mtybilly/Instruct2DS huggingface dataset:
Moniqua: Modulo Quantized Communication in Decentralized SGD
Authors: Yucheng Lu, Christopher De Sa
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Running Stochastic Gradient Descent (SGD) in a decentralized fashion has shown promising results. In this paper we propose Moniqua, a technique that allows decentralized SGD to use quantized communication. We prove in theory that Moniqua communicates a provably bounded number of bits per iteration, while converging at the same asymptotic rate as the original algorithm does with full-precision communication. Moniqua improves upon prior works in that it (1) requires zero additional memory, (2) works with 1-bit quantization, and (3) is applicable to a variety of decentralized algorithms. We demonstrate empirically that Moniqua converges faster with respect to wall clock time than other quantized decentralized algorithms. We also show that Moniqua is robust to very low bit-budgets, allowing $1$-bit-per-parameter communication without compromising validation accuracy when training ResNet20 and ResNet110 on CIFAR10.
A Mean Field Analysis Of Deep ResNet And Beyond: Towards Provably Optimization Via Overparameterization From Depth
Authors: Yiping Lu, Chao Ma, Yulong Lu, Jianfeng Lu, Lexing Ying
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for training deep neural networks, this work presents a mean-field analysis of deep residual networks, based on a line of works which interpret the continuum limit of the deep residual network as an ordinary differential equation as the the network capacity tends to infinity. Specifically, we propose a \textbfnew continuum limit of deep residual networks, which enjoys a good landscape in the sense that \textbfevery local minimizer is global. This characterization enables us to derive the first global convergence result for multilayer neural networks in the mean-field regime. Furthermore, our proof does not rely on the convexity of the loss landscape, but instead, an assumption on the global minimizer should achieve zero loss which can be achieved when the model shares a universal approximation property. Key to our result is the observation that a deep residual network resembles a shallow network ensemble i̧teveit2016residual, \emphi.e. a two-layer network. We bound the difference between the shallow network and our ResNet model via the adjoint sensitivity method, which enables us to transfer previous mean-field analysis of two-layer networks to deep networks. Furthermore, we propose several novel training schemes based on our new continuous model, among which one new training procedure introduces the operation of switching the order of the residual blocks and results in strong empirical performance on benchmark datasets.
Countering Language Drift with Seeded Iterated Learning
Authors: Yuchen Lu, Soumye Singhal, Florian Strub, Aaron Courville, Olivier Pietquin
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Pretraining on human corpus and then finetuning in a simulator has become a standard pipeline for training a goal-oriented dialogue agent. Nevertheless, as soon as the agents are finetuned to maximize task completion, they suffer from the so-called language drift phenomenon: they slowly lose syntactic and semantic properties of language as they only focus on solving the task. In this paper, we propose a generic approach to counter language drift called Seeded iterated learning (SIL). We periodically refine a pretrained student agent by imitating data sampled from a newly generated teacher agent. At each time step, the teacher is created by copying the student agent, before being finetuned to maximize task completion. SIL does not require external syntactic constraint nor semantic knowledge, making it a valuable task-agnostic finetuning protocol. We evaluate SIL in a toy-setting Lewis Game, and then scale it up to the translation game with natural language. In both settings, SIL helps counter language drift as well as it improves the task completion compared to baselines.
Does label smoothing mitigate label noise?
Authors: Michal Lukasik, Srinadh Bhojanapalli, Aditya Menon, Sanjiv Kumar
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Label smoothing is commonly used in training deep learning models, wherein one-hot training labels are mixed with uniform label vectors. Empirically, smoothing has been shown to improve both predictive performance and model calibration. In this paper, we study whether label smoothing is also effective as a means of coping with label noise. While label smoothing apparently amplifies this problem — being equivalent to injecting symmetric noise to the labels — we show how it relates to a general family of loss-correction techniques from the label noise literature. Building on this connection, we show that label smoothing is competitive with loss-correction under label noise. Further, we show that when distilling models from noisy data, label smoothing of the teacher is beneficial; this is in contrast to recent findings for noise-free problems, and sheds further light on settings where label smoothing is beneficial.
Improved Communication Cost in Distributed PageRank Computation – A Theoretical Study
Authors: Siqiang Luo
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: PageRank is a widely used approach for measuring the importance of a node in a graph. Due to the rapid growth of the graph size in the real world, the importance of computing PageRanks in a distributed environment has been increasingly recognized. However, only a few previous works can provide a provable complexity and accuracy for distributed PageRank computation. Given a constant $d\ge 1$ and a graph of $n$ nodes, the state-of-the-art approach, Radar-Push, uses $O(łogłogn+łogd)$ communication rounds to approximate the PageRanks within a relative error $Θ(\frac1łog^dn)$ under a generalized congested clique distributed computation model. However, Radar-Push entails as large as $O(łog^2d+3n)$ bits of bandwidth (e.g., the communication cost between a pair of nodes per round). In this paper, we provide a new algorithm that uses asymptotically the same communication round complexity while using only $O(dłog^3n)$ bits of bandwidth.
Progressive Graph Learning for Open-Set Domain Adaptation
Authors: Yadan Luo, Zijian Wang, Zi Huang, Mahsa Baktashmotlagh
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Domain shift is a fundamental problem in visual recognition which typically arises when the source and target data follow different distributions. The existing domain adaptation approaches which tackle this problem work in the "closed-set" setting with the assumption that the source and the target data share exactly the same classes of objects. In this paper, we tackle a more realistic problem of the "open-set" domain shift where the target data contains additional classes that were not present in the source data. More specifically, we introduce an end-to-end Progressive Graph Learning (PGL) framework where a graph neural network with episodic training is integrated to suppress underlying conditional shift and adversarial learning is adopted to close the gap between the source and target distributions. Compared to the existing open-set adaptation approaches, our approach guarantees to achieve a tighter upper bound of the target error. Extensive experiments on three standard open-set benchmarks evidence that our approach significantly outperforms the state-of-the-arts in open-set domain adaptation.
Adversarial Nonnegative Matrix Factorization
Authors: Lei Luo, Yanfu Zhang, Heng Huang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Nonnegative Matrix Factorization (NMF) has become an increasingly important research topic in machine learning. Despite all the practical success, most of existing NMF models are still vulnerable to adversarial attacks. To overcome this limitation, we propose a novel Adversarial NMF (ANMF) approach in which an adversary can exercise some control over the perturbed data generation process. Different from the traditional NMF models which focus on either the regular input or certain types of noise, our model considers potential test adversaries that are beyond the pre-defined constraints, which can cope with various noises (or perturbations). We formulate the proposed model as a bilevel optimization problem and use Alternating Direction Method of Multipliers (ADMM) to solve it with convergence analysis. Theoretically, the robustness analysis of ANMF is established under mild conditions dedicating asymptotically unbiased prediction. Extensive experiments verify that ANMF is robust to a broad categories of perturbations, and achieves state-of-the-art performances on distinct real-world benchmark datasets.
Learning Algebraic Multigrid Using Graph Neural Networks
Authors: Ilay Luz, Meirav Galun, Haggai Maron, Ronen Basri, Irad Yavneh
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of AMG algorithms is the selection of the prolongation operator—a problem-dependent sparse matrix which governs the multiscale hierarchy of the solver and is critical to its efficiency. Over many years, numerous methods have been developed for this task, and yet there is no known single right answer except in very special cases. Here we propose a framework for learning AMG prolongation operators for linear systems with sparse symmetric positive (semi-) definite matrices. We train a single graph neural network to learn a mapping from an entire class of such matrices to prolongation operators, using an efficient unsupervised loss function. Experiments on a broad class of problems demonstrate improved convergence rates compared to classical AMG, demonstrating the potential utility of neural networks for developing sparse system solvers.
Progressive Identification of True Labels for Partial-Label Learning
Authors: Jiaqi Lv, Miao Xu, Lei Feng, Gang Niu, Xin Geng, Masashi Sugiyama
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Partial-label learning (PLL) is a typical weakly supervised learning problem, where each training instance is equipped with a set of candidate labels among which only one is the true label. Most existing methods elaborately designed learning objectives as constrained optimizations that must be solved in specific manners, making their computational complexity a bottleneck for scaling up to big data. The goal of this paper is to propose a novel framework of PLL with flexibility on the model and optimization algorithm. More specifically, we propose a novel estimator of the classification risk, theoretically analyze the classifier-consistency, and establish an estimation error bound. Then we propose a progressive identification algorithm for approximately minimizing the proposed risk estimator, where the update of the model and identification of true labels are conducted in a seamless manner. The resulting algorithm is model-independent and loss-independent, and compatible with stochastic optimization. Thorough experiments demonstrate it sets the new state of the art.
Bandits with Adversarial Scaling
Authors: Thodoris Lykouris, Vahab Mirrokni, Renato Paes Leme
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We study "adversarial scaling", a multi-armed bandit model where rewards have a stochastic and an adversarial component. Our model captures display advertising where the "click-through-rate" can be decomposed to a (fixed across time) arm-quality component and a non-stochastic user-relevance component (fixed across arms). Despite the relative stochasticity of our model, we demonstrate two settings where most bandit algorithms suffer. On the positive side, we show that two algorithms, one from the action elimination and one from the mirror descent family are adaptive enough to be robust to adversarial scaling. Our results shed light on the robustness of adaptive parameter selection in stochastic bandits, which may be of independent interest.
Efficient Continuous Pareto Exploration in Multi-Task Learning
Authors: Pingchuan Ma, Tao Du, Wojciech Matusik
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Tasks in multi-task learning often correlate, conflict, or even compete with each other. As a result, a single solution that is optimal for all tasks rarely exists. Recent papers introduced the concept of Pareto optimality to this field and directly cast multi-task learning as multi-objective optimization problems, but solutions returned by existing methods are typically finite, sparse, and discrete. We present a novel, efficient method that generates locally continuous Pareto sets and Pareto fronts, which opens up the possibility of continuous analysis of Pareto optimal solutions in machine learning problems. We scale up theoretical results in multi-objective optimization to modern machine learning problems by proposing a sample-based sparse linear system, for which standard Hessian-free solvers in machine learning can be applied. We compare our method to the state-of-the-art algorithms and demonstrate its usage of analyzing local Pareto sets on various multi-task classification and regression problems. The experimental results confirm that our algorithm reveals the primary directions in local Pareto sets for trade-off balancing, finds more solutions with different trade-offs efficiently, and scales well to tasks with millions of parameters.
Convex Representation Learning for Generalized Invariance in Semi-Inner-Product Space
Authors: Yingyi Ma, Vignesh Ganapathiraman, Yaoliang Yu, Xinhua Zhang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Invariance (defined in a general sense) has been one of the most effective priors for representation learning. Direct factorization of parametric models is feasible only for a small range of invariances, while regularization approaches, despite improved generality, lead to nonconvex optimization. In this work, we develop a \emphconvex representation learning algorithm for a variety of generalized invariances that can be modeled as semi-norms. Novel Euclidean embeddings are introduced for kernel representers in a semi-inner-product space, and approximation bounds are established. This allows invariant representations to be learned efficiently and effectively as confirmed in our experiments, along with accurate predictions.
Normalized Loss Functions for Deep Learning with Noisy Labels
Authors: Xingjun Ma, Hanxun Huang, Yisen Wang, Simone Romano, Sarah Erfani, James Bailey
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Robust loss functions are essential for training accurate deep neural networks (DNNs) in the presence of noisy (incorrect) labels. It has been shown that the commonly used Cross Entropy (CE) loss is not robust to noisy labels. Whilst new loss functions have been designed, they are only partially robust. In this paper, we theoretically show by applying a simple normalization that: \emphany loss can be made robust to noisy labels. However, in practice, simply being robust is not sufficient for a loss function to train accurate DNNs. By investigating several robust loss functions, we find that they suffer from a problem of \emphunderfitting. To address this, we propose a framework to build robust loss functions called \emphActive Passive Loss (APL). APL combines two robust loss functions that mutually boost each other. Experiments on benchmark datasets demonstrate that the family of new loss functions created by our APL framework can consistently outperform state-of-the-art methods by large margins, especially under large noise rates such as 60% or 80% incorrect labels.
Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraints
Authors: Runchao Ma, Qihang Lin, Tianbao Yang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed with theoretical convergence guarantees for non-convex unconstrained problems, it remains a challenge to design provably efficient algorithms for problems with non-convex functional constraints. This paper proposes a class of subgradient methods for constrained optimization where the objective function and the constraint functions are weakly convex and nonsmooth. Our methods solve a sequence of strongly convex subproblems, where a quadratic regularization term is added to both the objective function and each constraint function. Each subproblem can be solved by various algorithms for strongly convex optimization. Under a uniform Slater’s condition, we establish the computation complexities of our methods for finding a nearly stationary point.
Understanding the Impact of Model Incoherence on Convergence of Incremental SGD with Random Reshuffle
Authors: Shaocong Ma, Yi Zhou
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Although SGD with random reshuffle has been widely-used in machine learning applications, there is a limited understanding of how model characteristics affect the convergence of the algorithm. In this work, we introduce model incoherence to characterize the diversity of model characteristics and study its impact on convergence of SGD with random reshuffle under weak strong convexity. Specifically, minimizer incoherence measures the discrepancy between the global minimizers of a sample loss and those of the total loss and affects the convergence error of SGD with random reshuffle. In particular, we show that the variable sequence generated by SGD with random reshuffle converges to a certain global minimizer of the total loss under full minimizer coherence. The other curvature incoherence measures the quality of condition numbers of the sample losses and determines the convergence rate of SGD. With model incoherence, our results show that SGD has a faster convergence rate and smaller convergence error under random reshuffle than those under random sampling, and hence provide justifications to the superior practical performance of SGD with random reshuffle.
Adversarial Neural Pruning with Latent Vulnerability Suppression
Authors: Divyam Madaan, Jinwoo Shin, Sung Ju Hwang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Despite the remarkable performance of deep neural networks on various computer vision tasks, they are known to be susceptible to adversarial perturbations, which makes it challenging to deploy them in real-world safety-critical applications. In this paper, we conjecture that the leading cause of adversarial vulnerability is the distortion in the latent feature space, and provide methods to suppress them effectively. Explicitly, we define \emphvulnerability for each latent feature and then propose a new loss for adversarial learning, \emphVulnerability Suppression (VS) loss, that aims to minimize the feature-level vulnerability during training. We further propose a Bayesian framework to prune features with high vulnerability to reduce both vulnerability and loss on adversarial samples. We validate our \emphAdversarial Neural Pruning with Vulnerability Suppression (ANP-VS) method on multiple benchmark datasets, on which it not only obtains state-of-the-art adversarial robustness but also improves the performance on clean examples, using only a fraction of the parameters used by the full network. Further qualitative analysis suggests that the improvements come from the suppression of feature-level vulnerability.
Individual Fairness for k-Clustering
Authors: Sepideh Mahabadi, Ali Vakilian
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We give a local search based algorithm for $k$-median and $k$-means (and more generally for any $k$-clustering with $\ell_p$ norm cost function) from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$ of size $n$, let $r(x)$ be the minimum radius such that the ball of radius $r(x)$ centered at $x$ has at least $n/k$ points from $P$. Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $xın P$ expects to have a center within radius $r(x)$. In this work, we show how to get an approximately optimal such fair $k$-clustering: The $k$-median ($k$-means) cost of our solution is within a constant factor of the cost of an optimal fair $k$-clustering, and our solution approximately satisfies the fairness condition (also within a constant factor).
Multi-Task Learning with User Preferences: Gradient Descent with Controlled Ascent in Pareto Optimization
Authors: Debabrata Mahapatra, Vaibhav Rajan
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Multi-Task Learning (MTL) is a well established paradigm for jointly learning models for multiple correlated tasks. Often the tasks conflict, requiring trade-offs between them during optimization. In such cases, multi-objective optimization based MTL methods can be used to find one or more Pareto optimal solutions. A common requirement in MTL applications, that cannot be addressed by these methods, is to find a solution satisfying userspecified preferences with respect to task-specific losses. We advance the state-of-the-art by developing the first gradient-based multi-objective MTL algorithm to solve this problem. Our unique approach combines multiple gradient descent with carefully controlled ascent to traverse the Pareto front in a principled manner, which also makes it robust to initialization. The scalability of our algorithm enables its use in large-scale deep networks for MTL. Assuming only differentiability of the task-specific loss functions, we provide theoretical guarantees for convergence. Our experiments show that our algorithm outperforms the best competing methods on benchmark datasets.
How recurrent networks implement contextual processing in sentiment analysis
Authors: Niru Maheswaranathan, David Sussillo
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Neural networks have a remarkable capacity for contextual processing—using recent or nearby inputs to modify processing of current input. For example, in natural language, contextual processing is necessary to correctly interpret negation (e.g. phrases such as "not bad"). However, our ability to understand how networks process context is limited. Here, we propose general methods for reverse engineering recurrent neural networks (RNNs) to identify and elucidate contextual processing. We apply these methods to understand RNNs trained on sentiment classification. This analysis reveals inputs that induce contextual effects, quantifies the strength and timescale of these effects, and identifies sets of these inputs with similar properties. Additionally, we analyze contextual effects related to differential processing of the beginning and end of documents. Using the insights learned from the RNNs we improve baseline Bag-of-Words models with simple extensions that incorporate contextual modification, recovering greater than 90% of the RNN’s performance increase over the baseline. This work yields a new understanding of how RNNs process contextual information, and provides tools that should provide similar insight more broadly.
Anderson Acceleration of Proximal Gradient Methods
Authors: Vien Mai, Mikael Johansson
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Anderson acceleration is a well-established and simple technique for speeding up fixed-point computations with countless applications. This work introduces novel methods for adapting Anderson acceleration to proximal gradient algorithms. Under some technical conditions, we extend existing local convergence results of Anderson acceleration for smooth fixed-point mappings to the proposed non-smooth setting. We also prove analytically that it is in general, impossible to guarantee global convergence of native Anderson acceleration. We therefore propose a simple scheme for stabilization that combines the global worst-case guarantees of proximal gradient methods with the local adaptation and practical speed-up of Anderson acceleration. Finally, we provide the first applications of Anderson acceleration to non-Euclidean geometry.
Convergence of a Stochastic Gradient Method with Momentum for Non-Smooth Non-Convex Optimization
Authors: Vien Mai, Mikael Johansson
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Stochastic gradient methods with momentum are widely used in applications and at the core of optimization subroutines in many popular machine learning libraries. However, their sample complexities have not been obtained for problems beyond those that are convex or smooth. This paper establishes the convergence rate of a stochastic subgradient method with a momentum term of Polyak type for a broad class of non-smooth, non-convex, and constrained optimization problems. Our key innovation is the construction of a special Lyapunov function for which the proven complexity can be achieved without any tuning of the momentum parameter. For smooth problems, we extend the known complexity bound to the constrained case and demonstrate how the unconstrained case can be analyzed under weaker assumptions than the state-of-the-art. Numerical results confirm our theoretical developments.
Adversarial Robustness Against the Union of Multiple Perturbation Models
Authors: Pratyush Maini, Eric Wong, Zico Kolter
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Owing to the susceptibility of deep learning systems to adversarial attacks, there has been a great deal of work in developing (both empirically and certifiably) robust classifiers. While most work has defended against a single type of attack, recent work has looked at defending against multiple perturbation models using simple aggregations of multiple attacks. However, these methods can be difficult to tune, and can easily result in imbalanced degrees of robustness to individual perturbation models, resulting in a sub-optimal worst-case loss over the union. In this work, we develop a natural generalization of the standard PGD-based procedure to incorporate multiple perturbation models into a single attack, by taking the worst-case over all steepest descent directions. This approach has the advantage of directly converging upon a trade-off between different perturbation models which minimizes the worst-case performance over the union. With this approach, we are able to train standard architectures which are simultaneously robust against $\ell_ınfty$, $\ell_2$, and $\ell_1$ attacks, outperforming past approaches on the MNIST and CIFAR10 datasets and achieving adversarial accuracy of 47.0% against the union of ($\ell_ınfty$, $\ell_2$, $\ell_1$) perturbations with radius = (0.03, 0.5, 12) on the latter, improving upon previous approaches which achieve 40.6% accuracy.
Evolutionary Reinforcement Learning for Sample-Efficient Multiagent Coordination
Authors: Somdeb Majumdar, Shauharda Khadka, Santiago Miret, Stephen Mcaleer, Kagan Tumer
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Many cooperative multiagent reinforcement learning environments provide agents with a sparse team-based reward, as well as a dense agent-specific reward that incentivizes learning basic skills. Training policies solely on the team-based reward is often difficult due to its sparsity. Also, relying solely on the agent-specific reward is sub-optimal because it usually does not capture the team coordination objective. A common approach is to use reward shaping to construct a proxy reward by combining the individual rewards. However, this requires manual tuning for each environment. We introduce Multiagent Evolutionary Reinforcement Learning (MERL), a split-level training platform that handles the two objectives separately through two optimization processes. An evolutionary algorithm maximizes the sparse team-based objective through neuroevolution on a population of teams. Concurrently, a gradient-based optimizer trains policies to only maximize the dense agent-specific rewards. The gradient-based policies are periodically added to the evolutionary population as a way of information transfer between the two optimization processes. This enables the evolutionary algorithm to use skills learned via the agent-specific rewards toward optimizing the global objective. Results demonstrate that MERL significantly outperforms state-of-the-art methods, such as MADDPG, on a number of difficult coordination benchmarks.
Estimation of Bounds on Potential Outcomes For Decision Making
Authors: Maggie Makar, Fredrik Johansson, John Guttag, David Sontag
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Estimation of individual treatment effects is commonly used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, it is often sufficient for the decision maker to have estimates of upper and lower bounds on the potential outcomes of decision alternatives to assess risks and benefits. We show that, in such cases, we can improve sample efficiency by estimating simple functions that bound these outcomes instead of estimating their conditional expectations, which may be complex and hard to estimate. Our analysis highlights a trade-off between the complexity of the learning task and the confidence with which the learned bounds hold. Guided by these findings, we develop an algorithm for learning upper and lower bounds on potential outcomes which optimize an objective function defined by the decision maker, subject to the probability that bounds are violated being small. Using a clinical dataset and a well-known causality benchmark, we demonstrate that our algorithm outperforms baselines, providing tighter, more reliable bounds.
Optimal transport mapping via input convex neural networks
Authors: Ashok Makkuva, Amirhossein Taghvaei, Sewoong Oh, Jason Lee
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel minimax optimization. Building upon recent advances in the field of input convex neural networks, we propose a new framework to estimate the optimal transport mapping as the gradient of a convex function that is trained via minimax optimization. Numerical experiments confirm the accuracy of the learned transport map. Our approach can be readily used to train a deep generative model. When trained between a simple distribution in the latent space and a target distribution, the learned optimal transport map acts as a deep generative model. Although scaling this to a large dataset is challenging, we demonstrate two important strengths over standard adversarial training: robustness and discontinuity. As we seek the optimal transport, the learned generative model provides the same mapping regardless of how we initialize the neural networks. Further, a gradient of a neural network can easily represent discontinuous mappings, unlike standard neural networks that are constrained to be continuous. This allows the learned transport map to match any target distribution with many discontinuous supports and achieve sharp boundaries.
Proving the Lottery Ticket Hypothesis: Pruning is All You Need
Authors: Eran Malach, Gilad Yehudai, Shai Shalev-Schwartz, Ohad Shamir
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The lottery ticket hypothesis (Frankle and Carbin, 2018), states that a randomly-initialized network contains a small subnetwork such that, when trained in isolation, can compete with the performance of the original network. We prove an even stronger hypothesis (as was also conjectured in Ramanujan et al., 2019), showing that for every bounded distribution and every target network with bounded weights, a sufficiently over-parameterized neural network with random weights contains a subnetwork with roughly the same accuracy as the target network, without any further training.
From Local SGD to Local Fixed-Point Methods for Federated Learning
Authors: Grigory Malinovskiy, Dmitry Kovalev, Elnur Gasanov, Laurent Condat, Peter Richtarik
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an approximation thereof, in a distributed setting. Our work is motivated by the needs of federated learning. In this context, each local operator models the computations done locally on a mobile device. We investigate two strategies to achieve such a consensus: one based on a fixed number of local steps, and the other based on randomized computations. In both cases, the goal is to limit communication of the locally-computed variables, which is often the bottleneck in distributed frameworks. We perform convergence analysis of both methods and conduct a number of experiments highlighting the benefits of our approach.
Adaptive Gradient Descent without Descent
Authors: Yura Malitsky, Konstantin Mishchenko
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the function except for the gradients. By following these rules, you get a method adaptive to the local geometry, with convergence guarantees depending only on the smoothness in a neighborhood of a solution. Given that the problem is convex, our method converges even if the global smoothness constant is infinity. As an illustration, it can minimize arbitrary continuously twice-differentiable convex function. We examine its performance on a range of convex and nonconvex problems, including logistic regression and matrix factorization.
Emergence of Separable Manifolds in Deep Language Representations
Authors: Jonathan Mamou, Hang Le, Miguel Del Rio, Cory Stephenson, Hanlin Tang, Yoon Kim, Sueyeon Chung
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Deep neural networks (DNNs) have shown much empirical success in solving perceptual tasks across various cognitive modalities. While they are only loosely inspired by the biological brain, recent studies report considerable similarities between representations extracted from task-optimized DNNs and neural populations in the brain. DNNs have subsequently become a popular model class to infer computational principles underlying complex cognitive functions, and in turn, they have also emerged as a natural testbed for applying methods originally developed to probe information in neural populations. In this work, we utilize mean-field theoretic manifold analysis, a recent technique from computational neuroscience that connects geometry of feature representations with linear separability of classes, to analyze language representations from large-scale contextual embedding models. We explore representations from different model families (BERT, RoBERTa, GPT, etc.) and find evidence for emergence of linguistic manifolds across layer depth (e.g., manifolds for part-of-speech tags), especially in ambiguous data (i.e, words with multiple part-of-speech tags, or part-of-speech classes including many words). In addition, we find that the emergence of linear separability in these manifolds is driven by a combined reduction of manifolds’ radius, dimensionality and inter-manifold correlations.
Adaptive Adversarial Multi-task Representation Learning
Authors: Yuren Mao, Weiwei Liu, Xuemin Lin
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Adversarial Multi-task Representation Learning (AMTRL) methods are able to boost the performance of Multi-task Representation Learning (MTRL) models. However, the theoretical mechanism behind AMTRL is less investigated. To fill this gap, we study the generalization error bound of AMTRL through the lens of Lagrangian duality . Based on the duality, we proposed an novel adaptive AMTRL algorithm which improves the performance of original AMTRL methods. The extensive experiments back up our theoretical analysis and validate the superiority of our proposed algorithm.
On Learning Sets of Symmetric Elements
Authors: Haggai Maron, Or Litany, Gal Chechik, Ethan Fetaya
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Learning from unordered sets is a fundamental learning setup, recently attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has been given to the common case where set elements themselves adhere to their own symmetries. That case is relevant to numerous applications, from deblurring image bursts to multi-view 3D shape recognition and reconstruction. In this paper, we present a principled approach to learning sets of general symmetric elements. We first characterize the space of linear layers that are equivariant both to element reordering and to the inherent symmetries of elements, like translation in the case of images. We further show that networks that are composed of these layers, called Deep Sets for Symmetric Elements layers (DSS), are universal approximators of both invariant and equivariant functions. DSS layers are also straightforward to implement. Finally, we show that they improve over existing set-learning architectures in a series of experiments with images, graphs, and point-clouds.
Stochastically Dominant Distributional Reinforcement Learning
Authors: John Martin, Michal Lyskawinski, Xiaohu Li, Brendan Englot
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic dominance (SSD) relation. This compares the inherent dispersion of random returns induced by actions, producing a comprehensive evaluation of the environment’s uncertainty. The necessary conditions for SSD require estimators to predict accurate second moments. To accommodate this, we map the distributional RL problem to a Wasserstein gradient flow, treating the distributional Bellman residual as a potential energy functional. We propose a particle-based algorithm for which we prove optimality and convergence. Our experiments characterize the algorithm’s performance and demonstrate how uncertainty and performance are better balanced using an SSD policy than with other risk measures.
Minimax Pareto Fairness: A Multi Objective Perspective
Authors: Natalia Martinez, Martin Bertran, Guillermo Sapiro
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: In this work we formulate and formally characterize group fairness as a multi-objective optimization problem, where each sensitive group risk is a separate objective. We propose a fairness criterion where a classifier achieves minimax risk and is Pareto-efficient w.r.t. all groups, avoiding unnecessary harm, and can lead to the best zero-gap model if policy dictates so. We provide a simple optimization algorithm compatible with deep neural networks to satisfy these constraints. Since our method does not require test-time access to sensitive attributes, it can be applied to reduce worst-case classification errors between outcomes in unbalanced classification problems. We test the proposed methodology on real case-studies of predicting income, ICU patient mortality, skin lesions classification, and assessing credit risk, demonstrating how our framework compares favorably to other approaches.
Predictive Multiplicity in Classification
Authors: Charles Marx, Flavio Calmon, Berk Ustun
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Prediction problems often admit competing models that perform almost equally well. This effect challenges key assumptions in machine learning when competing models assign conflicting predictions. In this paper, we define predictive multiplicity as the ability of a prediction problem to admit competing models with conflicting predictions. We introduce measures to evaluate the severity of predictive multiplicity, and develop integer programming tools to compute these measures exactly for linear classification problems. We apply our tools to measure predictive multiplicity in recidivism prediction problems. Our results show that real-world datasets may admit competing models that assign wildly conflicting predictions, and motivate the need to report predictive multiplicity in model development.
Adding seemingly uninformative labels helps in low data regimes
Authors: Christos Matsoukas, Albert Bou Hernandez, Yue Liu, Karin Dembrower, Gisele Miranda, Emir Konuk, Johan Fredin Haslum, Athanasios Zouzos, Peter Lindholm, Fredrik Strand, Kevin Smith
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Evidence suggests that networks trained on large datasets generalize well not solely because of the numerous training examples, but also class diversity which encourages learning of enriched features. This raises the question of whether this remains true when data is scarce - is there an advantage to learning with additional labels in low-data regimes? In this work, we consider a task that requires difficult-to-obtain expert annotations: tumor segmentation in mammography images. We show that, in low-data settings, performance can be improved by complementing the expert annotations with seemingly uninformative labels from non-expert annotators, turning the task into a multi-class problem. We reveal that these gains increase when less expert data is available, and uncover several interesting properties through further studies. We demonstrate our findings on CSAW-S, a new dataset that we introduce here, and confirm them on two public datasets.
Fast and Consistent Learning of Hidden Markov Models by Incorporating Non-Consecutive Correlations
Authors: Robert Mattila, Cristian Rojas, Eric Moulines, Vikram Krishnamurthy, Bo Wahlberg
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Can the parameters of a hidden Markov model (HMM) be estimated from a single sweep through the observations – and additionally, without being trapped at a local optimum in the likelihood surface? That is the premise of recent method of moments algorithms devised for HMMs. In these, correlations between consecutive pair- or triplet-wise observations are empirically estimated and used to compute estimates of the HMM parameters. Albeit computationally very attractive, the main drawback is that by restricting to only low-order correlations in the data, information is being neglected which results in a loss of accuracy (compared to standard maximum likelihood schemes). In this paper, we propose extending these methods (both pair- and triplet-based) by also including non-consecutive correlations in a way which does not significantly increase the computational cost (which scales linearly with the number of additional lags included). We prove strong consistency of the new methods, and demonstrate an improved performance in numerical experiments on both synthetic and real-world financial time-series datasets.
On Approximate Thompson Sampling with Langevin Algorithms
Authors: Eric Mazumdar, Aldo Pacchiano, Yian Ma, Michael Jordan, Peter Bartlett
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Thompson sampling for multi-armed bandit problems is known to enjoy favorable performance in both theory and practice. However, its wider deployment is restricted due to a significant computational limitation: the need for samples from posterior distributions at every iteration. In practice, this limitation is alleviated by making use of approximate sampling methods, yet provably incorporating approximate samples into Thompson Sampling algorithms remains an open problem. In this work we address this by proposing two efficient Langevin MCMC algorithms tailored to Thompson sampling. The resulting approximate Thompson Sampling algorithms are efficiently implementable and provably achieve optimal instance-dependent regret for the Multi-Armed Bandit (MAB) problem. To prove these results we derive novel posterior concentration bounds and MCMC convergence rates for log-concave distributions which may be of independent interest.
Neural Datalog Through Time: Informed Temporal Modeling via Logical Specification
Authors: Hongyuan Mei, Guanghui Qin, Minjie Xu, Jason Eisner
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Learning how to predict future events from patterns of past events is difficult when the set of possible event types is large. Training an unrestricted neural model might overfit to spurious patterns. To exploit domain-specific knowledge of how past events might affect an event’s present probability, we propose using a temporal deductive database to track structured facts over time. Rules serve to prove facts from other facts and from past events. Each fact has a time-varying state—a vector computed by a neural net whose topology is determined by the fact’s provenance, including its experience of past events. The possible event types at any time are given by special facts, whose probabilities are neurally modeled alongside their states. In both synthetic and real-world domains, we show that neural probabilistic models derived from concise Datalog programs improve prediction by encoding appropriate domain knowledge in their architecture.