ICML 2021 Papers

We study episodic reinforcement learning under unknown adversarial corruptions in both the rewards and the transition probabilities of the underlying system. We propose new algorithms which, compared to the existing results in \cite{lykouris2020corruption}, achieve strictly better regret bounds in terms of total corruptions for the tabular setting. To be specific, firstly, our regret bounds depend on more precise numerical values of total rewards corruptions and transition corruptions, instead of only on the total number of corrupted episodes. Secondly, our regret bounds are the first of their kind in the reinforcement learning setting to have the number of corruptions show up additively with respect to $\min\{ \sqrt{T},\text{PolicyGapComplexity} \}$ rather than multiplicatively. Our results follow from a general algorithmic framework that combines corruption-robust policy elimination meta-algorithms, and plug-in reward-free exploration sub-algorithms. Replacing the meta-algorithm or sub-algorithm may extend the framework to address other corrupted settings with potentially more structure.

Contrastive divergence is a popular method of training energy-based models, but is known to have difficulties with training stability. We propose an adaptation to improve contrastive divergence training by scrutinizing a gradient term that is difficult to calculate and is often left out for convenience. We show that this gradient term is numerically significant and in practice is important to avoid training instabilities, while being tractable to estimate. We further highlight how data augmentation and multi-scale processing can be used to improve model robustness and generation quality. Finally, we empirically evaluate stability of model architectures and show improved performance on a host of benchmarks and use cases, such as image generation, OOD detection, and compositional generation.

We propose improved fixed-design confidence bounds for the linear logistic model. Our bounds significantly improve upon the state-of-the-art bound by Li et al. (2017) via recent developments of the self-concordant analysis of the logistic loss (Faury et al., 2020). Specifically, our confidence bound avoids a direct dependence on $1/\kappa$, where $\kappa$ is the minimal variance over all arms’ reward distributions. In general, $1/\kappa$ scales exponentially with the norm of the unknown linear parameter $\theta^*$. Instead of relying on this worst case quantity, our confidence bound for the reward of any given arm depends directly on the variance of that arm’s reward distribution. We present two applications of our novel bounds to pure exploration and regret minimization logistic bandits improving upon state-of-the-art performance guarantees. For pure exploration we also provide a lower bound highlighting a dependence on $1/\kappa$ for a family of instances.

We consider active learning for binary classification in the agnostic pool-based setting. The vast majority of works in active learning in the agnostic setting are inspired by the CAL algorithm where each query is uniformly sampled from the disagreement region of the current version space. The sample complexity of such algorithms is described by a quantity known as the disagreement coefficient which captures both the geometry of the hypothesis space as well as the underlying probability space. To date, the disagreement coefficient has been justified by minimax lower bounds only, leaving the door open for superior instance dependent sample complexities. In this work we propose an algorithm that, in contrast to uniform sampling over the disagreement region, solves an experimental design problem to determine a distribution over examples from which to request labels. We show that the new approach achieves sample complexity bounds that are never worse than the best disagreement coefficient-based bounds, but in specific cases can be dramatically smaller. From a practical perspective, the proposed algorithm requires no hyperparameters to tune (e.g., to control the aggressiveness of sampling), and is computationally efficient by means of assuming access to an empirical risk minimization oracle (without any constraints). Empirically, we demonstrate that our algorithm is superior to state of the art agnostic active learning algorithms on image classification datasets.

In the deep learning era, the vast majority of methods to predict pose from a single image are trained to classify or regress to a single given ground truth pose per image. Such methods have two main shortcomings, i) they cannot represent uncertainty about the predictions, and ii) they cannot handle symmetric objects, where multiple (potentially infinite) poses may be correct. Only recently these shortcomings have been addressed, but current approaches as limited in that they cannot express the full rich space of distributions on the rotation manifold. To this end, we introduce a method to estimate arbitrary, non-parametric distributions on SO(3). Our key idea is to represent the distributions implicitly, with a neural network that estimates the probability density, given the input image and a candidate pose. At inference time, grid sampling or gradient ascent can be used to find the most likely pose, but it is also possible to evaluate the density at any pose, enabling reasoning about symmetries and uncertainty. This is the most general way of representing distributions on manifolds, and to demonstrate its expressive power we introduce a new dataset containing symmetric and nearly-symmetric objects. Our method also shows advantages on the popular object pose estimation benchmarks ModelNet10-SO(3) and T-LESS. Code, data, and visualizations may be found at implicit-pdf.github.io.

We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest. Examples of such problems include optimizing false negative rate at a fixed false positive rate, optimizing precision at a fixed recall, optimizing the area under the precision-recall or ROC curves, etc. Our key idea is to formulate a rate-constrained optimization that expresses the threshold parameter as a function of the model parameters via the Implicit Function theorem. We show how the resulting optimization problem can be solved using standard gradient based methods. Experiments on benchmark datasets demonstrate the effectiveness of our proposed method over existing state-of-the-art approaches for these problems.

Recent efforts to unravel the mystery of implicit regularization in deep learning have led to a theoretical focus on matrix factorization — matrix completion via linear neural network. As a step further towards practical deep learning, we provide the first theoretical analysis of implicit regularization in tensor factorization — tensor completion via certain type of non-linear neural network. We circumvent the notorious difficulty of tensor problems by adopting a dynamical systems perspective, and characterizing the evolution induced by gradient descent. The characterization suggests a form of greedy low tensor rank search, which we rigorously prove under certain conditions, and empirically demonstrate under others. Motivated by tensor rank capturing the implicit regularization of a non-linear neural network, we empirically explore it as a measure of complexity, and find that it captures the essence of datasets on which neural networks generalize. This leads us to believe that tensor rank may pave way to explaining both implicit regularization in deep learning, and the properties of real-world data translating this implicit regularization to generalization.

Contemporary wisdom based on empirical studies suggests that standard recurrent neural networks (RNNs) do not perform well on tasks requiring long-term memory. However, RNNs’ poor ability to capture long-term dependencies has not been fully understood. This paper provides a rigorous explanation of this property in the special case of linear RNNs. Although this work is limited to linear RNNs, even these systems have traditionally been difficult to analyze due to their non-linear parameterization. Using recently-developed kernel regime analysis, our main result shows that as the number of hidden units goes to infinity, linear RNNs learned from random initializations are functionally equivalent to a certain weighted 1D-convolutional network. Importantly, the weightings in the equivalent model cause an implicit bias to elements with smaller time lags in the convolution, and hence shorter memory. The degree of this bias depends on the variance of the transition matrix at initialization and is related to the classic exploding and vanishing gradients problem. The theory is validated with both synthetic and real data experiments.

Imitation learning enables agents to reuse and adapt the hard-won expertise of others, offering a solution to several key challenges in learning behavior. Although it is easy to observe behavior in the real-world, the underlying actions may not be accessible. We present a new method for imitation solely from observations that achieves comparable performance to experts on challenging continuous control tasks while also exhibiting robustness in the presence of observations unrelated to the task. Our method, which we call FORM (for "Future Observation Reward Model") is derived from an inverse RL objective and imitates using a model of expert behavior learned by generative modelling of the expert’s observations, without needing ground truth actions. We show that FORM performs comparably to a strong baseline IRL method (GAIL) on the DeepMind Control Suite benchmark, while outperforming GAIL in the presence of task-irrelevant features.

Training on datasets with long-tailed distributions has been challenging for major recognition tasks such as classification and detection. To deal with this challenge, image resampling is typically introduced as a simple but effective approach. However, we observe that long-tailed detection differs from classification since multiple classes may be present in one image. As a result, image resampling alone is not enough to yield a sufficiently balanced distribution at the object-level. We address object-level resampling by introducing an object-centric sampling strategy based on a dynamic, episodic memory bank. Our proposed strategy has two benefits: 1) convenient object-level resampling without significant extra computation, and 2) implicit feature-level augmentation from model updates. We show that image-level and object-level resamplings are both important, and thus unify them with a joint resampling strategy. Our method achieves state-of-the-art performance on the rare categories of LVIS, with 1.89% and 3.13% relative improvements over Forest R-CNN on detection and instance segmentation.

We present deep learning methods for the design of arrays and single instances of small antennas. Each design instance is conditioned on a target radiation pattern and is required to conform to specific spatial dimensions and to include, as part of its metallic structure, a set of predetermined locations. The solution, in the case of a single antenna, is based on a composite neural network that combines a simulation network, a hypernetwork, and a refinement network. In the design of the antenna array, we add an additional design level and employ a hypernetwork within a hypernetwork. The learning objective is based on measuring the similarity of the obtained radiation pattern to the desired one. Our experiments demonstrate that our approach is able to design novel antennas and antenna arrays that are compliant with the design requirements, considerably better than the baseline methods. We compare the solutions obtained by our method to existing designs and demonstrate a high level of overlap. When designing the antenna array of a cellular phone, the obtained solution displays improved properties over the existing one.

Performative distribution shift captures the setting where the choice of which ML model is deployed changes the data distribution. For example, a bank which uses the number of open credit lines to determine a customer’s risk of default on a loan may induce customers to open more credit lines in order to improve their chances of being approved. Because of the interactions between the model and data distribution, finding the optimal model parameters is challenging. Works in this area have focused on finding stable points, which can be far from optimal. Here we introduce \emph{performative gradient descent} (PerfGD), an algorithm for computing performatively optimal points. Under regularity assumptions on the performative loss, PerfGD is the first algorithm which provably converges to an optimal point. PerfGD explicitly captures how changes in the model affects the data distribution and is simple to use. We support our findings with theory and experiments.

Kernel ridge regression is well-known to achieve minimax optimal rates in low-dimensional settings. However, its behavior in high dimensions is much less understood. Recent work establishes consistency for high-dimensional kernel regression for a number of specific assumptions on the data distribution. In this paper, we show that in high dimensions, the rotational invariance property of commonly studied kernels (such as RBF, inner product kernels and fully-connected NTK of any depth) leads to inconsistent estimation unless the ground truth is a low-degree polynomial. Our lower bound on the generalization error holds for a wide range of distributions and kernels with different eigenvalue decays. This lower bound suggests that consistency results for kernel ridge regression in high dimensions generally require a more refined analysis that depends on the structure of the kernel beyond its eigenvalue decay.

Semantic understanding of programs is a fundamental problem for programming language processing (PLP). Recent works that learn representations of code based on pre-training techniques in NLP have pushed the frontiers in this direction. However, the semantics of PL and NL have essential differences. These being ignored, we believe it is difficult to build a model to better understand programs, by either directly applying off-the-shelf NLP pre-training techniques to the source code, or adding features to the model by the heuristic. In fact, the semantics of a program can be rigorously defined by formal semantics in PL theory. For example, the operational semantics, describes the meaning of a valid program as updating the environment (i.e., the memory address-value function) through fundamental operations, such as memory I/O and conditional branching. Inspired by this, we propose a novel program semantics learning paradigm, that the model should learn from information composed of (1) the representations which align well with the fundamental operations in operational semantics, and (2) the information of environment transition, which is indispensable for program understanding. To validate our proposal, we present a hierarchical Transformer-based pre-training model called OSCAR to better facilitate the understanding of programs. OSCAR learns from intermediate representation (IR) and an encoded representation derived from static analysis, which are used for representing the fundamental operations and approximating the environment transitions respectively. OSCAR empirically shows the outstanding capability of program semantics understanding on many practical software engineering tasks. Code and models are released at: \url{https://github.com/pdlan/OSCAR}.

Methods that infer causal dependence from observational data are central to many areas of science, including medicine, economics, and the social sciences. A variety of theoretical properties of these methods have been proven, but empirical evaluation remains a challenge, largely due to the lack of observational data sets for which treatment effect is known. We describe and analyze observational sampling from randomized controlled trials (OSRCT), a method for evaluating causal inference methods using data from randomized controlled trials (RCTs). This method can be used to create constructed observational data sets with corresponding unbiased estimates of treatment effect, substantially increasing the number of data sets available for evaluating causal inference methods. We show that, in expectation, OSRCT creates data sets that are equivalent to those produced by randomly sampling from empirical data sets in which all potential outcomes are available. We then perform a large-scale evaluation of seven causal inference methods over 37 data sets, drawn from RCTs, as well as simulators, real-world computational systems, and observational data sets augmented with a synthetic response variable. We find notable performance differences when comparing across data from different sources, demonstrating the importance of using data from a variety of sources when evaluating any causal inference method.

Meta-learning aims to perform fast adaptation on a new task through learning a “prior” from multiple existing tasks. A common practice in meta-learning is to perform a train-validation split (\emph{train-val method}) where the prior adapts to the task on one split of the data, and the resulting predictor is evaluated on another split. Despite its prevalence, the importance of the train-validation split is not well understood either in theory or in practice, particularly in comparison to the more direct \emph{train-train method}, which uses all the per-task data for both training and evaluation. We provide a detailed theoretical study on whether and when the train-validation split is helpful in the linear centroid meta-learning problem. In the agnostic case, we show that the expected loss of the train-val method is minimized at the optimal prior for meta testing, and this is not the case for the train-train method in general without structural assumptions on the data. In contrast, in the realizable case where the data are generated from linear models, we show that both the train-val and train-train losses are minimized at the optimal prior in expectation. Further, perhaps surprisingly, our main result shows that the train-train method achieves a \emph{strictly better} excess loss in this realizable case, even when the regularization parameter and split ratio are optimally tuned for both methods. Our results highlight that sample splitting may not always be preferable, especially when the data is realizable by the model. We validate our theories by experimentally showing that the train-train method can indeed outperform the train-val method, on both simulations and real meta-learning tasks.

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. We decompose an input graph into low-pass and high-pass frequencies coefficients for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds high-frequency information at different scales. Compared to ReLU, shrinkage activation improves model performance on denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with well-preserved prediction performance.

Good generalization performance across a wide variety of domains caused by many external and internal factors is the fundamental goal of any machine learning algorithm. This paper theoretically proves that the choice of loss function matters for improving the generalization performance of deep learning-based systems. By deriving the generalization error bound for deep neural models trained by stochastic gradient descent, we pinpoint the characteristics of the loss function that is linked to the generalization error and can therefore be used for guiding the loss function selection process. In summary, our main statement in this paper is: choose a stable loss function, generalize better. Focusing on human age estimation from the face which is a challenging topic in computer vision, we then propose a novel loss function for this learning problem. We theoretically prove that the proposed loss function achieves stronger stability, and consequently a tighter generalization error bound, compared to the other common loss functions for this problem. We have supported our findings theoretically, and demonstrated the merits of the guidance process experimentally, achieving significant improvements.

The best performing Binary Neural Networks (BNNs) are usually attained using Adam optimization and its multi-step training variants. However, to the best of our knowledge, few studies explore the fundamental reasons why Adam is superior to other optimizers like SGD for BNN optimization or provide analytical explanations that support specific training strategies. To address this, in this paper we first investigate the trajectories of gradients and weights in BNNs during the training process. We show the regularization effect of second-order momentum in Adam is crucial to revitalize the weights that are dead due to the activation saturation in BNNs. We find that Adam, through its adaptive learning rate strategy, is better equipped to handle the rugged loss surface of BNNs and reaches a better optimum with higher generalization ability. Furthermore, we inspect the intriguing role of the real-valued weights in binary networks, and reveal the effect of weight decay on the stability and sluggishness of BNN optimization. Through extensive experiments and analysis, we derive a simple training scheme, building on existing Adam-based optimization, which achieves 70.5% top-1 accuracy on the ImageNet dataset using the same architecture as the state-of-the-art ReActNet while achieving 1.1% higher accuracy. Code and models are available at https://github.com/liuzechun/AdamBNN.