NeurIPS 2019 Papers

Deep neural networks achieve stellar generalisation even when they have enough parameters to easily fit all their training data. We study this phenomenon by analysing the dynamics and the performance of over-parameterised two-layer neural networks in the teacher-student setup, where one network, the student, is trained on data generated by another network, called the teacher. We show how the dynamics of stochastic gradient descent (SGD) is captured by a set of differential equations and prove that this description is asymptotically exact in the limit of large inputs. Using this framework, we calculate the final generalisation error of student networks that have more parameters than their teachers. We find that the final generalisation error of the student increases with network size when training only the first layer, but stays constant or even decreases with size when training both layers. We show that these different behaviours have their root in the different solutions SGD finds for different activation functions. Our results indicate that achieving good generalisation in neural networks goes beyond the properties of SGD alone and depends on the interplay of at least the algorithm, the model architecture, and the data set.

We consider online forecasting problems for non-convex machine learning models. Forecasting introduces several challenges such as (i) frequent updates are necessary to deal with concept drift issues since the dynamics of the environment change over time, and (ii) the state of the art models are non-convex models. We address these challenges with a novel regret framework. Standard regret measures commonly do not consider both dynamic environment and non-convex models. We introduce a local regret for non-convex models in a dynamic environment. We present an update rule incurring a cost, according to our proposed local regret, which is sublinear in time T. Our update uses time-smoothed gradients. Using a real-world dataset we show that our time-smoothed approach yields several benefits when compared with state-of-the-art competitors: results are more stable against new data; training is more robust to hyperparameter selection; and our approach is more computationally efficient than the alternatives.

Motivated by pricing in ad exchange markets, we consider the problem of robust learning of reserve prices against strategic buyers in repeated contextual second-price auctions. Buyers' valuations \new{for} an item depend on the context that describes the item. However, the seller is not aware of the relationship between the context and buyers' valuations, i.e., buyers' preferences. The seller's goal is to design a learning policy to set reserve prices via observing the past sales data, and her objective is to minimize her regret for revenue, where the regret is computed against a clairvoyant policy that knows buyers' heterogeneous preferences. Given the seller's goal, utility-maximizing buyers have the incentive to bid untruthfully in order to manipulate the seller's learning policy. We propose two learning policies that are robust to such strategic behavior. These policies use the outcomes of the auctions, rather than the submitted bids, to estimate the preferences while controlling the long-term effect of the outcome of each auction on the future reserve prices. The first policy called Contextual Robust Pricing (CORP) is designed for the setting where the market noise distribution is known to the seller and achieves a T-period regret of $O(d\log(Td) \log (T))$, where $d$ is the dimension of {the} contextual information. The second policy, which is a variant of the first policy, is called Stable CORP (SCORP). This policy is tailored to the setting where the market noise distribution is unknown to the seller and belongs to an ambiguity set. We show that the SCORP policy has a T-period regret of $O(\sqrt{d\log(Td)}\;T^{2/3})$.

Brain-computer interfaces (BCIs) have enabled prosthetic device control by decoding motor movements from neural activities. Neural signals recorded from cortex exhibit nonstationary property due to abrupt noises and neuroplastic changes in brain activities during motor control. Current state-of-the-art neural signal decoders such as Kalman filter assume fixed relationship between neural activities and motor movements, thus will fail if this assumption is not satisfied. We propose a dynamic ensemble modeling (DyEnsemble) approach that is capable of adapting to changes in neural signals by employing a proper combination of decoding functions. The DyEnsemble method firstly learns a set of diverse candidate models. Then, it dynamically selects and combines these models online according to Bayesian updating mechanism. Our method can mitigate the effect of noises and cope with different task behaviors by automatic model switching, thus gives more accurate predictions. Experiments with neural data demonstrate that the DyEnsemble method outperforms Kalman filters remarkably, and its advantage is more obvious with noisy signals.

We study a variant of decision-theoretic online learning in which the set of experts that are available to Learner can shrink over time. This is a restricted version of the well-studied sleeping experts problem, itself a generalization of the fundamental game of prediction with expert advice. Similar to many works in this direction, our benchmark is the ranking regret. Various results suggest that achieving optimal regret in the fully adversarial sleeping experts problem is computationally hard. This motivates our relaxation where any expert that goes to sleep will never again wake up. We call this setting "dying experts" and study it in two different cases: the case where the learner knows the order in which the experts will die and the case where the learner does not. In both cases, we provide matching upper and lower bounds on the ranking regret in the fully adversarial setting. Furthermore, we present new, computationally efficient algorithms that obtain our optimal upper bounds.

In many real-world reinforcement learning applications, access to the environment is limited to a fixed dataset, instead of direct (online) interaction with the environment. When using this data for either evaluation or training of a new policy, accurate estimates of discounted stationary distribution ratios -- correction terms which quantify the likelihood that the new policy will experience a certain state-action pair normalized by the probability with which the state-action pair appears in the dataset -- can improve accuracy and performance. In this work, we propose an algorithm, DualDICE, for estimating these quantities. In contrast to previous approaches, our algorithm is agnostic to knowledge of the behavior policy (or policies) used to generate the dataset. Furthermore, our algorithm eschews any direct use of importance weights, thus avoiding potential optimization instabilities endemic of previous methods. In addition to providing theoretical guarantees, we present an empirical study of our algorithm applied to off-policy policy evaluation and find that our algorithm significantly improves accuracy compared to existing techniques.

Heterogeneous Face Recognition (HFR) is a challenging issue because of the large domain discrepancy and a lack of heterogeneous data. This paper considers HFR as a dual generation problem, and proposes a novel Dual Variational Generation (DVG) framework. It generates large-scale new paired heterogeneous images with the same identity from noise, for the sake of reducing the domain gap of HFR. Specifically, we first introduce a dual variational autoencoder to represent a joint distribution of paired heterogeneous images. Then, in order to ensure the identity consistency of the generated paired heterogeneous images, we impose a distribution alignment in the latent space and a pairwise identity preserving in the image space. Moreover, the HFR network reduces the domain discrepancy by constraining the pairwise feature distances between the generated paired heterogeneous images. Extensive experiments on four HFR databases show that our method can significantly improve state-of-the-art results. When using the generated paired images for training, our method gains more than 18\% True Positive Rate improvements over the baseline model when False Positive Rate is at $10^{-5}$.

Generalized zero-shot learning (GZSL) is a challenging class of vision and knowledge transfer problems in which both seen and unseen classes appear during testing. Existing GZSL approaches either suffer from semantic loss and discard discriminative information at the embedding stage, or cannot guarantee the visual-semantic interactions. To address these limitations, we propose a Dual Adversarial Semantics-Consistent Network (referred to as DASCN), which learns both primal and dual Generative Adversarial Networks (GANs) in a unified framework for GZSL. In DASCN, the primal GAN learns to synthesize inter-class discriminative and semantics-preserving visual features from both the semantic representations of seen/unseen classes and the ones reconstructed by the dual GAN. The dual GAN enforces the synthetic visual features to represent prior semantic knowledge well via semantics-consistent adversarial learning. To the best of our knowledge, this is the first work that employs a novel dual-GAN mechanism for GZSL. Extensive experiments show that our approach achieves significant improvements over the state-of-the-art approaches.

This paper explores the task of interactive image retrieval using natural language queries, where a user progressively provides input queries to refine a set of retrieval results. Moreover, our work explores this problem in the context of complex image scenes containing multiple objects. We propose Drill-down, an effective framework for encoding multiple queries with an efficient compact state representation that significantly extends current methods for single-round image retrieval. We show that using multiple rounds of natural language queries as input can be surprisingly effective to find arbitrarily specific images of complex scenes. Furthermore, we find that existing image datasets with textual captions can provide a surprisingly effective form of weak supervision for this task. We compare our method with existing sequential encoding and embedding networks, demonstrating superior performance on two proposed benchmarks: automatic image retrieval on a simulated scenario that uses region captions as queries, and interactive image retrieval using real queries from human evaluators.

Determinantal point processes (DPPs) provide an elegant and versatile way to sample sets of items that balance the point-wise quality with the set-wise diversity of selected items. For this reason, they have gained prominence in many machine learning applications that rely on subset selection. However, sampling from a DPP over a ground set of size N is a costly operation, requiring in general an O(N^3) preprocessing cost and an O(Nk^3) sampling cost for subsets of size k. We approach this problem by introducing DppNets: generative deep models that produce DPP-like samples for arbitrary ground sets. We develop an inhibitive attention mechanism based on transformer networks that captures a notion of dissimilarity between feature vectors. We show theoretically that such an approximation is sensible as it maintains the guarantees of inhibition or dissimilarity that makes DPPs so powerful and unique. Empirically, we show across multiple datasets that DPPNET is orders of magnitude faster than competing approaches for DPP sampling, while generating high-likelihood samples and performing as well as DPPs on downstream tasks.

Contextual multi-armed bandit algorithms are widely used in sequential decision tasks such as news article recommendation systems, web page ad placement algorithms, and mobile health. Most of the existing algorithms have regret proportional to a polynomial function of the context dimension, $d$. In many applications however, it is often the case that contexts are high-dimensional with only a sparse subset of size $s_0 (\ll d)$ being correlated with the reward. We consider the stochastic linear contextual bandit problem and propose a novel algorithm, namely the Doubly-Robust Lasso Bandit algorithm, which exploits the sparse structure of the regression parameter as in Lasso, while blending the doubly-robust technique used in missing data literature. The high-probability upper bound of the regret incurred by the proposed algorithm does not depend on the number of arms and scales with $\mathrm{log}(d)$ instead of a polynomial function of $d$. The proposed algorithm shows good performance when contexts of different arms are correlated and requires less tuning parameters than existing methods.

Modern distributed training of machine learning models often suffers from high communication overhead for synchronizing stochastic gradients and model parameters. In this paper, to reduce the communication complexity, we propose \emph{double quantization}, a general scheme for quantizing both model parameters and gradients. Three communication-efficient algorithms are proposed based on this general scheme. Specifically, (i) we propose a low-precision algorithm AsyLPG with asynchronous parallelism, (ii) we explore integrating gradient sparsification with double quantization and develop Sparse-AsyLPG, (iii) we show that double quantization can be accelerated by the momentum technique and design accelerated AsyLPG. We establish rigorous performance guarantees for the algorithms, and conduct experiments on a multi-server test-bed with real-world datasets to demonstrate that our algorithms can effectively save transmitted bits without performance degradation, and significantly outperform existing methods with either model parameter or gradient quantization.

In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware for rapid random projections which leverages the propagation of light in random media. A signal of interest $\mathbf{\xi} \in \mathbb{R}^N$ is mixed by a random scattering medium to compute the projection $\mathbf{y} = \mathbf{A} \mathbf{\xi}$, with $\mathbf{A} \in \mathbb{C}^{M \times N}$ being a realization of a standard complex Gaussian iid random matrix. Such optics-based matrix multiplications can be much faster and energy-efficient than their CPU or GPU counterparts, yet two difficulties must be resolved: only the intensity ${|\mathbf{y}|}^2$ can be recorded by the camera, and the transmission matrix $\mathbf{A}$ is unknown. We show that even without knowing $\mathbf{A}$, we can recover the unknown phase of $\mathbf{y}$ for some equivalent transmission matrix with the same distribution as $\mathbf{A}$. Our method is based on two observations: first, conjugating or changing the phase of any row of $\mathbf{A}$ does not change its distribution; and second, since we control the input we can interfere $\mathbf{\xi}$ with arbitrary reference signals. We show how to leverage these observations to cast the measurement phase retrieval problem as a Euclidean distance geometry problem. We demonstrate appealing properties of the proposed algorithm in both numerical simulations and real hardware experiments. Not only does our algorithm accurately recover the missing phase, but it mitigates the effects of quantization and the sensitivity threshold, thus improving the measured magnitudes.

Posterior collapse in Variational Autoencoders (VAEs) with uninformative priors arises when the variational posterior distribution closely matches the prior for a subset of latent variables. This paper presents a simple and intuitive explanation for posterior collapse through the analysis of linear VAEs and their direct correspondence with Probabilistic PCA (pPCA). We explain how posterior collapse may occur in pPCA due to local maxima in the log marginal likelihood. Unexpectedly, we prove that the ELBO objective for the linear VAE does not introduce additional spurious local maxima relative to log marginal likelihood. We show further that training a linear VAE with exact variational inference recovers a uniquely identifiable global maximum corresponding to the principal component directions. Empirically, we find that our linear analysis is predictive even for high-capacity, non-linear VAEs and helps explain the relationship between the observation noise, local maxima, and posterior collapse in deep Gaussian VAEs.

Existing state-of-the-art estimation systems can detect 2d poses of multiple people in images quite reliably. In contrast, 3d pose estimation from a single image is ill-posed due to occlusion and depth ambiguities. Assuming access to multiple cameras, or given an active system able to position itself to observe the scene from multiple viewpoints, reconstructing 3d pose from 2d measurements becomes well-posed within the framework of standard multi-view geometry. Less clear is what is an informative set of viewpoints for accurate 3d reconstruction, particularly in complex scenes, where people are occluded by others or by scene objects. In order to address the view selection problem in a principled way, we here introduce ACTOR, an active triangulation agent for 3d human pose reconstruction. Our fully trainable agent consists of a 2d pose estimation network (any of which would work) and a deep reinforcement learning-based policy for camera viewpoint selection. The policy predicts observation viewpoints, the number of which varies adaptively depending on scene content, and the associated images are fed to an underlying pose estimator. Importantly, training the policy requires no annotations - given a 2d pose estimator, ACTOR is trained in a self-supervised manner. In extensive evaluations on complex multi-people scenes filmed in a Panoptic dome, under multiple viewpoints, we compare our active triangulation agent to strong multi-view baselines, and show that ACTOR produces significantly more accurate 3d pose reconstructions. We also provide a proof-of-concept experiment indicating the potential of connecting our view selection policy to a physical drone observer.

Generalization capability to unseen domains is crucial for machine learning models when deploying to real-world conditions. We investigate the challenging problem of domain generalization, i.e., training a model on multi-domain source data such that it can directly generalize to target domains with unknown statistics. We adopt a model-agnostic learning paradigm with gradient-based meta-train and meta-test procedures to expose the optimization to domain shift. Further, we introduce two complementary losses which explicitly regularize the semantic structure of the feature space. Globally, we align a derived soft confusion matrix to preserve general knowledge of inter-class relationships. Locally, we promote domain-independent class-specific cohesion and separation of sample features with a metric-learning component. The effectiveness of our method is demonstrated with new state-of-the-art results on two common object recognition benchmarks. Our method also shows consistent improvement on a medical image segmentation task.

Recent work in variational inference (VI) has used ideas from Monte Carlo estimation to obtain tighter lower bounds on the log-likelihood to be used as objectives for VI. However, there is not a systematic understanding of how optimizing different objectives relates to approximating the posterior distribution. Developing such a connection is important if the ideas are to be applied to inference—i.e., applications that require an approximate posterior and not just an approximation of the log-likelihood. Given a VI objective defined by a Monte Carlo estimator of the likelihood, we use a "divide and couple" procedure to identify augmented proposal and target distributions so that the gap between the VI objective and the log-likelihood is equal to the divergence between these distributions. Thus, after maximizing the VI objective, the augmented variational distribution may be used to approximate the posterior distribution.

In deep reinforcement learning, policy optimization methods need to deal with issues such as function approximation and the reuse of off-policy data. Standard policy gradient methods do not handle off-policy data well, leading to premature convergence and instability. This paper introduces a method to stabilize policy optimization when off-policy data are reused. The idea is to include a Bregman divergence between the behavior policy that generates the data and the current policy to ensure small and safe policy updates with off-policy data. The Bregman divergence is calculated between the state distributions of two policies, instead of only on the action probabilities, leading to a divergence augmentation formulation. Empirical experiments on Atari games show that in the data-scarce scenario where the reuse of off-policy data becomes necessary, our method can achieve better performance than other state-of-the-art deep reinforcement learning algorithms.

Distributionally robust optimization (DRO) has attracted attention in machine learning due to its connections to regularization, generalization, and robustness. Existing work has considered uncertainty sets based on phi-divergences and Wasserstein distances, each of which have drawbacks. In this paper, we study DRO with uncertainty sets measured via maximum mean discrepancy (MMD). We show that MMD DRO is roughly equivalent to regularization by the Hilbert norm and, as a byproduct, reveal deep connections to classic results in statistical learning. In particular, we obtain an alternative proof of a generalization bound for Gaussian kernel ridge regression via a DRO lense. The proof also suggests a new regularizer. Our results apply beyond kernel methods: we derive a generically applicable approximation of MMD DRO, and show that it generalizes recent work on variance-based regularization.