mtybilly/Instruct2DS huggingface dataset:
Decision Trees for Decision-Making under the Predict-then-Optimize Framework
Authors: Adam N. Elmachtoub, Jason Cheuk Nam Liang, Ryan Mcnellis
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We consider the use of decision trees for decision-making problems under the predict-then-optimize framework. That is, we would like to first use a decision tree to predict unknown input parameters of an optimization problem, and then make decisions by solving the optimization problem using the predicted parameters. A natural loss function in this framework is to measure the suboptimality of the decisions induced by the predicted input parameters, as opposed to measuring loss using input parameter prediction error. This natural loss function is known in the literature as the Smart Predict-then-Optimize (SPO) loss, and we propose a tractable methodology called SPO Trees (SPOTs) for training decision trees under this loss. SPOTs benefit from the interpretability of decision trees, providing an interpretable segmentation of contextual features into groups with distinct optimal solutions to the optimization problem of interest. We conduct several numerical experiments on synthetic and real data including the prediction of travel times for shortest path problems and predicting click probabilities for news article recommendation. We demonstrate on these datasets that SPOTs simultaneously provide higher quality decisions and significantly lower model complexity than other machine learning approaches (e.g., CART) trained to minimize prediction error.
Revisiting Spatial Invariance with Low-Rank Local Connectivity
Authors: Gamaleldin Elsayed, Prajit Ramachandran, Jonathon Shlens, Simon Kornblith
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Convolutional neural networks are among the most successful architectures in deep learning with this success at least partially attributable to the efficacy of spatial invariance as an inductive bias. Locally connected layers, which differ from convolutional layers only in their lack of spatial invariance, usually perform poorly in practice. However, these observations still leave open the possibility that some degree of relaxation of spatial invariance may yield a better inductive bias than either convolution or local connectivity. To test this hypothesis, we design a method to relax the spatial invariance of a network layer in a controlled manner; we create a \emphlow-rank locally connected layer, where the filter bank applied at each position is constructed as a linear combination of basis set of filter banks with spatially varying combining weights. By varying the number of basis filter banks, we can control the degree of relaxation of spatial invariance. In experiments with small convolutional networks, we find that relaxing spatial invariance improves classification accuracy over both convolution and locally connected layers across MNIST, CIFAR-10, and CelebA datasets, thus suggesting that spatial invariance may be an overly restrictive prior.
Divide and Conquer: Leveraging Intermediate Feature Representations for Quantized Training of Neural Networks
Authors: Ahmed Taha Elthakeb, Prannoy Pilligundla, Fatemeh Mireshghallah, Alexander Cloninger, Hadi Esmaeilzadeh
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The deep layers of modern neural networks extract a rather rich set of features as an input propagates through the network, this paper sets out to harvest these rich intermediate representations for quantization with minimal accuracy loss while significantly reducing the memory footprint and compute intensity of the DNN. This paper utilizes knowledge distillation through teacher-student paradigm (Hinton et al., 2015) in a novel setting that exploits the feature extraction capability of DNNs for higher accuracy quantization. As such, our algorithm logically divides a pretrained full-precision DNN to multiple sections, each of which exposes intermediate features to train a team of students independently in the quantized domain and simply stitching them afterwards. This divide and conquer strategy, makes the training of each student section possible in isolation, speeding up training by enabling parallelization. Experiments on various DNNs (AlexNet, LeNet, MobileNet, ResNet-18, ResNet-20, SVHN and VGG-11) show that, this approach—called DCQ (Divide and Conquer Quantization)—on average, improves the performance of a state-of-the-art quantized training technique, DoReFa-Net (Zhou et al., 2016) by 21.6% and 9.3% for binary and ternary quantization, respectively. Additionally, we show that incorporating DCQ to existing quantized training methods leads to improved accuracies as compared to previously reported by multiple state-of-the-art quantized training methods.
Generalization Error of Generalized Linear Models in High Dimensions
Authors: Melikasadat Emami, Mojtaba Sahraee-Ardakan, Parthe Pandit, Sundeep Rangan, Alyson Fletcher
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our understanding of their generalization capabilities is incomplete and this task is made harder by the non-convexity of the underlying learning problems. We provide a general framework to characterize the asymptotic generalization error for single-layer neural networks (i.e., generalized linear models) with arbitrary non-linearities, making it applicable to regression as well as classification problems. This framework enables analyzing the effect of (i) over-parameterization and non-linearity during modeling; (ii) choices of loss function, initialization, and regularizer during learning; and (iii) mismatch between training and test distributions. As examples, we analyze a few special cases, namely linear regression and logistic regression. We are also able to rigorously and analytically explain the \emphdouble descent phenomenon in generalized linear models.
Parallel Algorithm for Non-Monotone DR-Submodular Maximization
Authors: Alina Ene, Huy Nguyen
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: In this work, we give a new parallel algorithm for the problem of maximizing a non-monotone diminishing returns submodular function subject to a cardinality constraint. For any desired accuracy $ε$, our algorithm achieves a $1/e - ε$ approximation using $O(łogn łog(1/ε) / ε^3)$ parallel rounds of function evaluations. The approximation guarantee nearly matches the best approximation guarantee known for the problem in the sequential setting and the number of parallel rounds is nearly-optimal for any constant $ε$. Previous algorithms achieve worse approximation guarantees using $Ømega(łog^2n)$ parallel rounds. Our experimental evaluation suggests that our algorithm obtains solutions whose objective value nearly matches the value obtained by the state of the art sequential algorithms, and it outperforms previous parallel algorithms in number of parallel rounds, iterations, and solution quality.
Continuous Time Bayesian Networks with Clocks
Authors: Nicolai Engelmann, Dominik Linzner, Heinz Koeppl
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Structured stochastic processes evolving in continuous time present a widely adopted framework to model phenomena occurring in nature and engineering. However, such models are often chosen to satisfy the Markov property to maintain tractability. One of the more popular of such memoryless models are Continuous Time Bayesian Networks (CTBNs). In this work, we lift its restriction to exponential survival times to arbitrary distributions. Current extensions achieve this via auxiliary states, which hinder tractability. To avoid that, we introduce a set of node-wise clocks to construct a collection of graph-coupled semi-Markov chains. We provide algorithms for parameter and structure inference, which make use of local dependencies and conduct experiments on synthetic data and a data-set generated through a benchmark tool for gene regulatory networks. In doing so, we point out advantages compared to current CTBN extensions.
Identifying Statistical Bias in Dataset Replication
Authors: Logan Engstrom, Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Jacob Steinhardt, Aleksander Madry
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Dataset replication is a useful tool for assessing whether improvements in test accuracy on a specific benchmark correspond to improvements in models’ ability to generalize reliably. In this work, we present unintuitive yet significant ways in which standard approaches to dataset replication introduce statistical bias, skewing the resulting observations. We study ImageNet-v2, a replication of the ImageNet dataset on which models exhibit a significant (11-14%) drop in accuracy, even after controlling for selection frequency, a human-in-the-loop measure of data quality. We show that after remeasuring selection frequencies and correcting for statistical bias, only an estimated 3.6% of the original 11.7% accuracy drop remains unaccounted for. We conclude with concrete recommendations for recognizing and avoiding bias in dataset replication. Code for our study is publicly available: https://git.io/data-rep-analysis.
Distributed Online Optimization over a Heterogeneous Network with Any-Batch Mirror Descent
Authors: Nima Eshraghi, Ben Liang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: In distributed online optimization over a computing network with heterogeneous nodes, slow nodes can adversely affect the progress of fast nodes, leading to drastic slowdown of the overall convergence process. To address this issue, we consider a new algorithm termed Distributed Any-Batch Mirror Descent (DABMD), which is based on distributed Mirror Descent but uses a fixed per-round computing time to limit the waiting by fast nodes to receive information updates from slow nodes. DABMD is characterized by varying minibatch sizes across nodes. It is applicable to a broader range of problems compared with existing distributed online optimization methods such as those based on dual averaging, and it accommodates time-varying network topology. We study two versions of DABMD, depending on whether the computing nodes average their primal variables via single or multiple consensus iterations. We show that both versions provide strong theoretical performance guarantee, by deriving upperbounds on their expected dynamic regret, which capture the variability in minibatch sizes. Our experimental results show substantial reduction in cost and acceleration in convergence compared with the known best alternative.
Rigging the Lottery: Making All Tickets Winners
Authors: Utku Evci, Trevor Gale, Jacob Menick, Pablo Samuel Castro, Erich Elsen
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Many applications require sparse neural networks due to space or inference time restrictions. There is a large body of work on training dense networks to yield sparse networks for inference, but this limits the size of the largest trainable sparse model to that of the largest trainable dense model. In this paper we introduce a method to train sparse neural networks with a fixed parameter count and a fixed computational cost throughout training, without sacrificing accuracy relative to existing dense-to-sparse training methods. Our method updates the topology of the sparse network during training by using parameter magnitudes and infrequent gradient calculations. We show that this approach requires fewer floating-point operations (FLOPs) to achieve a given level of accuracy compared to prior techniques. We demonstrate state-of-the-art sparse training results on a variety of networks and datasets, including ResNet-50, MobileNets on Imagenet-2012, and RNNs on WikiText-103. Finally, we provide some insights into why allowing the topology to change during the optimization can overcome local minima encountered when the topology remains static.
Faster Graph Embeddings via Coarsening
Authors: Matthew Fahrbach, Gramoz Goranci, Richard Peng, Sushant Sachdeva, Chi Wang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we are interested only in a small subset of relevant vertices. To address this, we present an efficient graph coarsening approach, based on Schur complements, for computing the embedding of the relevant vertices. We prove that these embeddings are preserved exactly by the Schur complement graph that is obtained via Gaussian elimination on the non-relevant vertices. As computing Schur complements is expensive, we give a nearly-linear time algorithm that generates a coarsened graph on the relevant vertices that provably matches the Schur complement in expectation in each iteration. Our experiments involving prediction tasks on graphs demonstrate that computing embeddings on the coarsened graph, rather than the entire graph, leads to significant time savings without sacrificing accuracy.
Latent Bernoulli Autoencoder
Authors: Jiri Fajtl, Vasileios Argyriou, Dorothy Monekosso, Paolo Remagnino
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: In this work, we pose the question whether it is possible to design and train an autoencoder model in an end-to-end fashion to learn representations in the multivariate Bernoulli latent space, and achieve performance comparable with the state-of-the-art variational methods. Moreover, we investigate how to generate novel samples and perform smooth interpolation and attributes modification in the binary latent space. To meet our objective, we propose a simplified, deterministic model with a straight-through gradient estimator to learn the binary latents and show its competitiveness with the latest VAE methods. Furthermore, we propose a novel method based on a random hyperplane rounding for sampling and smooth interpolation in the latent space. Our method performs on a par or better than the current state-of-the-art methods on common CelebA, CIFAR-10 and MNIST datasets.
Optimal Sequential Maximization: One Interview is Enough!
Authors: Moein Falahatgar, Alon Orlitsky, Venkatadheeraj Pichapati
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Maximum selection under probabilistic queries \emph(probabilistic maximization) is a fundamental algorithmic problem arising in numerous theoretical and practical contexts. We derive the first query-optimal sequential algorithm for probabilistic-maximization. Departing from previous assumptions, the algorithm and performance guarantees apply even for infinitely many items, hence in particular do not require a-priori knowledge of the number of items. The algorithm has linear query complexity, and is optimal also in the streaming setting. To derive these results we consider a probabilistic setting where several candidates for a position are asked multiple questions with the goal of finding who has the highest probability of answering interview questions correctly. Previous work minimized the total number of questions asked by alternating back and forth between the best performing candidates, in a sense, inviting them to multiple interviews. We show that the same order-wise selection accuracy can be achieved by querying the candidates sequentially, never returning to a previously queried candidate. Hence one interview is enough!
Spectral Graph Matching and Regularized Quadratic Relaxations: Algorithm and Theory
Authors: Zhou Fan, Cheng Mao, Yihong Wu, Jiaming Xu
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Graph matching, also known as network alignment, aims at recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. To tackle this task, we propose a spectral method, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), which first constructs a similarity matrix as a weighted sum of outer products between all pairs of eigenvectors of the two graphs, and then outputs a matching by a simple rounding procedure. For a universality class of correlated Wigner models, GRAMPA achieves exact recovery of the latent matching between two graphs with edge correlation $1 - 1/\mathrmpolylog(n)$ and average degree at least $\mathrmpolylog(n)$. This matches the state-of-the-art guarantees for polynomial-time algorithms established for correlated Erdős-Rényi graphs, and significantly improves over existing spectral methods. The superiority of GRAMPA is also demonstrated on a variety of synthetic and real datasets, in terms of both statistical accuracy and computational efficiency.
On hyperparameter tuning in general clustering problemsm
Authors: Xinjie Fan, Yuguang Yue, Purnamrita Sarkar, Y. X. Rachel Wang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Tuning hyperparameters for unsupervised learning problems is difficult in general due to the lack of ground truth for validation. However, the success of most clustering methods depends heavily on the correct choice of the involved hyperparameters. Take for example the Lagrange multipliers of penalty terms in semidefinite programming (SDP) relaxations of community detection in networks, or the bandwidth parameter needed in the Gaussian kernel used to construct similarity matrices for spectral clustering. Despite the popularity of these clustering algorithms, there are not many provable methods for tuning these hyperparameters. In this paper, we provide an overarching framework with provable guarantees for tuning hyperparameters in the above class of problems under two different models. Our framework can be augmented with a cross validation procedure to do model selection as well. In a variety of simulation and real data experiments, we show that our framework outperforms other widely used tuning procedures in a broad range of parameter settings.
Online mirror descent and dual averaging: keeping pace in the dynamic case
Authors: Huang Fang, Nick Harvey, Victor Portella, Michael Friedlander
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Online mirror descent (OMD) and dual averaging (DA)—two fundamental algorithms for online convex optimization—are known to have very similar (and sometimes identical) performance guarantees when used with a fixed learning rate. Under dynamic learning rates, however, OMD is provably inferior to DA and suffers a linear regret, even in common settings such as prediction with expert advice. We modify the OMD algorithm through a simple technique that we call stabilization. We give essentially the same abstract regret bound for OMD with stabilization and for DA by modifying the classical OMD convergence analysis in a careful and modular way that allows for straightforward and flexible proofs. Simple corollaries of these bounds show that OMD with stabilization and DA enjoy the same performance guarantees in many applications—even under dynamic learning rates. We also shed light on the similarities between OMD and DA and show simple conditions under which stabilized-OMD and DA generate the same iterates.
Stochastic Regret Minimization in Extensive-Form Games
Authors: Gabriele Farina, Christian Kroer, Tuomas Sandholm
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Monte-Carlo counterfactual regret minimization (MCCFR) is the state-of-the-art algorithm for solving sequential games that are too large for full tree traversals. It works by using gradient estimates that can be computed via sampling. However, stochastic methods for sequential games have not been investigated extensively beyond MCCFR. In this paper we develop a new framework for developing stochastic regret minimization methods. This framework allows us to use any regret-minimization algorithm, coupled with any gradient estimator. The MCCFR algorithm can be analyzed as a special case of our framework, and this analysis leads to significantly stronger theoretical guarantees on convergence, while simultaneously yielding a simplified proof. Our framework allows us to instantiate several new stochastic methods for solving sequential games. We show extensive experiments on five games, where some variants of our methods outperform MCCFR.
Do GANs always have Nash equilibria?
Authors: Farzan Farnia, Asuman Ozdaglar
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and empirical challenges. GANs trained using first-order optimization methods commonly fail to converge to a stable solution where the players cannot improve their objective, i.e., the Nash equilibrium of the underlying game. Such issues raise the question of the existence of Nash equilibria in GAN zero-sum games. In this work, we show through theoretical and numerical results that indeed GAN zero-sum games may have no Nash equilibria. To characterize an equilibrium notion applicable to GANs, we consider the equilibrium of a new zero-sum game with an objective function given by a proximal operator applied to the original objective, a solution we call the proximal equilibrium. Unlike the Nash equilibrium, the proximal equilibrium captures the sequential nature of GANs, in which the generator moves first followed by the discriminator. We prove that the optimal generative model in Wasserstein GAN problems provides a proximal equilibrium. Inspired by these results, we propose a new approach, which we call proximal training, for solving GAN problems. We perform several numerical experiments indicating the existence of proximal equilibria in GANs.
Growing Action Spaces
Authors: Gregory Farquhar, Laura Gustafson, Zeming Lin, Shimon Whiteson, Nicolas Usunier, Gabriel Synnaeve
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: In complex tasks, such as those with large combinatorial action spaces, random exploration may be too inefficient to achieve meaningful learning progress. In this work, we use a curriculum of progressively growing action spaces to accelerate learning. We assume the environment is out of our control, but that the agent may set an internal curriculum by initially restricting its action space. Our approach uses off-policy reinforcement learning to estimate optimal value functions for multiple action spaces simultaneously and efficiently transfers data, value estimates, and state representations from restricted action spaces to the full task. We show the efficacy of our approach in proof-of-concept control tasks and on challenging large-scale StarCraft micromanagement tasks with large, multi-agent action spaces.
Improved Optimistic Algorithms for Logistic Bandits
Authors: Louis Faury, Marc Abeille, Clement Calauzenes, Olivier Fercoq
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The generalized linear bandit framework has attracted a lot of attention in recent years by extending the well-understood linear setting and allowing to model richer reward structures. It notably covers the logistic model, widely used when rewards are binary. For logistic bandits, the frequentist regret guarantees of existing algorithms are $\tilde\mathcalO(ąppa \sqrtT)$, where $\p̨pa$ is a problem-dependent constant. Unfortunately, $\kp̨a$ can be arbitrarily large as it scales exponentially with the size of the decision set. This may lead to significantly loose regret bounds and poor empirical performance. In this work, we study the logistic bandit with a focus on the prohibitive dependencies introduced by $\kaą$. We propose a new optimistic algorithm based on a finer examination of the non-linearities of the reward function. We show that it enjoys a $\tilde\mathcalO(\sqrtT)$ regret with no dependency in $\kap$̨, but for a second order term. Our analysis is based on a new tail-inequality for self-normalized martingales, of independent interest.
Revisiting Fundamentals of Experience Replay
Authors: William Fedus, Prajit Ramachandran, Rishabh Agarwal, Yoshua Bengio, Hugo Larochelle, Mark Rowland, Will Dabney
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Experience replay is central to off-policy algorithms in deep reinforcement learning (RL), but there remain significant gaps in our understanding. We therefore present a systematic and extensive analysis of experience replay in Q-learning methods, focusing on two fundamental properties: the replay capacity and the ratio of learning updates to experience collected (replay ratio). Our additive and ablative studies upend conventional wisdom around experience replay — greater capacity is found to substantially increase the performance of certain algorithms, while leaving others unaffected. Counterintuitively we show that theoretically ungrounded, uncorrected n-step returns are uniquely beneficial while other techniques confer limited benefit for sifting through larger memory. Separately, by directly controlling the replay ratio we contextualize previous observations in the literature and empirically measure its importance across a variety of deep RL algorithms. Finally, we conclude by testing a set of hypotheses on the nature of these performance benefits.
Learning with Multiple Complementary Labels
Authors: Lei Feng, Takuo Kaneko, Bo Han, Gang Niu, Bo An, Masashi Sugiyama
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: A complementary label (CL) simply indicates an incorrect class of an example, but learning with CLs results in multi-class classifiers that can predict the correct class. Unfortunately, the problem setting only allows a single CL for each example, which notably limits its potential since our labelers may easily identify multiple CLs (MCLs) to one example. In this paper, we propose a novel problem setting to allow MCLs for each example and two ways for learning with MCLs. In the first way, we design two wrappers that decompose MCLs into many single CLs, so that we could use any method for learning with CLs. However, the supervision information that MCLs hold is conceptually diluted after decomposition. Thus, in the second way, we derive an unbiased risk estimator; minimizing it processes each set of MCLs as a whole and possesses an estimation error bound. We further improve the second way into minimizing properly chosen upper bounds. Experiments show that the former way works well for learning with MCLs but the latter is even better.
Global Concavity and Optimization in a Class of Dynamic Discrete Choice Models
Authors: Yiding Feng, Ekaterina Khmelnitskaya, Denis Nekipelov
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Discrete choice models with unobserved heterogeneity are commonly used Econometric models for dynamic Economic behavior which have been adopted in practice to predict behavior of individuals and firms from schooling and job choices to strategic decisions in market competition. These models feature optimizing agents who choose among a finite set of options in a sequence of periods and receive choice-specific payoffs that depend on both variables that are observed by the agent and recorded in the data and variables that are only observed by the agent but not recorded in the data. Existing work in Econometrics assumes that optimizing agents are fully rational and requires finding a functional fixed point to find the optimal policy. We show that in an important class of discrete choice models the value function is globally concave in the policy. That means that simple algorithms that do not require fixed point computation, such as the policy gradient algorithm, globally converge to the optimal policy. This finding can both be used to relax behavioral assumption regarding the optimizing agents and to facilitate Econometric analysis of dynamic behavior. In particular, we demonstrate significant computational advantages in using a simple implementation policy gradient algorithm over existing “nested fixed point” algorithms used in Econometrics.
The Intrinsic Robustness of Stochastic Bandits to Strategic Manipulation
Authors: Zhe Feng, David Parkes, Haifeng Xu
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Motivated by economic applications such as recommender systems, we study the behavior of stochastic bandits algorithms under \emphstrategic behavior conducted by rational actors, i.e., the arms. Each arm is a \emphself-interested strategic player who can modify its own reward whenever pulled, subject to a cross-period budget constraint, in order to maximize its own expected number of times of being pulled. We analyze the robustness of three popular bandit algorithms: UCB, $ɛ$-Greedy, and Thompson Sampling. We prove that all three algorithms achieve a regret upper bound $\mathcalO(\max \ B, Kłn T\)$ where $B$ is the total budget across arms, $K$ is the total number of arms and $T$ is the running time of the algorithms. This regret guarantee holds for \empharbitrary adaptive manipulation strategy of arms. Our second set of main results shows that this regret bound is \emphtight— in fact, for UCB, it is tight even when we restrict the arms’ manipulation strategies to form a \emphNash equilibrium. We do so by characterizing the Nash equilibrium of the game induced by arms’ strategic manipulations and show a regret lower bound of $Ømega(\max \ B, Kłn T\)$ at the equilibrium.
Accountable Off-Policy Evaluation With Kernel Bellman Statistics
Authors: Yihao Feng, Tongzheng Ren, Ziyang Tang, Qiang Liu
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We consider off-policy evaluation (OPE), which evaluates the performance of a new policy from observed data collected from previous experiments, without requiring the execution of the new policy. This finds important applications in areas with high execution cost or safety concerns, such as medical diagnosis, recommendation systems and robotics. In practice, due to the limited information from off-policy data, it is highly desirable to construct rigorous confidence intervals, not just point estimation, for the policy performance. In this work, we propose a new variational framework which reduces the problem of calculating tight confidence bounds in OPE into an optimization problem on a feasible set that catches the true state-action value function with high probability. The feasible set is constructed by leveraging statistical properties of a recently proposed kernel Bellman loss (Feng et al., 2019). We design an efficient computational approach for calculating our bounds, and extend it to perform post-hoc diagnosis and correction for existing estimators. Empirical results show that our method yields tight confidence intervals in different settings.
Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data
Authors: Tamara Fernandez, Nicolas Rivera, Wenkai Xu, Arthur Gretton
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Survival Analysis and Reliability Theory are concerned with the analysis of time-to-event data, in which observations correspond to waiting times until an event of interest such as death from a particular disease or failure of a component in a mechanical system. This type of data is unique due to the presence of censoring, a type of missing data that occurs when we do not observe the actual time of the event of interest but, instead, we have access to an approximation for it given by random interval in which the observation is known to belong. Most traditional methods are not designed to deal with censoring, and thus we need to adapt them to censored time-to-event data. In this paper, we focus on non-parametric goodness-of-fit testing procedures based on combining the Stein’s method and kernelized discrepancies. While for uncensored data, there is a natural way of implementing a kernelized Stein discrepancy test, for censored data there are several options, each of them with different advantages and disadvantages. In this paper, we propose a collection of kernelized Stein discrepancy tests for time-to-event data, and we study each of them theoretically and empirically; our experimental results show that our proposed methods perform better than existing tests, including previous tests based on a kernelized maximum mean discrepancy.
Why Are Learned Indexes So Effective?
Authors: Paolo Ferragina, Fabrizio Lillo, Giorgio Vinciguerra
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: A recent trend in algorithm design consists of augmenting classic data structures with machine learning models, which are better suited to reveal and exploit patterns and trends in the input data so to achieve outstanding practical improvements in space occupancy and time efficiency. This is especially known in the context of indexing data structures where, despite few attempts in evaluating their asymptotic efficiency, theoretical results are yet missing in showing that learned indexes are provably better than classic indexes, such as B+ trees and their variants. In this paper, we present the first mathematically-grounded answer to this open problem. We obtain this result by discovering and exploiting a link between the original problem and a mean exit time problem over a proper stochastic process which, we show, is related to the space and time occupancy of those learned indexes. Our general result is then specialised to five well-known distributions: Uniform, Lognormal, Pareto, Exponential, and Gamma; and it is corroborated in precision and robustness by a large set of experiments.
Implicit Learning Dynamics in Stackelberg Games: Equilibria Characterization, Convergence Analysis, and Empirical Study
Authors: Tanner Fiez, Benjamin Chasnov, Lillian Ratliff
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Contemporary work on learning in continuous games has commonly overlooked the hierarchical decision-making structure present in machine learning problems formulated as games, instead treating them as simultaneous play games and adopting the Nash equilibrium solution concept. We deviate from this paradigm and provide a comprehensive study of learning in Stackelberg games. This work provides insights into the optimization landscape of zero-sum games by establishing connections between Nash and Stackelberg equilibria along with the limit points of simultaneous gradient descent. We derive novel gradient-based learning dynamics emulating the natural structure of a Stackelberg game using the implicit function theorem and provide convergence analysis for deterministic and stochastic updates for zero-sum and general-sum games. Notably, in zero-sum games using deterministic updates, we show the only critical points the dynamics converge to are Stackelberg equilibria and provide a local convergence rate. Empirically, our learning dynamics mitigate rotational behavior and exhibit benefits for training generative adversarial networks compared to simultaneous gradient descent.
Can Autonomous Vehicles Identify, Recover From, and Adapt to Distribution Shifts?
Authors: Angelos Filos, Panagiotis Tigkas, Rowan Mcallister, Nicholas Rhinehart, Sergey Levine, Yarin Gal
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Out-of-training-distribution (OOD) scenarios are a common challenge of learning agents at deployment, typically leading to arbitrary deductions and poorly-informed decisions. In principle, detection of and adaptation to OOD scenes can mitigate their adverse effects. In this paper, we highlight the limitations of current approaches to novel driving scenes and propose an epistemic uncertainty-aware planning method, called \emphrobust imitative planning (RIP). Our method can detect and recover from some distribution shifts, reducing the overconfident and catastrophic extrapolations in OOD scenes. If the model’s uncertainty is too great to suggest a safe course of action, the model can instead query the expert driver for feedback, enabling sample-efficient online adaptation, a variant of our method we term \emphadaptive robust imitative planning (AdaRIP). Our methods outperform current state-of-the-art approaches in the nuScenes \emphprediction challenge, but since no benchmark evaluating OOD detection and adaption currently exists to assess \emphcontrol, we introduce an autonomous car novel-scene benchmark, \textttCARNOVEL, to evaluate the robustness of driving agents to a suite of tasks with distribution shifts, where our methods outperform all the baselines.
How to Train Your Neural ODE: the World of Jacobian and Kinetic Regularization
Authors: Chris Finlay, Joern-Henrik Jacobsen, Levon Nurbekyan, Adam Oberman
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Training neural ODEs on large datasets has not been tractable due to the necessity of allowing the adaptive numerical ODE solver to refine its step size to very small values. In practice this leads to dynamics equivalent to many hundreds or even thousands of layers. In this paper, we overcome this apparent difficulty by introducing a theoretically-grounded combination of both optimal transport and stability regularizations which encourage neural ODEs to prefer simpler dynamics out of all the dynamics that solve a problem well. Simpler dynamics lead to faster convergence and to fewer discretizations of the solver, considerably decreasing wall-clock time without loss in performance. Our approach allows us to train neural ODE-based generative models to the same performance as the unregularized dynamics, with significant reductions in training time. This brings neural ODEs closer to practical relevance in large-scale applications.
Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
Authors: Marc Finzi, Samuel Stanton, Pavel Izmailov, Andrew Gordon Wilson
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: The translation equivariance of convolutional layers enables CNNs to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum.
Information Particle Filter Tree: An Online Algorithm for POMDPs with Belief-Based Rewards on Continuous Domains
Authors: Johannes Fischer, Ömer Sahin Tas
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Planning in Partially Observable Markov Decision Processes (POMDPs) inherently gathers the information necessary to act optimally under uncertainties. The framework can be extended to model pure information gathering tasks by considering belief-based rewards. This allows us to use reward shaping to guide POMDP planning to informative beliefs by using a weighted combination of the original reward and the expected information gain as the objective. In this work we propose a novel online algorithm, Information Particle Filter Tree (IPFT), to solve problems with belief-dependent rewards on continuous domains. It simulates particle-based belief trajectories in a Monte Carlo Tree Search (MCTS) approach to construct a search tree in the belief space. The evaluation shows that the consideration of information gain greatly improves the performance in problems where information gathering is an essential part of the optimal policy.
Topic Modeling via Full Dependence Mixtures
Authors: Dan Fisher, Mark Kozdoba, Shie Mannor
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: In this paper we introduce a new approach to topic modelling that scales to large datasets by using a compact representation of the data and by leveraging the GPU architecture. In this approach, topics are learned directly from the co-occurrence data of the corpus. In particular, we introduce a novel mixture model which we term the Full Dependence Mixture (FDM) model. FDMs model second moment under general generative assumptions on the data. While there is previous work on topic modeling using second moments, we develop a direct stochastic optimization procedure for fitting an FDM with a single Kullback Leibler objective. Moment methods in general have the benefit that an iteration no longer needs to scale with the size of the corpus. Our approach allows us to leverage standard optimizers and GPUs for the problem of topic modeling. In particular, we evaluate the approach on two large datasets, NeurIPS papers and a Twitter corpus, with a large number of topics, and show that the approach performs comparably or better than the standard benchmarks.
Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles
Authors: Dylan Foster, Alexander Rakhlin
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: A fundamental challenge in contextual bandits is to develop flexible, general-purpose algorithms with computational requirements no worse than classical supervised learning tasks such as classification and regression. Algorithms based on regression have shown promising empirical success, but theoretical guarantees have remained elusive except in special cases. We provide the first universal and optimal reduction from contextual bandits to online regression. We show how to transform any oracle for online regression with a given value function class into an algorithm for contextual bandits with the induced policy class, with no overhead in runtime or memory requirements. We characterize the minimax rates for contextual bandits with general, potentially nonparametric function classes, and show that our algorithm is minimax optimal whenever the oracle obtains the optimal rate for regression. Compared to previous results, our algorithm requires no distributional assumptions beyond realizability, and works even when contexts are chosen adversarially.
Logarithmic Regret for Adversarial Online Control
Authors: Dylan Foster, Max Simchowitz
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: We introduce a new algorithm for online linear-quadratic control in a known system subject to adversarial disturbances. Existing regret bounds for this setting scale as $\sqrtT$ unless strong stochastic assumptions are imposed on the disturbance process. We give the first algorithm with logarithmic regret for arbitrary adversarial disturbance sequences, provided the state and control costs are given by known quadratic functions. Our algorithm and analysis use a characterization for the optimal offline control law to reduce the online control problem to (delayed) online learning with approximate advantage functions. Compared to previous techniques, our approach does not need to control movement costs for the iterates, leading to logarithmic regret.
p-Norm Flow Diffusion for Local Graph Clustering
Authors: Kimon Fountoulakis, Di Wang, Shenghao Yang
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, semi-supervised learning, nodes ranking and feature inference. Prior work on local graph clustering mostly falls into two categories with numerical and combinatorial roots respectively, in this work we draw inspiration from both fields and propose a family of convex optimization formulations based on the idea of diffusion with $p$-norm network flow for $pın (1,ınfty)$. In the context of local clustering, we characterize the optimal solutions for these optimization problems and show their usefulness in finding low conductance cuts around input seed set. In particular, we achieve quadratic approximation of conductance in the case of $p=2$ similar to the Cheeger-type bounds of spectral methods, constant factor approximation when $pi̊ghtarrowınfty$ similar to max-flow based methods, and a smooth transition for general $p$ values in between. Thus, our optimization formulation can be viewed as bridging the numerical and combinatorial approaches, and we can achieve the best of both worlds in terms of speed and noise robustness. We show that the proposed problem can be solved in strongly local running time for $p\ge 2$ and conduct empirical evaluations on both synthetic and real-world graphs to illustrate our approach compares favorably with existing methods.
Stochastic Latent Residual Video Prediction
Authors: Jean-Yves Franceschi, Edouard Delasalles, Mickael Chen, Sylvain Lamprier, Patrick Gallinari
Published in: Proceedings of the 37th International Conference on Machine Learning (Main Conference Track), 2020

Abstract: Designing video prediction models that account for the inherent uncertainty of the future is challenging. Most works in the literature are based on stochastic image-autoregressive recurrent networks, which raises several performance and applicability issues. An alternative is to use fully latent temporal models which untie frame synthesis and temporal dynamics. However, no such model for stochastic video prediction has been proposed in the literature yet, due to design and training difficulties. In this paper, we overcome these difficulties by introducing a novel stochastic temporal model whose dynamics are governed in a latent space by a residual update rule. This first-order scheme is motivated by discretization schemes of differential equations. It naturally models video dynamics as it allows our simpler, more interpretable, latent model to outperform prior state-of-the-art methods on challenging datasets.