ICML 2019 Papers

We study robust distributed learning that involves minimizing a non-convex loss function with saddle points. We consider the Byzantine setting where some worker machines have abnormal or even arbitrary and adversarial behavior, and in this setting, the Byzantine machines may create fake local minima near a saddle point that is far away from any true local minimum, even when robust gradient estimators are used. We develop ByzantinePGD, a robust first-order algorithm that can provably escape saddle points and fake local minima, and converge to an approximate true local minimizer with low iteration complexity. As a by-product, we give a simpler algorithm and analysis for escaping saddle points in the usual non-Byzantine setting. We further discuss three robust gradient estimators that can be used in ByzantinePGD, including median, trimmed mean, and iterative filtering. We characterize their performance in concrete statistical settings, and argue for their near-optimality in low and high dimensional regimes.

The olfactory system employs an ensemble of odorant receptors (ORs) to sense odorants and to derive olfactory percepts. We trained artificial neural networks to represent the chemical space of odorants and used this representation to predict human olfactory percepts. We hypothesized that ORs may be considered 3D convolutional filters that extract molecular features and, as such, can be trained using machine learning methods. First, we trained a convolutional autoencoder, called DeepNose, to deduce a low-dimensional representation of odorant molecules which were represented by their 3D spatial structure. Next, we tested the ability of DeepNose features in predicting physical properties and odorant percepts based on 3D molecular structure alone. We found that, despite the lack of human expertise, DeepNose features often outperformed molecular descriptors used in computational chemistry in predicting both physical properties and human perceptions. We propose that DeepNose network can extract

Many reinforcement learning (RL) tasks provide the agent with high-dimensional observations that can be simplified into low-dimensional continuous states. To formalize this process, we introduce the concept of a \texit{DeepMDP}, a parameterized latent space model that is trained via the minimization of two tractable latent space losses: prediction of rewards and prediction of the distribution over next latent states. We show that the optimization of these objectives guarantees (1) the quality of the embedding function as a representation of the state space and (2) the quality of the DeepMDP as a model of the environment. Our theoretical findings are substantiated by the experimental result that a trained DeepMDP recovers the latent structure underlying high-dimensional observations on a synthetic environment. Finally, we show that learning a DeepMDP as an auxiliary task in the Atari 2600 domain leads to large performance improvements over model-free RL.

Many tasks, including language generation, benefit from learning the structure of the output space, particularly when the space of output labels is large and the data is sparse. State-of-the-art neural language models indirectly capture the output space structure in their classifier weights since they lack parameter sharing across output labels. Learning shared output label mappings helps, but existing methods have limited expressivity and are prone to overfitting. In this paper, we investigate the usefulness of more powerful shared mappings for output labels, and propose a deep residual output mapping with dropout between layers to better capture the structure of the output space and avoid overfitting. Evaluations on three language generation tasks show that our output label mapping can match or improve state-of-the-art recurrent and self-attention architectures, and suggest that the classifier does not necessarily need to be high-rank to better model natural language if it is better at capturing the structure of the output space.

We propose a framework to learn deep generative models via \textbf{V}ariational \textbf{Gr}adient Fl\textbf{ow} (VGrow) on probability spaces. The evolving distribution that asymptotically converges to the target distribution is governed by a vector field, which is the negative gradient of the first variation of the $f$-divergence between them. We prove that the evolving distribution coincides with the pushforward distribution through the infinitesimal time composition of residual maps that are perturbations of the identity map along the vector field. The vector field depends on the density ratio of the pushforward distribution and the target distribution, which can be consistently learned from a binary classification problem. Connections of our proposed VGrow method with other popular methods, such as VAE, GAN and flow-based methods, have been established in this framework, gaining new insights of deep generative learning. We also evaluated several commonly used divergences, including Kullback-Leibler, Jensen-Shannon, Jeffreys divergences as well as our newly discovered “logD” divergence which serves as the objective function of the logD-trick GAN. Experimental results on benchmark datasets demonstrate that VGrow can generate high-fidelity images in a stable and efficient manner, achieving competitive performance with state-of-the-art GANs.

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables to the model. Previous work in the DGP model has introduced noise additively, and used variational inference with a combination of sparse Gaussian processes and mean-field Gaussians for the approximate posterior. Additive noise attenuates the signal, and the Gaussian form of variational distribution may lead to an inaccurate posterior. We instead incorporate noisy variables as latent covariates, and propose a novel importance-weighted objective, which leverages analytic results and provides a mechanism to trade off computation for improved accuracy. Our results demonstrate that the importance-weighted objective works well in practice and consistently outperforms classical variational inference, especially for deeper models.

Producing probabilistic forecasts for large collections of similar and/or dependent time series is a practically highly relevant, yet challenging task. Classical time series models fail to capture complex patterns in the data and multivariate techniques struggle to scale to large problem sizes, but their reliance on strong structural assumptions makes them data-efficient and allows them to provide estimates of uncertainty. The converse is true for models based on deep neural networks, which can learn complex patterns and dependencies given enough data. In this paper, we propose a hybrid model that incorporates the benefits of both approaches. Our new method is data-driven and scalable via a latent, global, deep component. It also handles uncertainty through a local classical model. We provide both theoretical and empirical evidence for the soundness of our approach through a necessary and sufficient decomposition of exchangeable time series into a global and a local part and extensive experiments. Our experiments demonstrate the advantages of our model both in term of data efficiency and computational complexity.

Counterfactual Regret Minimization (CFR) is the leading algorithm for solving large imperfect-information games. It converges to an equilibrium by iteratively traversing the game tree. In order to deal with extremely large games, abstraction is typically applied before running CFR. The abstracted game is solved with tabular CFR, and its solution is mapped back to the full game. This process can be problematic because aspects of abstraction are often manual and domain specific, abstraction algorithms may miss important strategic nuances of the game, and there is a chicken-and-egg problem because determining a good abstraction requires knowledge of the equilibrium of the game. This paper introduces

Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. Unlike popular autoencoding models, reconstruction in CS is posed as an optimisation problem that is separate from sensing. CS is flexible and data efficient, but its application has been restricted by the strong assumption of sparsity and costly reconstruction process. A recent approach that combines CS with neural network generators has removed the constraint of sparsity, but reconstruction remains slow. Here we propose a novel framework that significantly improves both the performance and speed of signal recovery by jointly training a generator and the optimisation process for reconstruction via meta-learning. We explore training the measurements with different objectives, and derive a family of models based on minimising measurement errors. We show that Generative Adversarial Nets (GANs) can be viewed as a special case in this family of models. Borrowing insights from the CS perspective, we develop a novel way of improving GANs using gradient information from the discriminator.

The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to interpret the model in terms of the original features themselves. Our goal is to characterise how feature-level variation depends on latent low-dimensional representations, external covariates, and non-linear interactions between the two. In this paper, we propose to achieve this through a structured kernel decomposition in a hybrid Gaussian Process model which we call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We demonstrate the utility of our model on simulated examples and applications in disease progression modelling from high-dimensional gene expression data in the presence of additional phenotypes. In each setting we show how the c-GPLVM can extract low-dimensional structures from high-dimensional data sets whilst allowing a breakdown of feature-level variability that is not present in other commonly used dimensionality reduction approaches.

We consider decentralized stochastic optimization with the objective function (e.g. data samples for machine learning tasks) being distributed over n machines that can only communicate to their neighbors on a fixed communication graph. To address the communication bottleneck, the nodes compress (e.g. quantize or sparsify) their model updates. We cover both unbiased and biased compression operators with quality denoted by \delta <= 1 (\delta=1 meaning no compression). We (i) propose a novel gossip-based stochastic gradient descent algorithm, CHOCO-SGD, that converges at rate O(1/(nT) + 1/(T \rho^2 \delta)^2) for strongly convex objectives, where T denotes the number of iterations and \rho the eigengap of the connectivity matrix. We (ii) present a novel gossip algorithm, CHOCO-GOSSIP, for the average consensus problem that converges in time O(1/(\rho^2\delta) \log (1/\epsilon)) for accuracy \epsilon > 0. This is (up to our knowledge) the first gossip algorithm that supports arbitrary compressed messages for \delta > 0 and still exhibits linear convergence. We (iii) show in experiments that both of our algorithms do outperform the respective state-of-the-art baselines and CHOCO-SGD can reduce communication by at least two orders of magnitudes.

We consider the decentralized exploration problem: a set of players collaborate to identify the best arm by asynchronously interacting with the same stochastic environment. The objective is to insure privacy in the best arm identification problem between asynchronous, collaborative, and thrifty players. In the context of a digital service, we advocate that this decentralized approach allows a good balance between conflicting interests: the providers optimize their services, while protecting privacy of users and saving resources. We define the privacy level as the amount of information an adversary could infer by intercepting all the messages concerning a single user. We provide a generic algorithm DECENTRALIZED ELIMINATION, which uses any best arm identification algorithm as a subroutine. We prove that this algorithm insures privacy, with a low communication cost, and that in comparison to the lower bound of the best arm identification problem, its sample complexity suffers from a penalty depending on the inverse of the probability of the most frequent players. Then, thanks to the genericity of the approach, we extend the proposed algorithm to the non-stationary bandits. Finally, experiments illustrate and complete the analysis.

Many interesting applications of reinforcement learning (RL) involve MDPs that include numerous “dead-end" states. Upon reaching a dead-end state, the agent continues to interact with the environment in a dead-end trajectory before reaching an undesired terminal state, regardless of whatever actions are chosen. The situation is even worse when existence of many dead-end states is coupled with distant positive rewards from any initial state (we term this as Bridge Effect). Hence, conventional exploration techniques often incur prohibitively many training steps before convergence. To deal with the bridge effect, we propose a condition for exploration, called security. We next establish formal results that translate the security condition into the learning problem of an auxiliary value function. This new value function is used to cap “any" given exploration policy and is guaranteed to make it secure. As a special case, we use this theory and introduce secure random-walk. We next extend our results to the deep RL settings by identifying and addressing two main challenges that arise. Finally, we empirically compare secure random-walk with standard benchmarks in two sets of experiments including the Atari game of Montezuma’s Revenge.

As data becomes the fuel driving technological and economic growth, a fundamental challenge is how to quantify the value of data in algorithmic predictions and decisions. For example, in healthcare and consumer markets, it has been suggested that individuals should be compensated for the data that they generate, but it is not clear what is an equitable valuation for individual data. In this work, we develop a principled framework to address data valuation in the context of supervised machine learning. Given a learning algorithm trained on $n$ data points to produce a predictor, we propose data Shapley as a metric to quantify the value of each training datum to the predictor performance. Data Shapley uniquely satisfies several natural properties of equitable data valuation. We develop Monte Carlo and gradient-based methods to efficiently estimate data Shapley values in practical settings where complex learning algorithms, including neural networks, are trained on large datasets. In addition to being equitable, extensive experiments across biomedical, image and synthetic data demonstrate that data Shapley has several other benefits: 1) it is more powerful than the popular leave-one-out or leverage score in providing insight on what data is more valuable for a given learning task; 2) low Shapley value data effectively capture outliers and corruptions; 3) high Shapley value data inform what type of new data to acquire to improve the predictor.

Stochastic multi-armed bandits form a class of online learning problems that have important applications in online recommendation systems, adaptive medical treatment, and many others. Even though potential attacks against these learning algorithms may hijack their behavior, causing catastrophic loss in real-world applications, little is known about adversarial attacks on bandit algorithms. In this paper, we propose a framework of offline attacks on bandit algorithms and study convex optimization based attacks on several popular bandit algorithms. We show that the attacker can force the bandit algorithm to pull a target arm with high probability by a slight manipulation of the rewards in the data. Then we study a form of online attacks on bandit algorithms and propose an adaptive attack strategy against any bandit algorithm without the knowledge of the bandit algorithm. Our adaptive attack strategy can hijack the behavior of the bandit algorithm to suffer a linear regret with only a logarithmic cost to the attacker. Our results demonstrate a significant security threat to stochastic bandits.

We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of the Dirichlet process as a specific structural prior allows our model to circumvent issues associated with previous Gaussian process latent variable models. Inference is performed by deriving an efficient variational bound on the marginal log-likelihood of the model. We demonstrate the efficacy of our approach via analysis of discovered structure and superior quantitative performance on missing data imputation.

We present DL2, a system for training and querying neural networks with logical constraints. Using DL2, one can declaratively specify domain knowledge constraints to be enforced during training, as well as pose queries on the model to find inputs that satisfy a set of constraints. DL2 works by translating logical constraints into a loss function with desirable mathematical properties. The loss is then minimized with standard gradient-based methods. We evaluate DL2 by training networks with interesting constraints in unsupervised, semi-supervised and supervised settings. Our experimental evaluation demonstrates that DL2 is more expressive than prior approaches combining logic and neural networks, and its loss functions are better suited for optimization. Further, we show that for a number of queries, DL2 can find the desired inputs in seconds (even for large models such as ResNet-50 on ImageNet).

DBSCAN is a classical density-based clustering procedure with tremendous practical relevance. However, DBSCAN implicitly needs to compute the empirical density for each sample point, leading to a quadratic worst-case time complexity, which is too slow on large datasets. We propose DBSCAN++, a simple modification of DBSCAN which only requires computing the densities for a chosen subset of points. We show empirically that, compared to traditional DBSCAN, DBSCAN++ can provide not only competitive performance but also added robustness in the bandwidth hyperparameter while taking a fraction of the runtime. We also present statistical consistency guarantees showing the trade-off between computational cost and estimation rates. Surprisingly, up to a certain point, we can enjoy the same estimation rates while lowering computational cost, showing that DBSCAN++ is a sub-quadratic algorithm that attains minimax optimal rates for level-set estimation, a quality that may be of independent interest.