mtybilly/Instruct2DS huggingface dataset:
An Optimistic Perspective on Offline Reinforcement Learning
Authors: Rishabh Agarwal, Dale Schuurmans, Mohammad Norouzi
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Off-policy reinforcement learning (RL) using a fixed offline dataset of logged interactions is an important consideration in real world applications. This paper studies offline RL using the DQN replay dataset comprising the entire replay experience of a DQN agent on 60 Atari 2600 games. We demonstrate that recent off-policy deep RL algorithms, even when trained solely on this fixed dataset, outperform the fully trained DQN agent. To enhance generalization in the offline setting, we present Random Ensemble Mixture (REM), a robust Q-learning algorithm that enforces optimal Bellman consistency on random convex combinations of multiple Q-value estimates. Offline REM trained on the DQN replay dataset surpasses strong RL baselines. Ablation studies highlight the role of offline dataset size and diversity as well as the algorithm choice in our positive results. Overall, the results here present an optimistic view that robust RL algorithms trained on sufficiently large and diverse offline datasets can lead to high quality policies. The DQN replay dataset can serve as an offline RL benchmark and is open-sourced.
Optimal Bounds between f-Divergences and Integral Probability Metrics
Authors: Rohit Agrawal, Thibaut Horel
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The families of f-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are commonly used in optimization and estimation. In this work, we systematically study the relationship between these two families from the perspective of convex duality. Starting from a tight variational representation of the f-divergence, we derive a generalization of the moment generating function, which we show exactly characterizes the best lower bound of the f-divergence as a function of a given IPM. Using this characterization, we obtain new bounds on IPMs defined by classes of unbounded functions, while also recovering in a unified manner well-known results for bounded and subgaussian functions (e.g. Pinsker’s inequality and Hoeffding’s lemma).
LazyIter: A Fast Algorithm for Counting Markov Equivalent DAGs and Designing Experiments
Authors: Ali Ahmaditeshnizi, Saber Salehkaleybar, Negar Kiyavash
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The causal relationships among a set of random variables are commonly represented by a Directed Acyclic Graph (DAG), where there is a directed edge from variable $X$ to variable $Y$ if $X$ is a direct cause of $Y$. From the purely observational data, the true causal graph can be identified up to a Markov Equivalence Class (MEC), which is a set of DAGs with the same conditional independencies between the variables. The size of an MEC is a measure of complexity for recovering the true causal graph by performing interventions. We propose a method for efficient iteration over possible MECs given intervention results. We utilize the proposed method for computing MEC sizes and experiment design in active and passive learning settings. Compared to previous work for computing the size of MEC, our proposed algorithm reduces the time complexity by a factor of $O(n)$ for sparse graphs where $n$ is the number of variables in the system. Additionally, integrating our approach with dynamic programming, we design an optimal algorithm for passive experiment design. Experimental results show that our proposed algorithms for both computing the size of MEC and experiment design outperform the state of the art.
Learning What to Defer for Maximum Independent Sets
Authors: Sungsoo Ahn, Younggyo Seo, Jinwoo Shin
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Designing efficient algorithms for combinatorial optimization appears ubiquitously in various scientific fields. Recently, deep reinforcement learning (DRL) frameworks have gained considerable attention as a new approach: they can automate the design of a solver while relying less on sophisticated domain knowledge of the target problem. However, the existing DRL solvers determine the solution using a number of stages proportional to the number of elements in the solution, which severely limits their applicability to large-scale graphs. In this paper, we seek to resolve this issue by proposing a novel DRL scheme, coined learning what to defer (LwD), where the agent adaptively shrinks or stretch the number of stages by learning to distribute the element-wise decisions of the solution at each stage. We apply the proposed framework to the maximum independent set (MIS) problem, and demonstrate its significant improvement over the current state-of-the-art DRL scheme. We also show that LwD can outperform the conventional MIS solvers on large-scale graphs having millions of vertices, under a limited time budget.
Invariant Risk Minimization Games
Authors: Kartik Ahuja, Karthikeyan Shanmugam, Kush Varshney, Amit Dhurandhar
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many environments and finding invariant predictors reduces the effect of spurious features by concentrating models on features that have a causal relationship with the outcome. In this work, we pose such invariant risk minimization as finding the Nash equilibrium of an ensemble game among several environments. By doing so, we develop a simple training algorithm that uses best response dynamics and, in our experiments, yields similar or better empirical accuracy with much lower variance than the challenging bi-level optimization problem of Arjovsky et al. (2019). One key theoretical contribution is showing that the set of Nash equilibria for the proposed game are equivalent to the set of invariant predictors for any finite number of environments, even with nonlinear classifiers and transformations. As a result, our method also retains the generalization guarantees to a large set of environments shown in Arjovsky et al. (2019). The proposed algorithm adds to the collection of successful game-theoretic machine learning algorithms such as generative adversarial networks.
Why bigger is not always better: on finite and infinite neural networks
Authors: Laurence Aitchison
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Recent work has argued that neural networks can be understood theoretically by taking the number of channels to infinity, at which point the outputs become Gaussian process (GP) distributed. However, we note that infinite Bayesian neural networks lack a key facet of the behaviour of real neural networks: the fixed kernel, determined only by network hyperparameters, implies that they cannot do any form of representation learning. The lack of representation or equivalently kernel learning leads to less flexibility and hence worse performance, giving a potential explanation for the inferior performance of infinite networks observed in the literature (e.g. Novak et al. 2019). We give analytic results characterising the prior over representations and representation learning in finite deep linear networks. We show empirically that the representations in SOTA architectures such as ResNets trained with SGD are much closer to those suggested by our deep linear results than by the corresponding infinite network. This motivates the introduction of a new class of network: infinite networks with bottlenecks, which inherit the theoretical tractability of infinite networks while at the same time allowing representation learning.
Discriminative Jackknife: Quantifying Uncertainty in Deep Learning via Higher-Order Influence Functions
Authors: Ahmed Alaa, Mihaela Van Der Schaar
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Deep learning models achieve high predictive accuracy across a broad spectrum of tasks, but rigorously quantifying their predictive uncertainty remains challenging. Usable estimates of predictive uncertainty should (1) cover the true prediction targets with high probability, and (2) discriminate between high- and low confidence prediction instances. Existing methods for uncertainty quantification are based predominantly on Bayesian neural networks; these may fall short of (1) and (2) — i.e., Bayesian credible intervals do not guarantee frequentist coverage, and approximate posterior inference undermines discriminative accuracy. In this paper, we develop the discriminative jackknife (DJ), a frequentist procedure that utilizes influence functions of a model’s loss functional to construct a jackknife (or leave one-out) estimator of predictive confidence intervals. The DJ satisfies (1) and (2), is applicable to a wide range of deep learning models, is easy to implement, and can be applied in a post-hoc fashion without interfering with model training or compromising its accuracy. Experiments demonstrate that DJ performs competitively compared to existing Bayesian and non-Bayesian regression baselines.
Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functions
Authors: Ahmed Alaa, Mihaela Van Der Schaar
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Yet, when using RNNs to inform decision-making, predictions by themselves are not sufficient — we also need estimates of predictive uncertainty. Existing approaches for uncertainty quantification in RNNs are based predominantly on Bayesian methods; these are computationally prohibitive, and require major alterations to the RNN architecture and training. Capitalizing on ideas from classical jackknife resampling, we develop a frequentist alternative that: (a) does not interfere with model training or compromise its accuracy, (b) applies to any RNN architecture, and (c) provides theoretical coverage guarantees on the estimated uncertainty intervals. Our method derives predictive uncertainty from the variability of the (jackknife) sampling distribution of the RNN outputs, which is estimated by repeatedly deleting “blocks” of (temporally-correlated) training data, and collecting the predictions of the RNN re-trained on the remaining data. To avoid exhaustive re-training, we utilize influence functions to estimate the effect of removing training data blocks on the learned RNN parameters. Using data from a critical care setting, we demonstrate the utility of uncertainty quantification in sequential decision-making.
Random extrapolation for primal-dual coordinate descent
Authors: Ahmet Alacaoglu, Olivier Fercoq, Volkan Cevher
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with sparse data, and it uses large step sizes with dense data, retaining the benefits of the specific methods designed for each case. In addition to adapting to sparsity, our method attains fast convergence guarantees in favorable cases \emphwithout any modifications. In particular, we prove linear convergence under metric subregularity, which applies to strongly convex-strongly concave problems and piecewise linear quadratic functions. We show almost sure convergence of the sequence and optimal sublinear convergence rates for the primal-dual gap and objective values, in the general convex-concave case. Numerical evidence demonstrates the state-of-the-art empirical performance of our method in sparse and dense settings, matching and improving the existing methods.
A new regret analysis for Adam-type algorithms
Authors: Ahmet Alacaoglu, Yura Malitsky, Panayotis Mertikopoulos, Volkan Cevher
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: In this paper, we focus on a theory-practice gap for Adam and its variants (AMSGrad, AdamNC, etc.). In practice, these algorithms are used with a constant first-order moment parameter $β_1$ (typically between $0.9$ and $0.99$). In theory, regret guarantees for online convex optimization require a rapidly decaying $β_1\to0$ schedule. We show that this is an artifact of the standard analysis, and we propose a novel framework that allows us to derive optimal, data-dependent regret bounds with a constant $β_1$, without further assumptions. We also demonstrate the flexibility of our analysis on a wide range of different algorithms and settings.
Restarted Bayesian Online Change-point Detector achieves Optimal Detection Delay
Authors: Reda Alami, Odalric Maillard, Raphael Feraud
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: we consider the problem of sequential change-point detection where    both the change-points and the distributions before and after the change are assumed to be unknown. For this problem of primary importance in statistical and sequential learning theory, we derive a variant of the Bayesian Online Change Point Detector proposed by i̧tefearnhead2007line         which is easier to analyze than the original version while keeping its powerful message-passing algorithm.      We provide a non-asymptotic analysis of the false-alarm rate and the detection delay that matches the existing lower-bound. We further provide the first explicit high-probability control of the detection delay for such approach. Experiments on synthetic and real-world data show that this proposal outperforms the state-of-art change-point detection strategy, namely the Improved Generalized Likelihood Ratio (Improved GLR) while compares favorably with the original Bayesian Online Change Point Detection strategy.
Maximum Likelihood with Bias-Corrected Calibration is Hard-To-Beat at Label Shift Adaptation
Authors: Amr Alexandari, Anshul Kundaje, Avanti Shrikumar
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Label shift refers to the phenomenon where the prior class probability p(y) changes between the training and test distributions, while the conditional probability p(x|y) stays fixed. Label shift arises in settings like medical diagnosis, where a classifier trained to predict disease given symptoms must be adapted to scenarios where the baseline prevalence of the disease is different. Given estimates of p(y|x) from a predictive model, Saerens et al. proposed an efficient maximum likelihood algorithm to correct for label shift that does not require model retraining, but a limiting assumption of this algorithm is that p(y|x) is calibrated, which is not true of modern neural networks. Recently, Black Box Shift Learning (BBSL) and Regularized Learning under Label Shifts (RLLS) have emerged as state-of-the-art techniques to cope with label shift when a classifier does not output calibrated probabilities, but both methods require model retraining with importance weights and neither has been benchmarked against maximum likelihood. Here we (1) show that combining maximum likelihood with a type of calibration we call bias-corrected calibration outperforms both BBSL and RLLS across diverse datasets and distribution shifts, (2) prove that the maximum likelihood objective is concave, and (3) introduce a principled strategy for estimating source-domain priors that improves robustness to poor calibration. This work demonstrates that the maximum likelihood with appropriate calibration is a formidable and efficient baseline for label shift adaptation; notebooks reproducing experiments available at https://github.com/kundajelab/labelshiftexperiments , video: https://youtu.be/ZBXjE9QTruE , blogpost: https://bit.ly/3kTds7J
The Implicit Regularization of Stochastic Gradient Flow for Least Squares
Authors: Alnur Ali, Edgar Dobriban, Ryan Tibshirani
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We study the implicit regularization of mini-batch stochastic gradient descent, when applied to the fundamental problem of least squares regression. We leverage a continuous-time stochastic differential equation having the same moments as stochastic gradient descent, which we call stochastic gradient flow. We give a bound on the excess risk of stochastic gradient flow at time $t$, over ridge regression with tuning parameter $łambda = 1/t$. The bound may be computed from explicit constants (e.g., the mini-batch size, step size, number of iterations), revealing precisely how these quantities drive the excess risk. Numerical examples show the bound can be small, indicating a tight relationship between the two estimators. We give a similar result relating the coefficients of stochastic gradient flow and ridge. These results hold under no conditions on the data matrix $X$, and across the entire optimization path (not just at convergence).
Structural Language Models of Code
Authors: Uri Alon, Roy Sadaka, Omer Levy, Eran Yahav
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We address the problem of any-code completion - generating a missing piece of source code in a given program without any restriction on the vocabulary or structure. We introduce a new approach to any-code completion that leverages the strict syntax of programming languages to model a code snippet as a tree - structural language modeling (SLM). SLM estimates the probability of the program’s abstract syntax tree (AST) by decomposing it into a product of conditional probabilities over its nodes. We present a neural model that computes these conditional probabilities by considering all AST paths leading to a target node. Unlike previous techniques that have severely restricted the kinds of expressions that can be generated in this task, our approach can generate arbitrary code in any programming language. Our model significantly outperforms both seq2seq and a variety of structured approaches in generating Java and C# code. Our code, data, and trained models are available at http://github.com/tech-srl/slm-code-generation/. An online demo is available at http://AnyCodeGen.org.
LowFER: Low-rank Bilinear Pooling for Link Prediction
Authors: Saadullah Amin, Stalin Varanasi, Katherine Ann Dunfield, Günter Neumann
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Knowledge graphs are incomplete by nature, with only a limited number of observed facts from the world knowledge being represented as structured relations between entities. To partly address this issue, an important task in statistical relational learning is that of link prediction or knowledge graph completion. Both linear and non-linear models have been proposed to solve the problem. Bilinear models, while expressive, are prone to overfitting and lead to quadratic growth of parameters in number of relations. Simpler models have become more standard, with certain constraints on bilinear map as relation parameters. In this work, we propose a factorized bilinear pooling model, commonly used in multi-modal learning, for better fusion of entities and relations, leading to an efficient and constraint-free model. We prove that our model is fully expressive, providing bounds on the embedding dimensionality and factorization rank. Our model naturally generalizes Tucker decomposition based TuckER model, which has been shown to generalize other models, as efficient low-rank approximation without substantially compromising the performance. Due to low-rank approximation, the model complexity can be controlled by the factorization rank, avoiding the possible cubic growth of TuckER. Empirically, we evaluate on real-world datasets, reaching on par or state-of-the-art performance. At extreme low-ranks, model preserves the performance while staying parameter efficient.
Discount Factor as a Regularizer in Reinforcement Learning
Authors: Ron Amit, Ron Meir, Kamil Ciosek
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Specifying a Reinforcement Learning (RL) task involves choosing a suitable planning horizon, which is typically modeled by a discount factor. It is known that applying RL algorithms with a lower discount factor can act as a regularizer, improving performance in the limited data regime. Yet the exact nature of this regularizer has not been investigated. In this work, we fill in this gap. For several Temporal-Difference (TD) learning methods, we show an explicit equivalence between using a reduced discount factor and adding an explicit regularization term to the algorithm’s loss. Motivated by the equivalence, we empirically study this technique compared to standard L2 regularization by extensive experiments in discrete and continuous domains, using tabular and functional representations. Our experiments suggest the regularization effectiveness is strongly related to properties of the available data, such as size, distribution, and mixing rate.
Neuro-Symbolic Visual Reasoning: Disentangling "Visual" from "Reasoning"
Authors: Saeed Amizadeh, Hamid Palangi, Alex Polozov, Yichen Huang, Kazuhito Koishida
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Visual reasoning tasks such as visual question answering (VQA) require an interplay of visual perception with reasoning about the question semantics grounded in perception. However, recent advances in this area are still primarily driven by perception improvements (e.g. scene graph generation) rather than reasoning. Neuro-symbolic models such as Neural Module Networks bring the benefits of compositional reasoning to VQA, but they are still entangled with visual representation learning, and thus neural reasoning is hard to improve and assess on its own. To address this, we propose (1) a framework to isolate and evaluate the reasoning aspect of VQA separately from its perception, and (2) a novel top-down calibration technique that allows the model to answer reasoning questions even with imperfect perception. To this end, we introduce a Differentiable First-Order Logic formalism for VQA that explicitly decouples question answering from visual perception. On the challenging GQA dataset, this framework is used to perform in-depth, disentangled comparisons between well-known VQA models leading to informative insights regarding the participating models as well as the task.
The Differentiable Cross-Entropy Method
Authors: Brandon Amos, Denis Yarats
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We study the Cross-Entropy Method (CEM) for the non-convex optimization of a continuous and parameterized objective function and introduce a differentiable variant that enables us to differentiate the output of CEM with respect to the objective function’s parameters. In the machine learning setting this brings CEM inside of the end-to-end learning pipeline where this has otherwise been impossible. We show applications in a synthetic energy-based structured prediction task and in non-convex continuous control. In the control setting we show how to embed optimal action sequences into a lower-dimensional space. This enables us to use policy optimization to fine-tune modeling components by differentiating through the CEM-based controller.
Customizing ML Predictions for Online Algorithms
Authors: Keerti Anand, Rong Ge, Debmalya Panigrahi
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: A popular line of recent research incorporates ML advice in the design of online algorithms to improve their performance in typical instances. These papers treat the ML algorithm as a black-box, and redesign online algorithms to take advantage of ML predictions. In this paper, we ask the complementary question: can we redesign ML algorithms to provide better predictions for online algorithms? We explore this question in the context of the classic rent-or-buy problem, and show that incorporating optimization benchmarks in ML loss functions leads to significantly better performance, while maintaining a worst-case adversarial result when the advice is completely wrong. We support this finding both through theoretical bounds and numerical simulations.
Fairwashing explanations with off-manifold detergent
Authors: Christopher Anders, Plamen Pasliev, Ann-Kathrin Dombrowski, Klaus-Robert Müller, Pan Kessel
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Explanation methods promise to make black-box classifiers more transparent. As a result, it is hoped that they can act as proof for a sensible, fair and trustworthy decision-making process of the algorithm and thereby increase its acceptance by the end-users. In this paper, we show both theoretically and experimentally that these hopes are presently unfounded. Specifically, we show that, for any classifier $g$, one can always construct another classifier $\tildeg$ which has the same behavior on the data (same train, validation, and test error) but has arbitrarily manipulated explanation maps. We derive this statement theoretically using differential geometry and demonstrate it experimentally for various explanation methods, architectures, and datasets. Motivated by our theoretical insights, we then propose a modification of existing explanation methods which makes them significantly more robust.
Population-Based Black-Box Optimization for Biological Sequence Design
Authors: Christof Angermueller, David Belanger, Andreea Gane, Zelda Mariet, David Dohan, Kevin Murphy, Lucy Colwell, D Sculley
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The use of black-box optimization for the design of new biological sequences is an emerging research area with potentially revolutionary impact. The cost and latency of wet-lab experiments requires methods that find good sequences in few experimental rounds of large batches of sequences — a setting that off-the-shelf black-box optimization methods are ill-equipped to handle. We find that the performance of existing methods varies drastically across optimization tasks, posing a significant obstacle to real-world applications. To improve robustness, we propose Population-Based Black-Box Optimization (P3BO), which generates batches of sequences by sampling from an ensemble of methods. The number of sequences sampled from any method is proportional to the quality of sequences it previously proposed, allowing P3BO to combine the strengths of individual methods while hedging against their innate brittleness. Adapting the hyper-parameters of each of the methods online using evolutionary optimization further improves performance. Through extensive experiments on in-silico optimization tasks, we show that P3BO outperforms any single method in its population, proposing higher quality sequences as well as more diverse batches. As such, P3BO and Adaptive-P3BO are a crucial step towards deploying ML to real-world sequence design.
Low-loss connection of weight vectors: distribution-based approaches
Authors: Ivan Anokhin, Dmitry Yarotsky
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Recent research shows that sublevel sets of the loss surfaces of overparameterized networks are connected, exactly or approximately. We describe and compare experimentally a panel of methods used to connect two low-loss points by a low-loss curve on this surface. Our methods vary in accuracy and complexity. Most of our methods are based on ”macroscopic” distributional assumptions and are insensitive to the detailed properties of the points to be connected. Some methods require a prior training of a ”global connection model” which can then be applied to any pair of points. The accuracy of the method generally correlates with its complexity and sensitivity to the endpoint detail.
Online metric algorithms with untrusted predictions
Authors: Antonios Antoniadis, Christian Coester, Marek Elias, Adam Polak, Bertrand Simon
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Machine-learned predictors, although achieving very good results for inputs resembling training data, cannot possibly provide perfect predictions in all situations. Still, decision-making systems that are based on such predictors need not only to benefit from good predictions but also to achieve a decent performance when the predictions are inadequate. In this paper, we propose a prediction setup for arbitrary metrical task systems (MTS) (e.g., caching, k-server and convex body chasing) and online matching on the line. We utilize results from the theory of online algorithms to show how to make the setup robust. Specifically for caching, we present an algorithm whose performance, as a function of the prediction error, is exponentially better than what is achievable for general MTS. Finally, we present an empirical evaluation of our methods on real world datasets, which suggests practicality.
NADS: Neural Architecture Distribution Search for Uncertainty Awareness
Authors: Randy Ardywibowo, Shahin Boluki, Xinyu Gong, Zhangyang Wang, Xiaoning Qian
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Machine learning (ML) systems often encounter Out-of-Distribution (OoD) errors when dealing with testing data coming from a distribution different from training data. It becomes important for ML systems in critical applications to accurately quantify its predictive uncertainty and screen out these anomalous inputs. However, existing OoD detection approaches are prone to errors and even sometimes assign higher likelihoods to OoD samples. Unlike standard learning tasks, there is currently no well established guiding principle for designing OoD detection architectures that can accurately quantify uncertainty. To address these problems, we first seek to identify guiding principles for designing uncertainty-aware architectures, by proposing Neural Architecture Distribution Search (NADS). NADS searches for a distribution of architectures that perform well on a given task, allowing us to identify common building blocks among all uncertainty-aware architectures. With this formulation, we are able to optimize a stochastic OoD detection objective and construct an ensemble of models to perform OoD detection. We perform multiple OoD detection experiments and observe that our NADS performs favorably, with up to 57% improvement in accuracy compared to state-of-the-art methods among 15 different testing configurations.
Provable Representation Learning for Imitation Learning via Bi-level Optimization
Authors: Sanjeev Arora, Simon Du, Sham Kakade, Yuping Luo, Nikunj Saunshi
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: A common strategy in modern learning systems is to learn a representation that is useful for many tasks, a.k.a. representation learning. We study this strategy in the imitation learning setting for Markov decision processes (MDPs) where multiple experts’ trajectories are available. We formulate representation learning as a bi-level optimization problem where the “outer" optimization tries to learn the joint representation and the “inner" optimization encodes the imitation learning setup and tries to learn task-specific parameters. We instantiate this framework for the imitation learning settings of behavior cloning and observation-alone. Theoretically, we show using our framework that representation learning can provide sample complexity benefits for imitation learning in both settings. We also provide proof-of-concept experiments to verify our theory.
Quantum Boosting
Authors: Srinivasan Arunachalam, Reevu Maity
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Boosting is a technique that boosts a weak and inaccurate machine learning algorithm into a strong accurate learning algorithm. The AdaBoost algorithm by Freund and Schapire (for which they were awarded the Gödel prize in 2003) is one of the widely used boosting algorithms, with many applications in theory and practice. Suppose we have a gamma-weak learner for a Boolean concept class C that takes time R(C), then the time complexity of AdaBoost scales as VC(C)poly(R(C), 1/gamma), where VC(C) is the VC-dimension of C. In this paper, we show how quantum techniques can improve the time complexity of classical AdaBoost. To this end, suppose we have a gamma-weak quantum learning algorithm for a Boolean concept class C that takes time Q(C), we introduce a quantum boosting algorithm whose complexity scales as sqrtVC(C)poly(Q(C),1/gamma); thereby achieving quadratic quantum improvement over classical AdaBoost in terms of  VC(C).
Black-box Certification and Learning under Adversarial Perturbations
Authors: Hassan Ashtiani, Vinayak Pathak, Ruth Urner
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We formally study the problem of classification under adversarial perturbations from a learner’s perspective as well as a third-party who aims at certifying the robustness of a given black-box classifier. We analyze a PAC-type framework of semi-supervised learning and identify possibility and impossibility results for proper learning of VC-classes in this setting. We further introduce a new setting of black-box certification under limited query budget, and analyze this for various classes of predictors and perturbation. We also consider the viewpoint of a black-box adversary that aims at finding adversarial examples, showing that the existence of an adversary with polynomial query complexity can imply the existence of a sample efficient robust learner.
Invertible generative models for inverse problems: mitigating representation error and dataset bias
Authors: Muhammad Asim, Max Daniels, Oscar Leong, Ali Ahmed, Paul Hand
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Trained generative models have shown remarkable performance as priors for inverse problems in imaging – for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training dataset. In this paper, we demonstrate that invertible neural networks, which have zero representation error by design, can be effective natural signal priors at inverse problems such as denoising, compressive sensing, and inpainting. Given a trained generative model, we study the empirical risk formulation of the desired inverse problem under a regularization that promotes high likelihood images, either directly by penalization or algorithmically by initialization. For compressive sensing, invertible priors can yield higher accuracy than sparsity priors across almost all undersampling ratios, and due to their lack of representation error, invertible priors can yield better reconstructions than GAN priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images. We additionally compare performance for compressive sensing to unlearned methods, such as the deep decoder, and we establish theoretical bounds on expected recovery error in the case of a linear invertible model.
On the Convergence of Nesterov’s Accelerated Gradient Method in Stochastic Settings
Authors: Mahmoud Assran, Mike Rabbat
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We study Nesterov’s accelerated gradient method with constant step-size and momentum parameters in the stochastic approximation setting (unbiased gradients with bounded variance) and the finite-sum setting (where randomness is due to sampling mini-batches). To build better insight into the behavior of Nesterov’s method in stochastic settings, we focus throughout on objectives that are smooth, strongly-convex, and twice continuously differentiable. In the stochastic approximation setting, Nesterov’s method converges to a neighborhood of the optimal point at the same accelerated rate as in the deterministic setting. Perhaps surprisingly, in the finite-sum setting, we prove that Nesterov’s method may diverge with the usual choice of step-size and momentum, unless additional conditions on the problem related to conditioning and data coherence are satisfied. Our results shed light as to why Nesterov’s method may fail to converge or achieve acceleration in the finite-sum setting.
Safe screening rules for L0-regression from Perspective Relaxations
Authors: Alper Atamturk, Andres Gomez
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We give safe screening rules to eliminate variables from regression with $\ell_0$ regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening rules can be computed from a convex relaxation solution in linear time, without solving the L0-optimization problem. Thus, they can be used in a preprocessing step to safely remove variables from consideration apriori. Numerical experiments on real and synthetic data indicate that a significant number of the variables can be removed quickly, hence reducing the computational burden for optimization substantially. Therefore, the proposed fast and effective screening rules extend the scope of algorithms for L0-regression to larger data sets.
Adversarial Learning Guarantees for Linear Hypotheses and Neural Networks
Authors: Pranjal Awasthi, Natalie Frank, Mehryar Mohri
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Adversarial or test time robustness measures the susceptibility of a classifier to perturbations to the test input. While there has been a flurry of recent work on designing defenses against such perturbations, the theory of adversarial robustness is not well understood. In order to make progress on this, we focus on the problem of understanding generalization in adversarial settings, via the lens of Rademacher complexity. We give upper and lower bounds for the adversarial empirical Rademacher complexity of linear hypotheses with adversarial perturbations measured in $l_r$-norm for an arbitrary $r ≥ 1$. We then extend our analysis to provide Rademacher complexity lower and upper bounds for a single ReLU unit. Finally, we give adversarial Rademacher complexity bounds for feed-forward neural networks with one hidden layer.
Sample Amplification: Increasing Dataset Size even when Learning is Impossible
Authors: Brian Axelrod, Shivam Garg, Vatsal Sharan, Gregory Valiant
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Given data drawn from an unknown distribution, D, to what extent is it possible to “amplify” this dataset and faithfully output an even larger set of samples that appear to have been drawn from D? We formalize this question as follows: an (n,m) amplification procedure takes as input n independent draws from an unknown distribution D, and outputs a set of m > n “samples” which must be indistinguishable from m samples drawn iid from D. We consider this sample amplification problem in two fundamental settings: the case where D is an arbitrary discrete distribution supported on k elements, and the case where D is a d-dimensional Gaussian with unknown mean, and fixed covariance matrix. Perhaps surprisingly, we show a valid amplification procedure exists for both of these settings, even in the regime where the size of the input dataset, n, is significantly less than what would be necessary to learn distribution D to non-trivial accuracy. We also show that our procedures are optimal up to constant factors. Beyond these results, we describe potential applications of such data amplification, and formalize a number of curious directions for future research along this vein.
Sparse Convex Optimization via Adaptively Regularized Hard Thresholding
Authors: Kyriakos Axiotis, Maxim Sviridenko
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $słeq s^*γ$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $γ≥ 1$ is an approximation factor. There has been a lot of work to analyze the sparsity guarantees of various algorithms (LASSO, Orthogonal Matching Pursuit (OMP), Iterative Hard Thresholding (IHT)) in terms of the Restricted Condition Number $ąppa$. The best known algorithms guarantee to find an approximate solution of value $f(x^*)+ε$ with the sparsity bound of $γ = Ołeft(\p̨pa\minłeft\łog \fracf(x^0)-f(x^*)ε, \kp̨ai̊ght\\g̊ht)$, where $x^*$ is the target solution. We present a new Adaptively Regularized Hard Thresholding (ARHT) algorithm that makes significant progress on this problem by bringing the bound down to $γ=O(\kaą)$, which has been shown to be tight for a general class of algorithms including LASSO, OMP, and IHT. This is achieved without significant sacrifice in the runtime efficiency compared to the fastest known algorithms. We also provide a new analysis of OMP with Replacement (OMPR) for general $f$, under the condition $s > s^* \frac\kap^̨24$, which yields Compressed Sensing bounds under the Restricted Isometry Property (RIP). When compared to other Compressed Sensing approaches, it has the advantage of providing a strong tradeoff between the RIP condition and the solution sparsity, while working for any general function $f$ that meets the RIP condition.
Model-Based Reinforcement Learning with Value-Targeted Regression
Authors: Alex Ayoub, Zeyu Jia, Csaba Szepesvari, Mengdi Wang, Lin Yang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: This paper studies model-based reinforcement learning (RL) for regret minimization. We focus on finite-horizon episodic RL where the transition model $P$ belongs to a known family of models $\mathcalP$, a special case of which is when models in $\mathcalP$ take the form of linear mixtures: $P_þeta = ∑_i=1^d þeta_iP_i$. We propose a model based RL algorithm that is based on the optimism principle: In each episode, the set of models that are ‘consistent’ with the data collected is constructed. The criterion of consistency is based on the total squared error that the model incurs on the task of predicting \emphstate values as determined by the last value estimate along the transitions. The next value function is then chosen by solving the optimistic planning problem with the constructed set of models. We derive a bound on the regret, which, in the special case of linear mixtures, takes the form $\tilde\mathcalO(d\sqrtH^3T)$, where $H$, $T$ and $d$ are the horizon, the total number of steps and the dimension of $þeta$, respectively. In particular, this regret bound is independent of the total number of states or actions, and is close to a lower bound $Ømega(\sqrtHdT)$. For a general model family $\mathcalP$, the regret bound is derived based on the Eluder dimension.
Forecasting Sequential Data Using Consistent Koopman Autoencoders
Authors: Omri Azencot, N. Benjamin Erichson, Vanessa Lin, Michael Mahoney
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our network is directly related to the derived analysis, and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems, and it achieves accurate estimates for significant prediction horizons, while also being robust to noise.
Constant Curvature Graph Convolutional Networks
Authors: Gregor Bachmann, Gary Becigneul, Octavian Ganea
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Interest has been rising lately towards methods representing data in non-Euclidean spaces, e.g. hyperbolic or spherical that provide specific inductive biases useful for certain real-world data properties, e.g. scale-free, hierarchical or cyclical. However, the popular graph neural networks are currently limited in modeling data only via Euclidean geometry and associated vector space operations. Here, we bridge this gap by proposing mathematically grounded generalizations of graph convolutional networks (GCN) to (products of) constant curvature spaces. We do this by i) introducing a unified formalism permitting a differentiable interpolation between all geometries of constant curvature irrespective of their sign, ii) leveraging gyro-barycentric coordinates that generalize the classic Euclidean concept of the center of mass. Our class of models smoothly recover their Euclidean counterparts when the curvature goes to zero from either side. Empirically, we outperform Euclidean GCNs in the tasks of node classification and distortion minimization for symbolic data exhibiting non-Euclidean behavior, according to their discrete curvature.
Scalable Nearest Neighbor Search for Optimal Transport
Authors: Arturs Backurs, Yihe Dong, Piotr Indyk, Ilya Razenshteyn, Tal Wagner
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The Optimal Transport (a.k.a. Wasserstein) distance is an increasingly popular similarity measure for rich data domains, such as images or text documents. This raises the necessity for fast nearest neighbor search algorithms according to this distance, which poses a substantial computational bottleneck on massive datasets. In this work we introduce Flowtree, a fast and accurate approximation algorithm for the Wasserstein-1 distance. We formally analyze its approximation factor and running time. We perform extensive experimental evaluation of nearest neighbor search algorithms in the W_1 distance on real-world dataset. Our results show that compared to previous state of the art, Flowtree achieves up to 7.4 times faster running time.