to speed up sampling, while keeping the model intact. We propose two variations of predictive sampling, namely sampling with ARM fixed-point iteration and learned forecasting modules. Their effectiveness is demonstrated in two settings: i) explicit likelihood modeling on binary MNIST, SVHN and CIFAR10, and ii) discrete latent modeling in an autoencoder trained on SVHN, CIFAR10 and Imagenet32. Empirically, we show considerable improvements over baselines in number of ARM inference calls and sampling speed.
Learning to Rank Learning Curves
Venue: Conference ICML 2020
Year: 2020

Many automated machine learning methods, such as those for hyperparameter and neural architecture optimization, are computationally expensive because they involve training many different model configurations. In this work, we present a new method that saves computational budget by terminating poor configurations early on in the training. In contrast to existing methods, we consider this task as a ranking and transfer learning problem. We qualitatively show that by optimizing a pairwise ranking loss and leveraging learning curves from other datasets, our model is able to effectively rank learning curves without having to observe many or very long learning curves. We further demonstrate that our method can be used to accelerate a neural architecture search by a factor of up to 100 without a significant performance degradation of the discovered architecture. In further experiments we analyze the quality of ranking, the influence of different model components as well as the predictive behavior of the model.
Near Input Sparsity Time Kernel Embeddings via Adaptive Sampling
Venue: Conference ICML 2020
Year: 2020

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for subsampling the feature space of a degree $q$ tensoring of data points in almost input sparsity time, improving the recent oblivious sketching method of (Ahle et al., 2020) by a factor of $q^{5/2}/ε^2$. This leads to a subspace embedding for the polynomial kernel, as well as the Gaussian kernel, with a target dimension that is only linearly dependent on the statistical dimension of the kernel and in time which is only linearly dependent on the sparsity of the input dataset. We show how our subspace embedding bounds imply new statistical guarantees for kernel ridge regression. Furthermore, we empirically show that in large-scale regression tasks, our algorithm outperforms state-of-the-art kernel approximation methods.
Is Local SGD Better than Minibatch SGD?
Venue: Conference ICML 2020
Year: 2020

We study local SGD (also known as parallel SGD and federated averaging), a natural and frequently used stochastic distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives we prove that local SGD strictly dominates minibatch SGD and that accelerated local SGD is minimax optimal for quadratics; (2) For general convex objectives we provide the first guarantee that at least sometimes improves over minibatch SGD; (3) We show that indeed local SGD does not dominate minibatch SGD by presenting a lower bound on the performance of local SGD that is worse than the minibatch SGD guarantee.
Obtaining Adjustable Regularization for Free via Iterate Averaging
Venue: Conference ICML 2020
Year: 2020

Regularization for optimization is a crucial technique to avoid overfitting in machine learning. In order to obtain the best performance, we usually train a model by tuning the regularization parameters. It becomes costly, however, when a single round of training takes significant amount of time. Very recently, Neu and Rosasco show that if we run stochastic gradient descent (SGD) on linear regression problems, then by averaging the SGD iterates properly, we obtain a regularized solution. It left open whether the same phenomenon can be achieved for other optimization problems and algorithms. In this paper, we establish an averaging scheme that provably converts the iterates of SGD on an arbitrary strongly convex and smooth objective function to its regularized counterpart with an adjustable regularization parameter. Our approaches can be used for accelerated and preconditioned optimization methods as well. We further show that the same methods work empirically on more general optimization objectives including neural networks. In sum, we obtain adjustable regularization for free for a large class of optimization problems and resolve an open question raised by Neu and Rosasco.
DeltaGrad: Rapid retraining of machine learning models
Venue: Conference ICML 2020
Year: 2020

Machine learning models are not static and may need to be retrained on slightly changed datasets, for instance, with the addition or deletion of a set of data points. This has many applications, including privacy, robustness, bias reduction, and uncertainty quantifcation. However, it is expensive to retrain models from scratch. To address this problem, we propose the DeltaGrad algorithm for rapid retraining machine learning models based on information cached during the training phase. We provide both theoretical and empirical support for the effectiveness of DeltaGrad, and show that it compares favorably to the state of the art.
On the Noisy Gradient Descent that Generalizes as SGD
Venue: Conference ICML 2020
Year: 2020

The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for regularization, it remains unclear whether or not the class of noise distributions is important. In this work we provide negative results by showing that noises in classes different from the SGD noise can also effectively regularize gradient descent. Our finding is based on a novel observation on the structure of the SGD noise: it is the multiplication of the gradient matrix and a sampling noise that arises from the mini-batch sampling procedure. Moreover, the sampling noises unify two kinds of gradient regularizing noises that belong to the Gaussian class: the one using (scaled) Fisher as covariance and the one using the gradient covariance of SGD as covariance. Finally, thanks to the flexibility of choosing noise class, an algorithm is proposed to perform noisy gradient descent that generalizes well, the variant of which even benefits large batch SGD training without hurting generalization.
Stronger and Faster Wasserstein Adversarial Attacks
Venue: Conference ICML 2020
Year: 2020

Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to "small, imperceptible" perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the $\ell_p$ metric, Wasserstein distance, which takes geometry in pixel space into account, has long been known to be a suitable metric for measuring image quality and has recently risen as a compelling alternative to the $\ell_p$ metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show that the Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to $3.4\%$ within a Wasserstein perturbation ball of radius $0.005$, in contrast to $65.6\%$ using the previous Wasserstein attack based on an \emph{approximate} projection operator. Furthermore, employing our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models.
Continuous Graph Neural Networks
Venue: Conference ICML 2020
Year: 2020

This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can be viewed as a specific discretisation scheme. The key idea is how to characterise the continuous dynamics of node representations, i.e. the derivatives of node representations, w.r.t. time. Inspired by existing diffusion-based methods on graphs (e.g. PageRank and epidemic models on social networks), we define the derivatives as a combination of the current node representations, the representations of neighbors, and the initial values of the nodes. We propose and analyse two possible dynamics on graphs---including each dimension of node representations (a.k.a. the feature channel) change independently or interact with each other---both with theoretical justification. The proposed continuous graph neural networks are robust to over-smoothing and hence allow us to build deeper networks, which in turn are able to capture the long-range dependencies between nodes. Experimental results on the task of node classification demonstrate the effectiveness of our proposed approach over competitive baselines.
Generative Flows with Matrix Exponential
Venue: Conference ICML 2020
Year: 2020

Generative flows models enjoy the properties of tractable exact likelihood and efficient sampling, which are composed of a sequence of invertible functions. In this paper, we incorporate matrix exponential into generative flows. Matrix exponential is a map from matrices to invertible matrices, this property is suitable for generative flows. Based on matrix exponential, we propose matrix exponential coupling layers that are a general case of affine coupling layers and matrix exponential invertible 1 x 1 convolutions that do not collapse during training. And we modify the networks architecture to make trainingstable andsignificantly speed up the training process. Our experiments show that our model achieves great performance on density estimation amongst generative flows models.
Disentangling Trainability and Generalization in Deep Neural Networks
Venue: Conference ICML 2020
Year: 2020

A longstanding goal in the theory of deep learning is to characterize the conditions under which a given neural network architecture will be trainable, and if so, how well it might generalize to unseen data. In this work, we provide such a characterization in the limit of very wide and very deep networks, for which the analysis simplifies considerably. For wide networks, the trajectory under gradient descent is governed by the Neural Tangent Kernel (NTK), and for deep networks the NTK itself maintains only weak data dependence. By analyzing the spectrum of the NTK, we formulate necessary conditions for trainability and generalization across a range of architectures, including Fully Connected Networks (FCNs) and Convolutional Neural Networks (CNNs). We identify large regions of hyperparameter space for which networks can memorize the training set but completely fail to generalize. We find that CNNs without global average pooling behave almost identically to FCNs, but that CNNs with pooling have markedly different and often better generalization performance. These theoretical results are corroborated experimentally on CIFAR10 for a variety of network architectures and we include a colab notebook that reproduces the essential results of the paper.
Maximum-and-Concatenation Networks
Venue: Conference ICML 2020
Year: 2020

While successful in many fields, deep neural networks (DNNs) still suffer from some open problems such as bad local minima and unsatisfactory generalization performance. In this work, we propose a novel architecture called Maximum-and-Concatenation Networks (MCN) to try eliminating bad local minima and improving generalization ability as well. Remarkably, we prove that MCN has a very nice property; that is, \emph{every local minimum of an $(l+1)$-layer MCN can be better than, at least as good as, the global minima of the network consisting of its first $l$ layers}. In other words, by increasing the network depth, MCN can autonomously improve its local minima's goodness, what is more, \emph{it is easy to plug MCN into an existing deep model to make it also have this property}. Finally, under mild conditions, we show that MCN can approximate certain continuous functions arbitrarily well with \emph{high efficiency}; that is, the covering number of MCN is much smaller than most existing DNNs such as deep ReLU. Based on this, we further provide a tight generalization bound to guarantee the inference ability of MCN when dealing with testing samples.
On the Number of Linear Regions of Convolutional Neural Networks
Venue: Conference ICML 2020
Year: 2020

One fundamental problem in deep learning is understanding the outstanding performance of deep Neural Networks (NNs) in practice. One explanation for the superiority of NNs is that they can realize a large class of complicated functions, i.e., they have powerful expressivity. The expressivity of a ReLU NN can be quantified by the maximal number of linear regions it can separate its input space into. In this paper, we provide several mathematical results needed for studying the linear regions of CNNs, and use them to derive the maximal and average numbers of linear regions for one-layer ReLU CNNs. Furthermore, we obtain upper and lower bounds for the number of linear regions of multi-layer ReLU CNNs. Our results suggest that deeper CNNs have more powerful expressivity than their shallow counterparts, while CNNs have more expressivity than fully-connected NNs per parameter.
On Layer Normalization in the Transformer Architecture
Venue: Conference ICML 2020
Year: 2020

The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow down the optimization and bring more hyper-parameter tunings. In this paper, we first study theoretically why the learning rate warm-up stage is essential and show that the location of layer normalization matters. Specifically, we prove with mean field theory that at initialization, for the original-designed Post-LN Transformer, which places the layer normalization between the residual blocks, the expected gradients of the parameters near the output layer are large. Therefore, using a large learning rate on those gradients makes the training unstable. The warm-up stage is practically helpful for avoiding this problem. On the other hand, our theory also shows that if the layer normalization is put inside the residual blocks (recently proposed as Pre-LN Transformer), the gradients are well-behaved at initialization. This motivates us to remove the warm-up stage for the training of Pre-LN Transformers. We show in our experiments that Pre-LN Transformers without the warm-up stage can reach comparable results with baselines while requiring significantly less training time and hyper-parameter tuning on a wide range of applications.
On Variational Learning of Controllable Representations for Text without Supervision
Venue: Conference ICML 2020
Year: 2020

The variational autoencoder (VAE) can learn the manifold of natural images on certain datasets, as evidenced by meaningful interpolating or extrapolating in the continuous latent space. However, on discrete data such as text, it is unclear if unsupervised learning can discover similar latent space that allows controllable manipulation. In this work, we find that sequence VAEs trained on text fail to properly decode when the latent codes are manipulated, because the modified codes often land in holes or vacant regions in the aggregated posterior latent space, where the decoding network fails to generalize. Both as a validation of the explanation and as a fix to the problem, we propose to constrain the posterior mean to a learned probability simplex, and performs manipulation within this simplex. Our proposed method mitigates the latent vacancy problem and achieves the first success in unsupervised learning of controllable representations for text. Empirically, our method outperforms unsupervised baselines and strong supervised approaches on text style transfer, and is capable of performing more flexible fine-grained control over text generation than existing methods.