mtybilly/Instruct2DS huggingface dataset:
Learning Models for Actionable Recourse
Authors: Alexis Ross, Himabindu Lakkaraju, Osbert Bastani
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: As machine learning models are increasingly deployed in high-stakes domains such as legal and financial decision-making, there has been growing interest in post-hoc methods for generating counterfactual explanations. Such explanations provide individuals adversely impacted by predicted outcomes (e.g., an applicant denied a loan) with recourse---i.e., a description of how they can change their features to obtain a positive outcome. We propose a novel algorithm that leverages adversarial training and PAC confidence sets to learn models that theoretically guarantee recourse to affected individuals with high probability without sacrificing accuracy. We demonstrate the efficacy of our approach via extensive experiments on real data.
Efficient and Accurate Gradients for Neural SDEs
Authors: Patrick Kidger, James Foster, Xuechen (Chen) Li, Terry Lyons
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Neural SDEs combine many of the best qualities of both RNNs and SDEs, and as such are a natural choice for modelling many types of temporal dynamics. They offer memory efficiency, high-capacity function approximation, and strong priors on model space. Neural SDEs may be trained as VAEs or as GANs; in either case it is necessary to backpropagate through the SDE solve. In particular this may be done by constructing a backwards-in-time SDE whose solution is the desired parameter gradients. However, this has previously suffered from severe speed and accuracy issues, due to high computational complexity, numerical errors in the SDE solve, and the cost of reconstructing Brownian motion. Here, we make several technical innovations to overcome these issues. First, we introduce the \textit{reversible Heun method}: a new SDE solver that is algebraically reversible -- which reduces numerical gradient errors to almost zero, improving several test metrics by substantial margins over state-of-the-art. Moreover it requires half as many function evaluations as comparable solvers, giving up to a $1.98\times$ speedup. Next, we introduce the \textit{Brownian interval}. This is a new and computationally efficient way of exactly sampling \textit{and reconstructing} Brownian motion; this is in contrast to previous reconstruction techniques that are both approximate and relatively slow. This gives up to a $10.6\times$ speed improvement over previous techniques. After that, when specifically training Neural SDEs as GANs (Kidger et al. 2021), we demonstrate how SDE-GANs may be trained through careful weight clipping and choice of activation function. This reduces computational cost (giving up to a $1.87\times$ speedup), and removes the truncation errors of the double adjoint required for gradient penalty, substantially improving several test metrics. Altogether these techniques offer substantial improvements over the state-of-the-art, with respect to both training speed and with respect to classification, prediction, and MMD test metrics. We have contributed implementations of all of our techniques to the \texttt{torchsde} library to help facilitate their adoption.
EIGNN: Efficient Infinite-Depth Graph Neural Networks
Authors: Juncheng Liu, Kenji Kawaguchi, Bryan Hooi, Yiwei Wang, Xiaokui Xiao
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Graph neural networks (GNNs) are widely used for modelling graph-structured data in numerous applications. However, with their inherently finite aggregation layers, existing GNN models may not be able to effectively capture long-range dependencies in the underlying graphs. Motivated by this limitation, we propose a GNN model with infinite depth, which we call Efficient Infinite-Depth Graph Neural Networks (EIGNN), to efficiently capture very long-range dependencies. We theoretically derive a closed-form solution of EIGNN which makes training an infinite-depth GNN model tractable. We then further show that we can achieve more efficient computation for training EIGNN by using eigendecomposition. The empirical results of comprehensive experiments on synthetic and real-world datasets show that EIGNN has a better ability to capture long-range dependencies than recent baselines, and consistently achieves state-of-the-art performance. Furthermore, we show that our model is also more robust against both noise and adversarial perturbations on node features.
Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms
Authors: Alexander Camuto, George Deligiannidis, Murat A Erdogdu, Mert Gurbuzbalaban, Umut Simsekli, Lingjiong Zhu
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the dataset and the training algorithm must be taken into account in order to obtain meaningful generalization bounds, it is still theoretically not clear which properties of the data and the algorithm determine the generalization performance. In this study, we approach this problem from a dynamical systems theory perspective and represent stochastic optimization algorithms as \emph{random iterated function systems} (IFS). Well studied in the dynamical systems literature, under mild assumptions, such IFSs can be shown to be ergodic with an invariant measure that is often supported on sets with a \emph{fractal structure}. As our main contribution, we prove that the generalization error of a stochastic optimization algorithm can be bounded based on the `complexity' of the fractal structure that underlies its invariant measure. Then, by leveraging results from dynamical systems theory, we show that the generalization error can be explicitly linked to the choice of the algorithm (e.g., stochastic gradient descent -- SGD), algorithm hyperparameters (e.g., step-size, batch-size), and the geometry of the problem (e.g., Hessian of the loss). We further specialize our results to specific problems (e.g., linear/logistic regression, one hidden-layered neural networks) and algorithms (e.g., SGD and preconditioned variants), and obtain analytical estimates for our bound. For modern neural networks, we develop an efficient algorithm to compute the developed bound and support our theory with various experiments on neural networks.
An Infinite-Feature Extension for Bayesian ReLU Nets That Fixes Their Asymptotic Overconfidence
Authors: Agustinus Kristiadi, Matthias Hein, Philipp Hennig
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: A Bayesian treatment can mitigate overconfidence in ReLU nets around the training data. But far away from them, ReLU Bayesian neural networks (BNNs) can still underestimate uncertainty and thus be asymptotically overconfident. This issue arises since the output variance of a BNN with finitely many features is quadratic in the distance from the data region. Meanwhile, Bayesian linear models with ReLU features converge, in the infinite-width limit, to a particular Gaussian process (GP) with a variance that grows cubically so that no asymptotic overconfidence can occur. While this may seem of mostly theoretical interest, in this work, we show that it can be used in practice to the benefit of BNNs. We extend finite ReLU BNNs with infinite ReLU features via the GP and show that the resulting model is asymptotically maximally uncertain far away from the data while the BNNs' predictive power is unaffected near the data. Although the resulting model approximates a full GP posterior, thanks to its structure, it can be applied post-hoc to any pre-trained ReLU BNN at a low cost.
Bandit Phase Retrieval
Authors: Tor Lattimore, Botao Hao
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We study a bandit version of phase retrieval where the learner chooses actions $(A_t)_{t=1}^n$ in the $d$-dimensional unit ball and the expected reward is $\langle A_t, \theta_\star \rangle^2$ with $\theta_\star \in \mathbb R^d$ an unknown parameter vector. We prove an upper bound on the minimax cumulative regret in this problem of $\smash{\tilde \Theta(d \sqrt{n})}$, which matches known lower bounds up to logarithmic factors and improves on the best known upper bound by a factor of $\smash{\sqrt{d}}$. We also show that the minimax simple regret is $\smash{\tilde \Theta(d / \sqrt{n})}$ and that this is only achievable by an adaptive algorithm. Our analysis shows that an apparently convincing heuristic for guessing lower bounds can be misleading and that uniform bounds on the information ratio for information-directed sampling (Russo and Van Roy, 2014) are not sufficient for optimal regret.
Lower Bounds on Metropolized Sampling Methods for Well-Conditioned Distributions
Authors: Yin Tat Lee, Ruoqi Shen, Kevin Tian
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We give lower bounds on the performance of two of the most popular sampling methods in practice, the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator, when applied to well-conditioned distributions. Our main result is a nearly-tight lower bound of $\widetilde{\Omega}(\kappa d)$ on the mixing time of MALA from an exponentially warm start, matching a line of algorithmic results \cite{DwivediCW018, ChenDWY19, LeeST20a} up to logarithmic factors and answering an open question of \cite{ChewiLACGR20}. We also show that a polynomial dependence on dimension is necessary for the relaxation time of HMC under any number of leapfrog steps, and bound the gains achievable by changing the step count. Our HMC analysis draws upon a novel connection between leapfrog integration and Chebyshev polynomials, which may be of independent interest.
Taming Communication and Sample Complexities in Decentralized Policy Evaluation for Cooperative Multi-Agent Reinforcement Learning
Authors: Xin Zhang, Zhuqing Liu, Jia Liu, Zhengyuan Zhu, Songtao Lu
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Cooperative multi-agent reinforcement learning (MARL) has received increasing attention in recent years and has found many scientific and engineering applications. However, a key challenge arising from many cooperative MARL algorithm designs (e.g., the actor-critic framework) is the policy evaluation problem, which can only be conducted in a {\em decentralized} fashion. In this paper, we focus on decentralized MARL policy evaluation with nonlinear function approximation, which is often seen in deep MARL. We first show that the empirical decentralized MARL policy evaluation problem can be reformulated as a decentralized nonconvex-strongly-concave minimax saddle point problem. We then develop a decentralized gradient-based descent ascent algorithm called GT-GDA that enjoys a convergence rate of $\mathcal{O}(1/T)$. To further reduce the sample complexity, we propose two decentralized stochastic optimization algorithms called GT-SRVR and GT-SRVRI, which enhance GT-GDA by variance reduction techniques. We show that all algorithms all enjoy an $\mathcal{O}(1/T)$ convergence rate to a stationary point of the reformulated minimax problem. Moreover, the fast convergence rates of GT-SRVR and GT-SRVRI imply $\mathcal{O}(\epsilon^{-2})$ communication complexity and $\mathcal{O}(m\sqrt{n}\epsilon^{-2})$ sample complexity, where $m$ is the number of agents and $n$ is the length of trajectories. To our knowledge, this paper is the first work that achieves both $\mathcal{O}(\epsilon^{-2})$ sample complexity and $\mathcal{O}(\epsilon^{-2})$ communication complexity in decentralized policy evaluation for cooperative MARL. Our extensive experiments also corroborate the theoretical performance of our proposed decentralized policy evaluation algorithms.
Federated Graph Classification over Non-IID Graphs
Authors: Han Xie, Jing Ma, Li Xiong, Carl Yang
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Federated learning has emerged as an important paradigm for training machine learning models in different domains. For graph-level tasks such as graph classification, graphs can also be regarded as a special type of data samples, which can be collected and stored in separate local systems. Similar to other domains, multiple local systems, each holding a small set of graphs, may benefit from collaboratively training a powerful graph mining model, such as the popular graph neural networks (GNNs). To provide more motivation towards such endeavors, we analyze real-world graphs from different domains to confirm that they indeed share certain graph properties that are statistically significant compared with random graphs. However, we also find that different sets of graphs, even from the same domain or same dataset, are non-IID regarding both graph structures and node features. To handle this, we propose a graph clustered federated learning (GCFL) framework that dynamically finds clusters of local systems based on the gradients of GNNs, and theoretically justify that such clusters can reduce the structure and feature heterogeneity among graphs owned by the local systems. Moreover, we observe the gradients of GNNs to be rather fluctuating in GCFL which impedes high-quality clustering, and design a gradient sequence-based clustering mechanism based on dynamic time warping (GCFL+). Extensive experimental results and in-depth analysis demonstrate the effectiveness of our proposed frameworks.
SubTab: Subsetting Features of Tabular Data for Self-Supervised Representation Learning
Authors: Talip Ucar, Ehsan Hajiramezanali, Lindsay Edwards
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Self-supervised learning has been shown to be very effective in learning useful representations, and yet much of the success is achieved in data types such as images, audio, and text. The success is mainly enabled by taking advantage of spatial, temporal, or semantic structure in the data through augmentation. However, such structure may not exist in tabular datasets commonly used in fields such as healthcare, making it difficult to design an effective augmentation method, and hindering a similar progress in tabular data setting. In this paper, we introduce a new framework, Subsetting features of Tabular data (SubTab), that turns the task of learning from tabular data into a multi-view representation learning problem by dividing the input features to multiple subsets. We argue that reconstructing the data from the subset of its features rather than its corrupted version in an autoencoder setting can better capture its underlying latent representation. In this framework, the joint representation can be expressed as the aggregate of latent variables of the subsets at test time, which we refer to as collaborative inference. Our experiments show that the SubTab achieves the state of the art (SOTA) performance of 98.31% on MNIST in tabular setting, on par with CNN-based SOTA models, and surpasses existing baselines on three other real-world datasets by a significant margin.
Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance
Authors: Hongjian Wang, Mert Gurbuzbalaban, Lingjiong Zhu, Umut Simsekli, Murat A Erdogdu
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging variance, which hinders the use of conventional convergence analysis techniques that rely on the existence of the second-order moments. In this paper, we provide convergence guarantees for SGD under a state-dependent and heavy-tailed noise with a potentially infinite variance, for a class of strongly convex objectives. In the case where the $p$-th moment of the noise exists for some $p\in [1,2)$, we first identify a condition on the Hessian, coined `$p$-positive (semi-)definiteness', that leads to an interesting interpolation between the positive semi-definite cone ($p=2$) and the cone of diagonally dominant matrices with non-negative diagonal entries ($p=1$). Under this condition, we provide a convergence rate for the distance to the global optimum in $L^p$. Furthermore, we provide a generalized central limit theorem, which shows that the properly scaled Polyak-Ruppert averaging converges weakly to a multivariate $\alpha$-stable random vector.Our results indicate that even under heavy-tailed noise with infinite variance, SGD can converge to the global optimum without necessitating any modification neither to the loss function nor to the algorithm itself, as typically required in robust statistics.We demonstrate the implications of our resultsover misspecified models, in the presence of heavy-tailed data.
Conflict-Averse Gradient Descent for Multi-task learning
Authors: Bo Liu, Xingchao Liu, Xiaojie Jin, Peter Stone, Qiang Liu
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: The goal of multi-task learning is to enable more efficient learning than single task learning by sharing model structures for a diverse set of tasks. A standard multi-task learning objective is to minimize the average loss across all tasks. While straightforward, using this objective often results in much worse final performance for each task than learning them independently. A major challenge in optimizing a multi-task model is the conflicting gradients, where gradients of different task objectives are not well aligned so that following the average gradient direction can be detrimental to specific tasks' performance. Previous work has proposed several heuristics to manipulate the task gradients for mitigating this problem. But most of them lack convergence guarantee and/or could converge to any Pareto-stationary point.In this paper, we introduce Conflict-Averse Gradient descent (CAGrad) which minimizes the average loss function, while leveraging the worst local improvement of individual tasks to regularize the algorithm trajectory. CAGrad balances the objectives automatically and still provably converges to a minimum over the average loss. It includes the regular gradient descent (GD) and the multiple gradient descent algorithm (MGDA) in the multi-objective optimization (MOO) literature as special cases. On a series of challenging multi-task supervised learning and reinforcement learning tasks, CAGrad achieves improved performance over prior state-of-the-art multi-objective gradient manipulation methods.
Amortized Synthesis of Constrained Configurations Using a Differentiable Surrogate
Authors: Xingyuan Sun, Tianju Xue, Szymon Rusinkiewicz, Ryan P. Adams
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: In design, fabrication, and control problems, we are often faced with the task of synthesis, in which we must generate an object or configuration that satisfies a set of constraints while maximizing one or more objective functions. The synthesis problem is typically characterized by a physical process in which many different realizations may achieve the goal. This many-to-one map presents challenges to the supervised learning of feed-forward synthesis, as the set of viable designs may have a complex structure. In addition, the non-differentiable nature of many physical simulations prevents efficient direct optimization. We address both of these problems with a two-stage neural network architecture that we may consider to be an autoencoder. We first learn the decoder: a differentiable surrogate that approximates the many-to-one physical realization process. We then learn the encoder, which maps from goal to design, while using the fixed decoder to evaluate the quality of the realization. We evaluate the approach on two case studies: extruder path planning in additive manufacturing and constrained soft robot inverse kinematics. We compare our approach to direct optimization of the design using the learned surrogate, and to supervised learning of the synthesis problem. We find that our approach produces higher quality solutions than supervised learning, while being competitive in quality with direct optimization, at a greatly reduced computational cost.
Efficient First-Order Contextual Bandits: Prediction, Allocation, and Triangular Discrimination
Authors: Dylan J Foster, Akshay Krishnamurthy
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: A recurring theme in statistical learning, online learning, and beyond is that faster convergence rates are possible for problems with low noise, often quantified by the performance of the best hypothesis; such results are known as first-order or small-loss guarantees. While first-order guarantees are relatively well understood in statistical and online learning, adapting to low noise in contextual bandits (and more broadly, decision making) presents major algorithmic challenges. In a COLT 2017 open problem, Agarwal, Krishnamurthy, Langford, Luo, and Schapire asked whether first-order guarantees are even possible for contextual bandits and---if so---whether they can be attained by efficient algorithms. We give a resolution to this question by providing an optimal and efficient reduction from contextual bandits to online regression with the logarithmic (or, cross-entropy) loss. Our algorithm is simple and practical, readily accommodates rich function classes, and requires no distributional assumptions beyond realizability. In a large-scale empirical evaluation, we find that our approach typically outperforms  comparable non-first-order methods.On the technical side, we show that the logarithmic loss and an information-theoretic quantity called the triangular discrimination play a fundamental role in obtaining first-order guarantees, and we combine this observation with new refinements to the regression oracle reduction framework of Foster and Rakhlin (2020). The use of triangular discrimination yields novel results even for the classical statistical learning model, and we anticipate that it will find broader use.
Distributed Estimation with Multiple Samples per User: Sharp Rates and Phase Transition
Authors: Jayadev Acharya, Clement Canonne, Yuhan Liu, Ziteng Sun, Himanshu Tyagi
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We obtain tight minimax rates for the problem of distributed estimation of discrete distributions under communication constraints, where $n$ users observing $m $ samples each can broadcast only $\ell$  bits. Our main result is a tight characterization (up to logarithmic factors) of the error rate as a function of $m$, $\ell$, the domain size, and the number of users under most regimes of interest. While previous work focused on the setting where each user only holds one sample, we show that as $m$ grows the $\ell_1$ error rate gets reduced by a factor of $\sqrt{m}$ for small $m$. However, for large $m$ we observe an interesting phase transition: the dependence of the error rate on the communication constraint $\ell$ changes from $1/\sqrt{2^{\ell}}$ to $1/\sqrt{\ell}$.
Revisiting Deep Learning Models for Tabular Data
Authors: Yury Gorishniy, Ivan Rubachev, Valentin Khrulkov, Artem Babenko
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: The existing literature on deep learning for tabular data proposes a wide range of novel architectures and reports competitive results on various datasets. However, the proposed models are usually not properly compared to each other and existing works often use different benchmarks and experiment protocols. As a result, it is unclear for both researchers and practitioners what models perform best. Additionally, the field still lacks effective baselines, that is, the easy-to-use models that provide competitive performance across different problems.In this work, we perform an overview of the main families of DL architectures for tabular data and raise the bar of baselines in tabular DL by identifying two simple and powerful deep architectures. The first one is a ResNet-like architecture which turns out to be a strong baseline that is often missing in prior works. The second model is our simple adaptation of the Transformer architecture for tabular data, which outperforms other solutions on most tasks. Both models are compared to many existing architectures on a diverse set of tasks under the same training and tuning protocols. We also compare the best DL models with Gradient Boosted Decision Trees and conclude that there is still no universally superior solution. The source code is available at https://github.com/yandex-research/rtdl.
Backdoor Attack with Imperceptible Input and Latent Modification
Authors: Khoa Doan, Yingjie Lao, Ping Li
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Recent studies have shown that deep neural networks (DNN) are vulnerable to various adversarial attacks. In particular, an adversary can inject a stealthy backdoor into a model such that the compromised model will behave normally without the presence of the trigger. Techniques for generating backdoor images that are visually imperceptible from clean images have also been developed recently, which further enhance the stealthiness of the backdoor attacks from the input space. Along with the development of attacks, defense against backdoor attacks is also evolving. Many existing countermeasures found that backdoor tends to leave tangible footprints in the latent or feature space, which can be utilized to mitigate backdoor attacks.In this paper, we extend the concept of imperceptible backdoor from the input space to the latent representation, which significantly improves the effectiveness against the existing defense mechanisms, especially those relying on the distinguishability between clean inputs and backdoor inputs in latent space. In the proposed framework, the trigger function will learn to manipulate the input by injecting imperceptible input noise while matching the latent representations of the clean and manipulated inputs via a Wasserstein-based regularization of the corresponding empirical distributions. We formulate such an objective as a non-convex and constrained optimization problem and solve the problem with an efficient stochastic alternating optimization procedure. We name the proposed backdoor attack as Wasserstein Backdoor (WB), which achieves a high attack success rate while being stealthy from both the input and latent spaces, as tested in several benchmark datasets, including MNIST, CIFAR10, GTSRB, and TinyImagenet.
SOPE: Spectrum of Off-Policy Estimators
Authors: Christina Yuan, Yash Chandak, Stephen Giguere, Philip S. Thomas, Scott Niekum
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Many sequential decision making problems are high-stakes and require off-policy evaluation (OPE) of a new policy using historical data collected using some other policy. One of the most common OPE techniques that provides unbiased estimates is trajectory based importance sampling (IS). However, due to the high variance of trajectory IS estimates, importance sampling methods based on state-action visitation distributions (SIS) have recently been adopted. Unfortunately, while SIS often provides lower variance estimates for long horizons, estimating the state-action distribution ratios can be challenging and lead to biased estimates. In this paper, we present a new perspective on this bias-variance trade-off and show the existence of a spectrum of estimators whose endpoints are SIS and IS. Additionally, we also establish a spectrum for doubly-robust and weighted version of these estimators. We provide empirical evidence that estimators in this spectrum can be used to trade-off between the bias and variance of IS and SIS and can achieve lower mean-squared error than both IS and SIS.
Label-Imbalanced and Group-Sensitive Classification under Overparameterization
Authors: Ganesh Ramachandra Kini, Orestis Paraskevas, Samet Oymak, Christos Thrampoulidis
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: The goal in label-imbalanced and group-sensitive classification is to optimize relevant metrics such as balanced error and equal opportunity. Classical methods, such as weighted cross-entropy, fail when training deep nets to the terminal phase of training (TPT), that is training beyond zero training error. This observation has motivated recent flurry of activity in developing heuristic alternatives following the intuitive mechanism of promoting larger margin for minorities. In contrast to previous heuristics, we follow a principled analysis explaining how different loss adjustments affect margins. First, we prove that for all linear classifiers trained in TPT, it is necessary to introduce multiplicative, rather than additive, logit adjustments so that the interclass margins change appropriately. To show this, we discover a connection of the multiplicative CE modification to the cost-sensitive support-vector machines. Perhaps counterintuitively, we also find that, at the start of training, the same multiplicative weights can actually harm the minority classes. Thus, while additive adjustments are ineffective in the TPT, we show that they can speed up convergence by countering the initial negative effect of the multiplicative weights. Motivated by these findings, we formulate the vector-scaling (VS) loss, that captures existing techniques as special cases. Moreover, we introduce a natural extension of the VS-loss to group-sensitive classification, thus treating the two common types of imbalances (label/group) in a unifying way. Importantly, our experiments on state-of-the-art datasets are fully consistent with our theoretical insights and confirm the superior performance of our algorithms. Finally, for imbalanced Gaussian-mixtures data, we perform a generalization analysis, revealing tradeoffs between balanced / standard error and equal opportunity.
Neural Program Generation Modulo Static Analysis
Authors: Rohan Mukherjee, Yeming Wen, Dipak Chaudhari, Thomas Reps, Swarat Chaudhuri, Christopher Jermaine
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: State-of-the-art neural models of source code tend to be evaluated on the generation of individual expressions and lines of code, and commonly fail on long-horizon tasks such as the generation of entire method bodies. We propose to address this deficiency using weak supervision from a static program analyzer. Our neurosymbolic method allows a deep generative model to symbolically compute, using calls to a static analysis tool, long-distance semantic relationships in the code that it has already generated. During training, the model observes these relationships and learns to generate programs conditioned on them. We apply our approach to the problem of generating entire Java methods given the remainder of the class that contains the method. Our experiments show that the approach substantially outperforms a state-of-the-art transformer and a model that explicitly tries to learn program semantics on this task, both in terms of producing programs free of basic semantic errors and in terms of syntactically matching the ground truth.
Unfolding Taylor's Approximations for Image Restoration
Authors: man zhou, Xueyang Fu, Zeyu Xiao, Gang Yang, Aiping Liu, Zhiwei Xiong
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Deep learning provides a new avenue for image restoration, which demands a delicate balance between fine-grained details and high-level contextualized information during recovering the latent clear image. In practice, however, existing methods empirically construct encapsulated end-to-end mapping networks without deepening into the rationality, and neglect the intrinsic prior knowledge of restoration task. To solve the above problems, inspired by Taylor’s Approximations, we unfold Taylor’s Formula to construct a novel framework for image restoration. We find the main part and the derivative part of Taylor’s Approximations take the same effect as the two competing goals of high-level contextualized information and spatial details of image restoration respectively. Specifically, our framework consists of two steps, which are correspondingly responsible for the mapping and derivative functions. The former first learns the high-level contextualized information and the later combines it with the degraded input to progressively recover local high-order spatial details. Our proposed framework is orthogonal to existing methods and thus can be easily integrated with them for further improvement, and extensive experiments demonstrate the effectiveness and scalability of our proposed framework.
Metropolis-Hastings Data Augmentation for Graph Neural Networks
Authors: Hyeonjin Park, Seunghun Lee, Sihyeon Kim, Jinyoung Park, Jisu Jeong, Kyung-Min Kim, Jung-Woo Ha, Hyunwoo J Kim
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Graph Neural Networks (GNNs) often suffer from weak-generalization due to sparsely labeled data despite their promising results on various graph-based tasks. Data augmentation is a prevalent remedy to improve the generalization ability of models in many domains. However, due to the non-Euclidean nature of data space and the dependencies between samples, designing effective augmentation on graphs is challenging. In this paper, we propose a novel framework Metropolis-Hastings Data Augmentation (MH-Aug) that draws augmented graphs from an explicit target distribution for semi-supervised learning. MH-Aug produces a sequence of augmented graphs from the target distribution enables flexible control of the strength and diversity of augmentation. Since the direct sampling from the complex target distribution is challenging, we adopt the Metropolis-Hastings algorithm to obtain the augmented samples. We also propose a simple and effective semi-supervised learning strategy with generated samples from MH-Aug. Our extensive experiments demonstrate that MH-Aug can generate a sequence of samples according to the target distribution to significantly improve the performance of GNNs.
Strategic Behavior is Bliss: Iterative Voting Improves Social Welfare
Authors: Joshua Kavner, Lirong Xia
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Recent work in iterative voting has defined the additive dynamic price of anarchy (ADPoA) as the difference in social welfare between the truthful and worst-case equilibrium profiles resulting from repeated strategic manipulations. While iterative plurality has been shown to only return alternatives with at most one less initial votes than the truthful winner, it is less understood how agents' welfare changes in equilibrium. To this end, we differentiate agents' utility from their manipulation mechanism and determine iterative plurality's ADPoA in the worst- and average-cases. We first prove that the worst-case ADPoA is linear in the number of agents. To overcome this negative result, we study the average-case ADPoA and prove that equilibrium winners have a constant order welfare advantage over the truthful winner in expectation. Our positive results illustrate the prospect for social welfare to increase due to strategic manipulation.
Agnostic Reinforcement Learning with Low-Rank MDPs and Rich Observations
Authors: Ayush Sekhari, Christoph Dann, Mehryar Mohri, Yishay Mansour, Karthik Sridharan
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: There have been many recent advances on provably efficient Reinforcement Learning (RL) in problems with rich observation spaces. However, all these works share a strong realizability assumption about the optimal value function of the true MDP. Such realizability assumptions are often too strong to hold in practice. In this work, we consider the more realistic setting of agnostic RL with rich observation spaces and a fixed class of policies $\Pi$ that may not contain any near-optimal policy. We provide an algorithm for this setting whose error is bounded in terms of the rank $d$ of the underlying MDP.  Specifically, our algorithm enjoys a sample complexity bound of $\widetilde{O}\left((H^{4d} K^{3d} \log |\Pi|)/\epsilon^2\right)$ where $H$ is the length of episodes, $K$ is the number of actions and $\epsilon>0$ is the desired sub-optimality.  We also provide a nearly matching lower bound for this agnostic setting that shows that the exponential dependence on rank is unavoidable, without further assumptions.
Functional Regularization for Reinforcement Learning via Learned Fourier Features
Authors: Alexander Li, Deepak Pathak
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We propose a simple architecture for deep reinforcement learning by embedding inputs into a learned Fourier basis and show that it improves the sample efficiency of both state-based and image-based RL. We perform infinite-width analysis of our architecture using the Neural Tangent Kernel and theoretically show that tuning the initial variance of the Fourier basis is equivalent to functional regularization of the learned deep network. That is, these learned Fourier features allow for adjusting the degree to which networks underfit or overfit different frequencies in the training data, and hence provide a controlled mechanism to improve the stability and performance of RL optimization. Empirically, this allows us to prioritize learning low-frequency functions and speed up learning by reducing networks' susceptibility to noise in the optimization process, such as during Bellman updates. Experiments on standard state-based and image-based RL benchmarks show clear benefits of our architecture over the baselines.
Adaptive First-Order Methods Revisited: Convex Minimization without Lipschitz Requirements
Authors: Kimon Antonakopoulos, Panayotis Mertikopoulos
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We propose a new family of adaptive first-order methods for a class of convex minimization problems that may fail to be Lipschitz continuous or smooth in the standard sense. Specifically, motivated by a recent flurry of activity on non-Lipschitz (NoLips) optimization, we consider problems that are continuous or smooth relative to a reference Bregman function – as opposed to a global, ambient norm (Euclidean or otherwise). These conditions encompass a wide range ofproblems with singular objective, such as Fisher markets, Poisson tomography, D-design, and the like. In this setting, the application of existing order-optimal adaptive methods – like UnixGrad or AcceleGrad – is not possible, especially in the presence of randomness and uncertainty. The proposed method, adaptive mirror descent (AdaMir), aims to close this gap by concurrently achieving min-max optimal rates in problems that are relatively continuous or smooth, including stochastic ones.
Adapting to function difficulty and growth conditions in private optimization
Authors: Hilal Asi, Daniel Levy, John C. Duchi
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We develop algorithms for private stochastic convex optimization that adapt to the hardness of the specific function we wish to optimize. While previous work provide worst-case bounds for arbitrary convex functions, it is often the case that the function at hand belongs to a smaller class that enjoys faster rates. Concretely, we show that for functions exhibiting $\kappa$-growth around the optimum, i.e., $f(x) \ge f(x^\star) + \lambda \kappa^{-1} \|x-x^\star\|_2^\kappa$ for $\kappa > 1$, our algorithms improve upon the standard ${\sqrt{d}}/{n\varepsilon}$ privacy rate to the faster $({\sqrt{d}}/{n\varepsilon})^{\tfrac{\kappa}{\kappa - 1}}$. Crucially, they achieve these rates without knowledge of the growth constant $\kappa$ of the function. Our algorithms build upon the inverse sensitivity mechanism, which adapts to instance difficulty [2], and recent localization techniques in private optimization [25]. We complement our algorithms with matching lower bounds for these function classes and demonstrate that our adaptive algorithm is simultaneously (minimax) optimal over all $\kappa \ge 1+c$ whenever $c = \Theta(1)$.
Support Recovery of Sparse Signals from a Mixture of Linear Measurements
Authors: Soumyabrata Pal, Arya Mazumdar, Venkata Gandikota
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Recovery of support of a sparse vector from simple measurements is a widely studied problem, considered under the frameworks of compressed sensing, 1-bit compressed sensing, and more general single index models. We consider generalizations of this problem: mixtures of linear regressions, and mixtures of linear classifiers, where the goal is to recover supports of multiple sparse vectors using only a small number of possibly noisy linear, and 1-bit measurements respectively. The key challenge is that the measurements from different vectors are randomly mixed. Both of these problems have also received attention recently. In mixtures of linear classifiers, an observation corresponds to the side of the queried hyperplane a random unknown vector lies in; whereas in mixtures of linear regressions we observe the projection of a random unknown vector on the queried hyperplane. The primary step in recovering the unknown vectors from the mixture is to first identify the support of all the individual component vectors. In this work, we study the number of measurements sufficient for recovering the supports of all the component vectors in a mixture in both these models. We provide algorithms that use a number of measurements polynomial in $k, \log n$ and quasi-polynomial in $\ell$, to recover the support of all the $\ell$ unknown vectors in the mixture with high probability when each individual component is a $k$-sparse $n$-dimensional vector.
Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity
Authors: Nicolas Loizou, Hugo Berard, Gauthier Gidel, Ioannis Mitliagkas, Simon Lacoste-Julien
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: Two of the most prominent algorithms for solving unconstrained smooth games are the classical stochastic gradient descent-ascent (SGDA) and the recently introduced stochastic consensus optimization (SCO) [Mescheder et al., 2017]. SGDA is known to converge to a stationary point for specific classes of games, but current convergence analyses require a bounded variance assumption. SCO is used successfully for solving large-scale adversarial problems, but its convergence guarantees are limited to its deterministic variant. In this work, we introduce the expected co-coercivity condition, explain its benefits, and provide the first last-iterate convergence guarantees of SGDA and SCO under this condition for solving a class of stochastic variational inequality problems that are potentially non-monotone. We prove linear convergence of both methods to a neighborhood of the solution when they use constant step-size, and we propose insightful stepsize-switching rules to guarantee convergence to the exact solution. In addition, our convergence guarantees hold under the arbitrary sampling paradigm, and as such, we give insights into the complexity of minibatching.
Tighter Expected Generalization Error Bounds via Wasserstein Distance
Authors: Borja Rodríguez Gálvez, German Bassi, Ragnar Thobaben, Mikael Skoglund
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogous in the randomized subsample setting from Steinke and Zakynthinou [1]. Moreover, when the loss function is bounded and the geometry of the space is ignored by the choice of the metric in the Wasserstein distance, these bounds recover from below (and thus, are tighter than) current bounds based on the relative entropy. In particular, they generate new, non-vacuous bounds based on the relative entropy. Therefore, these results can be seen as a bridge between works that account for the geometry of the hypothesis space and those based on the relative entropy, which is agnostic to such geometry. Furthermore, it is shown how to produce various new bounds based on different information measures (e.g., the lautum information or several $f$-divergences) based on these bounds and how to derive similar bounds with respect to the backward channel using the presented proof techniques.
Unifying Width-Reduced Methods for Quasi-Self-Concordant Optimization
Authors: Deeksha Adil, Brian Bullins, Sushant Sachdeva
Published in: Advances in Neural Information Processing Systems 34  (NeurIPS 2021) (Main Conference Track), 2021

Abstract: We provide several algorithms for constrained optimization of a large class of convex problems, including softmax, $\ell_p$ regression, and logistic regression. Central to our approach is the notion of width reduction, a technique which has proven immensely useful in the context of maximum flow [Christiano et al., STOC'11] and, more recently, $\ell_p$ regression [Adil et al., SODA'19], in terms of improving the iteration complexity from $O(m^{1/2})$ to $\tilde{O}(m^{1/3})$, where $m$ is the number of rows of the design matrix, and where each iteration amounts to a linear system solve. However, a considerable drawback is that these methods require both problem-specific potentials and individually tailored analyses.As our main contribution, we initiate a new direction of study by presenting the first \emph{unified} approach to achieving $m^{1/3}$-type rates. Notably, our method goes beyond these previously considered problems to more broadly capture \emph{quasi-self-concordant} losses, a class which has recently generated much interest and includes the well-studied problem of logistic regression, among others. In order to do so, we develop a unified width reduction method for carefully handling these losses based on a more general set of potentials. Additionally, we directly achieve $m^{1/3}$-type rates in the constrained setting without the need for any explicit acceleration schemes, thus naturally complementing recent work based on a ball-oracle approach [Carmon et al., NeurIPS'20].