NeurIPS 2021 Papers

Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches. In this work, we seek to understand these issues in the simpler setting of linear regression (including both underparameterized and overparameterized regimes), where our goal is to make sharp instance-based comparisons of the implicit regularization afforded by (unregularized) average SGD with the explicit regularization of ridge regression. For a broad class of least squares problem instances (that are natural in high-dimensional settings), we show: (1) for every problem instance and for every ridge parameter, (unregularized) SGD, when provided with \emph{logarithmically} more samples than that provided to the ridge algorithm, generalizes no worse than the ridge solution (provided SGD uses a tuned constant stepsize); (2) conversely, there exist instances (in this wide problem class) where optimally-tuned ridge regression requires \emph{quadratically} more samples than SGD in order to have the same generalization performance. Taken together, our results show that, up to the logarithmic factors, the generalization performance of SGD is always no worse than that of ridge regression in a wide range of overparameterized problems, and, in fact, could be much better for some problem instances. More generally, our results show how algorithmic regularization has important consequences even in simpler (overparameterized) convex settings.

We study the generalization performance of $\text{\emph{full-batch}}$ optimization algorithms for stochastic convex optimization: these are first-order methods that only access the exact gradient of the empirical risk (rather than gradients with respect to individual data points), that include a wide range of algorithms such as gradient descent, mirror descent, and their regularized and/or accelerated variants. We provide a new separation result showing that, while algorithms such as stochastic gradient descent can generalize and optimize the population risk to within $\epsilon$ after $O(1/\epsilon^2)$ iterations, full-batch methods either need at least $\Omega(1/\epsilon^4)$ iterations or exhibit a dimension-dependent sample complexity.

Despite recent advances in its theoretical understanding, there still remains a significant gap in the ability of existing PAC-Bayesian theories on meta-learning to explain performance improvements in the few-shot learning setting, where the number of training examples in the target tasks is severely limited. This gap originates from an assumption in the existing theories which supposes that the number of training examples in the observed tasks and the number of training examples in the target tasks follow the same distribution, an assumption that rarely holds in practice. By relaxing this assumption, we develop two PAC-Bayesian bounds tailored for the few-shot learning setting and show that two existing meta-learning algorithms (MAML and Reptile) can be derived from our bounds, thereby bridging the gap between practice and PAC-Bayesian theories. Furthermore, we derive a new computationally-efficient PACMAML algorithm, and show it outperforms existing meta-learning algorithms on several few-shot benchmark datasets.

The goal of program synthesis from examples is to find a computer program that is consistent with a given set of input-output examples. Most learning-based approaches try to find a program that satisfies all examples at once. Our work, by contrast, considers an approach that breaks the problem into two stages: (a) find programs that satisfy only one example, and (b) leverage these per-example solutions to yield a program that satisfies all examples. We introduce the Cross Aggregator neural network module based on a multi-head attention mechanism that learns to combine the cues present in these per-example solutions to synthesize a global solution. Evaluation across programs of different lengths and under two different experimental settings reveal that when given the same time budget, our technique significantly improves the success rate over PCCoder [Zohar et. al 2018] and other ablation baselines.

Models like LASSO and ridge regression are extensively used in practice due to their interpretability, ease of use, and strong theoretical guarantees. Cross-validation (CV) is widely used for hyperparameter tuning in these models, but do practical methods minimize the true out-of-sample loss? A recent line of research promises to show that the optimum of the CV loss matches the optimum of the out-of-sample loss (possibly after simple corrections). It remains to show how tractable it is to minimize the CV loss. In the present paper, we show that, in the case of ridge regression, the CV loss may fail to be quasiconvex and thus may have multiple local optima. We can guarantee that the CV loss is quasiconvex in at least one case: when the spectrum of the covariate matrix is nearly flat and the noise in the observed responses is not too high. More generally, we show that quasiconvexity status is independent of many properties of the observed data (response norm, covariate-matrix right singular vectors and singular-value scaling) and has a complex dependence on the few that remain. We empirically confirm our theory using simulated experiments.

Representation learning has served as a key tool for meta-learning, enabling rapid learning of new tasks. Recent works like MAML learn task-specific representations by finding an initial representation requiring minimal per-task adaptation (i.e. a fine-tuning-based objective). We present a theoretical framework for analyzing a MAML-like algorithm, assuming all available tasks require approximately the same representation. We then provide risk bounds on predictors found by fine-tuning via gradient descent, demonstrating that the method provably leverages the shared structure. We illustrate these bounds in the logistic regression and neural network settings. In contrast, we establish settings where learning one representation for all tasks (i.e. using a "frozen representation" objective) fails. Notably, any such algorithm cannot outperform directly learning the target task with no other information, in the worst case. This separation underscores the benefit of fine-tuning-based over “frozen representation” objectives in few-shot learning.

Recognizing and localizing objects in the 3D space is a crucial ability for an AI agent to perceive its surrounding environment. While significant progress has been achieved with expensive LiDAR point clouds, it poses a great challenge for 3D object detection given only a monocular image. While there exist different alternatives for tackling this problem, it is found that they are either equipped with heavy networks to fuse RGB and depth information or empirically ineffective to process millions of pseudo-LiDAR points. With in-depth examination, we realize that these limitations are rooted in inaccurate object localization. In this paper, we propose a novel and lightweight approach, dubbed {\em Progressive Coordinate Transforms} (PCT) to facilitate learning coordinate representations. Specifically, a localization boosting mechanism with confidence-aware loss is introduced to progressively refine the localization prediction. In addition, semantic image representation is also exploited to compensate for the usage of patch proposals. Despite being lightweight and simple, our strategy allows us to establish a new state-of-the-art among the monocular 3D detectors on the competitive KITTI benchmark. At the same time, our proposed PCT shows great generalization to most coordinate-based 3D detection frameworks.

Collecting training data from untrusted sources exposes machine learning services to poisoning adversaries, who maliciously manipulate training data to degrade the model accuracy. When trained on offline datasets, poisoning adversaries have to inject the poisoned data in advance before training, and the order of feeding these poisoned batches into the model is stochastic. In contrast, practical systems are more usually trained/fine-tuned on sequentially captured real-time data, in which case poisoning adversaries could dynamically poison each data batch according to the current model state. In this paper, we focus on the real-time settings and propose a new attacking strategy, which affiliates an accumulative phase with poisoning attacks to secretly (i.e., without affecting accuracy) magnify the destructive effect of a (poisoned) trigger batch. By mimicking online learning and federated learning on MNIST and CIFAR-10, we show that model accuracy significantly drops by a single update step on the trigger batch after the accumulative phase. Our work validates that a well-designed but straightforward attacking strategy can dramatically amplify the poisoning effects, with no need to explore complex techniques.

Machine learning has successfully framed many sequential decision making problems as either supervised prediction, or optimal decision-making policy identification via reinforcement learning. In data-constrained offline settings, both approaches may fail as they assume fully optimal behavior or rely on exploring alternatives that may not exist. We introduce an inherently different approach that identifies "dead-ends" of a state space. We focus on patient condition in the intensive care unit, where a "medical dead-end" indicates that a patient will expire, regardless of all potential future treatment sequences. We postulate "treatment security" as avoiding treatments with probability proportional to their chance of leading to dead-ends, present a formal proof, and frame discovery as an RL problem. We then train three independent deep neural models for automated state construction, dead-end discovery and confirmation. Our empirical results discover that dead-ends exist in real clinical data among septic patients, and further reveal gaps between secure treatments and those administered.

Despite the potential of reinforcement learning (RL) for building general-purpose robotic systems, training RL agents to solve robotics tasks still remains challenging due to the difficulty of exploration in purely continuous action spaces. Addressing this problem is an active area of research with the majority of focus on improving RL methods via better optimization or more efficient exploration. An alternate but important component to consider improving is the interface of the RL algorithm with the robot. In this work, we manually specify a library of robot action primitives (RAPS), parameterized with arguments that are learned by an RL policy. These parameterized primitives are expressive, simple to implement, enable efficient exploration and can be transferred across robots, tasks and environments. We perform a thorough empirical study across challenging tasks in three distinct domains with image input and a sparse terminal reward. We find that our simple change to the action interface substantially improves both the learning efficiency and task performance irrespective of the underlying RL algorithm, significantly outperforming prior methods which learn skills from offline expert data.

In typical few-shot learning, each task is not equipped with enough data to be learned in isolation. To cope with such data scarcity, meta-representation learning methods train across many related tasks to find a shared (lower-dimensional) representation of the data where all tasks can be solved accurately. It is hypothesized that any new arriving tasks can be rapidly trained on this low-dimensional representation using only a few samples. Despite the practical successes of this approach, its statistical and computational properties are less understood. Moreover, the prescribed algorithms in these studies have little resemblance to those used in practice or they are computationally intractable. To understand and explain the success of popular meta-representation learning approaches such as ANIL, MetaOptNet, R2D2, and OML, we study a alternating gradient-descent minimization (AltMinGD) method (and its variant alternating minimization (AltMin)) which underlies the aforementioned methods. For a simple but canonical setting of shared linear representations, we show that AltMinGD achieves nearly-optimal estimation error, requiring only $\Omega(\mathrm{polylog}\,d)$ samples per task. This agrees with the observed efficacy of this algorithm in the practical few-shot learning scenarios.

A neural network model of a differential equation, namely neural ODE, has enabled the learning of continuous-time dynamical systems and probabilistic distributions with high accuracy. The neural ODE uses the same network repeatedly during a numerical integration. The memory consumption of the backpropagation algorithm is proportional to the number of uses times the network size. This is true even if a checkpointing scheme divides the computation graph into sub-graphs. Otherwise, the adjoint method obtains a gradient by a numerical integration backward in time. Although this method consumes memory only for a single network use, it requires high computational cost to suppress numerical errors. This study proposes the symplectic adjoint method, which is an adjoint method solved by a symplectic integrator. The symplectic adjoint method obtains the exact gradient (up to rounding error) with memory proportional to the number of uses plus the network size. The experimental results demonstrate that the symplectic adjoint method consumes much less memory than the naive backpropagation algorithm and checkpointing schemes, performs faster than the adjoint method, and is more robust to rounding errors.

We consider the following variant of contextual linear bandits motivated by routing applications in navigational engines and recommendation systems. We wish to learn a hidden $d$-dimensional value $w^*$. Every round, we are presented with a subset $\mathcal{X}_t \subseteq \mathbb{R}^d$ of possible actions. If we choose (i.e. recommend to the user) action $x_t$, we obtain utility $\langle x_t, w^* \rangle$ but only learn the identity of the best action $\arg\max_{x \in \X_t} \langle x, w^* \rangle$. We design algorithms for this problem which achieve regret $O(d\log T)$ and $\exp(O(d \log d))$. To accomplish this, we design novel cutting-plane algorithms with low “regret” -- the total distance between the true point $w^*$ and the hyperplanes the separation oracle returns. We also consider the variant where we are allowed to provide a list of several recommendations. In this variant, we give an algorithm with $O(d^2 \log d)$ regret and list size $\poly(d)$. Finally, we construct nearly tight algorithms for a weaker variant of this problem where the learner only learns the identity of an action that is better than the recommendation. Our results rely on new algorithmic techniques in convex geometry (including a variant of Steiner’s formula for the centroid of a convex set) which may be of independent interest.

Multi-label classification (MLC) allows complex dependencies among labels, making it more suitable to model many real-world problems. However, data annotation for training MLC models becomes much more labor-intensive due to the correlated (hence non-exclusive) labels and a potential large and sparse label space. We propose to conduct multi-label active learning (ML-AL) through a novel integrated Gaussian Process-Bayesian Bernoulli Mixture model (GP-B$^2$M) to accurately quantify a data sample's overall contribution to a correlated label space and choose the most informative samples for cost-effective annotation. In particular, the B$^2$M encodes label correlations using a Bayesian Bernoulli mixture of label clusters, where each mixture component corresponds to a global pattern of label correlations. To tackle highly sparse labels under AL, the B$^2$M is further integrated with a predictive GP to connect data features as an effective inductive bias and achieve a feature-component-label mapping. The GP predicts coefficients of mixture components that help to recover the final set of labels of a data sample. A novel auxiliary variable based variational inference algorithm is developed to tackle the non-conjugacy introduced along with the mapping process for efficient end-to-end posterior inference. The model also outputs a predictive distribution that provides both the label prediction and their correlations in the form of a label covariance matrix. A principled sampling function is designed accordingly to naturally capture both the feature uncertainty (through GP) and label covariance (through B$^2$M) for effective data sampling. Experiments on real-world multi-label datasets demonstrate the state-of-the-art AL performance of the proposed GP-B$^2$M model.

To train networks, lookahead algorithm~\cite{zhang2019lookahead} updates its fast weights $k$ times via an inner-loop optimizer before updating its slow weights once by using the latest fast weights. Any optimizer, e.g. SGD, can serve as the inner-loop optimizer, and the derived lookahead generally enjoys remarkable test performance improvement over the vanilla optimizer. But theoretical understandings on the test performance improvement of lookahead remain absent yet. To solve this issue, we theoretically justify the advantages of lookahead in terms of the excess risk error which measures the test performance. Specifically, we prove that lookahead using SGD as its inner-loop optimizer can better balance the optimization error and generalization error to achieve smaller excess risk error than vanilla SGD on (strongly) convex problems and nonconvex problems with Polyak-{\L}ojasiewicz condition which has been observed/proved in neural networks. Moreover, we show the stagewise optimization strategy~\cite{barshan2015stage} which decays learning rate several times during training can also benefit lookahead in improving its optimization and generalization errors on strongly convex problems. Finally, we propose a stagewise locally-regularized lookahead (SLRLA) algorithm which sums up the vanilla objective and a local regularizer to minimize at each stage and provably enjoys optimization and generalization improvement over the conventional (stagewise) lookahead. Experimental results on CIFAR10/100 and ImageNet testify its advantages. Codes is available at \url{https://github.com/sail-sg/SLRLA-optimizer}.

Continual learning (CL) is widely regarded as crucial challenge for lifelong AI. However, existing CL benchmarks, e.g. Permuted-MNIST and Split-CIFAR, make use of artificial temporal variation and do not align with or generalize to the real- world. In this paper, we introduce CLEAR, the first continual image classification benchmark dataset with a natural temporal evolution of visual concepts in the real world that spans a decade (2004-2014). We build CLEAR from existing large-scale image collections (YFCC100M) through a novel and scalable low-cost approach to visio-linguistic dataset curation. Our pipeline makes use of pretrained vision-language models (e.g. CLIP) to interactively build labeled datasets, which are further validated with crowd-sourcing to remove errors and even inappropriate images (hidden in original YFCC100M). The major strength of CLEAR over prior CL benchmarks is the smooth temporal evolution of visual concepts with real-world imagery, including both high-quality labeled data along with abundant unlabeled samples per time period for continual semi-supervised learning. We find that a simple unsupervised pre-training step can already boost state-of-the-art CL algorithms that only utilize fully-supervised data. Our analysis also reveals that mainstream CL evaluation protocols that train and test on iid data artificially inflate performance of CL system. To address this, we propose novel "streaming" protocols for CL that always test on the (near) future. Interestingly, streaming protocols (a) can simplify dataset curation since today’s testset can be repurposed for tomorrow’s trainset and (b) can produce more generalizable models with more accurate estimates of performance since all labeled data from each time-period is used for both training and testing (unlike classic iid train-test splits).

The (partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical efforts on multi-label ranking mainly focus on (Fisher) consistency analyses. However, there is a gap between existing theory and practice --- some inconsistent pairwise losses can lead to promising performance, while some consistent univariate losses usually have no clear superiority in practice. To take a step towards filling up this gap, this paper presents a systematic study from two complementary perspectives of consistency and generalization error bounds of learning algorithms. We theoretically find two key factors of the distribution (or dataset) that affect the learning guarantees of algorithms: the instance-wise class imbalance and the label size $c$. Specifically, in an extremely imbalanced case, the algorithm with the consistent univariate loss has an error bound of $O(c)$, while the one with the inconsistent pairwise loss depends on $O(\sqrt{c})$ as shown in prior work. This may shed light on the superior performance of pairwise methods in practice, where real datasets are usually highly imbalanced. Moreover, we present an inconsistent reweighted univariate loss-based algorithm that enjoys an error bound of $O(\sqrt{c})$ for promising performance as well as the computational efficiency of univariate losses. Finally, experimental results confirm our theoretical findings.

In Vision-and-Language Navigation (VLN) task, an agent is asked to navigate inside 3D indoor environments following given instructions. Cross-modal alignment is one of the most critical challenges in VLN because the predicted trajectory needs to match the given instruction accurately. In this paper, we address the cross-modal alignment challenge from the perspective of fine-grain. Firstly, to alleviate weak cross-modal alignment supervision from coarse-grained data, we introduce a human-annotated fine-grained VLN dataset, namely Landmark-RxR. Secondly, to further enhance local cross-modal alignment under fine-grained supervision, we investigate the focal-oriented rewards with soft and hard forms, by focusing on the critical points sampled from fine-grained Landmark-RxR. Moreover, to fully evaluate the navigation process, we also propose a re-initialization mechanism that makes metrics insensitive to difficult points, which can cause the agent to deviate from the correct trajectories. Experimental results show that our agent has superior navigation performance on Landmark-RxR, en-RxR and R2R. Our dataset and code are available at https://github.com/hekj/Landmark-RxR.

Contextual bandit algorithms are increasingly replacing non-adaptive A/B tests in e-commerce, healthcare, and policymaking because they can both improve outcomes for study participants and increase the chance of identifying good or even best policies. To support credible inference on novel interventions at the end of the study, nonetheless, we still want to construct valid confidence intervals on average treatment effects, subgroup effects, or value of new policies. The adaptive nature of the data collected by contextual bandit algorithms, however, makes this difficult: standard estimators are no longer asymptotically normally distributed and classic confidence intervals fail to provide correct coverage. While this has been addressed in non-contextual settings by using stabilized estimators, variance stabilized estimators in the contextual setting pose unique challenges that we tackle for the first time in this paper. We propose the Contextual Adaptive Doubly Robust (CADR) estimator, a novel estimator for policy value that is asymptotically normal under contextual adaptive data collection. The main technical challenge in constructing CADR is designing adaptive and consistent conditional standard deviation estimators for stabilization. Extensive numerical experiments using 57 OpenML datasets demonstrate that confidence intervals based on CADR uniquely provide correct coverage.