AISTATS 2022 论文列表

The PhD thesis of Maillard (2013) presents a rather obscure algorithm for the $K$-armed bandit problem. This less-known algorithm, which we call Maillard sampling (MS), computes the probability of choosing each arm in a closed form, which is not true for Thompson sampling, a widely-adopted bandit algorithm in the industry. This means that the bandit-logged data from running MS can be readily used for counterfactual evaluation, unlike Thompson sampling. Motivated by such merit, we revisit MS and perform an improved analysis to show that it achieves both the asymptotical optimality and $\sqrt{KT\log{T}}$ minimax regret bound where $T$ is the time horizon, which matches the known bounds for asymptotically optimal UCB. We then propose a variant of MS called MS$^+$ that improves its minimax bound to $\sqrt{KT\log{K}}$. MS$^+$ can also be tuned to be aggressive (i.e., less exploration) without losing the asymptotic optimality, a unique feature unavailable from existing bandit algorithms. Our numerical evaluation shows the effectiveness of MS$^+$.

An unresolved problem in Deep Learning is the ability of neural networks to cope with domain shifts during test-time, imposed by commonly fixing network parameters after training. Our proposed method Meta Test-Time Training (MT3), however, breaks this paradigm and enables adaption at test-time. We combine meta-learning, self-supervision and test-time training to learn to adapt to unseen test distributions. By minimizing the self-supervised loss, we learn task-specific model parameters for different tasks. A meta-model is optimized such that its adaption to the different task-specific models leads to higher performance on those tasks. During test-time a single unlabeled image is sufficient to adapt the meta-model parameters. This is achieved by minimizing only the self-supervised loss component resulting in a better prediction for that image. Our approach significantly improves the state-of-the-art results on the CIFAR-10-Corrupted image classification benchmark.

Post-deployment monitoring of ML systems is critical for ensuring reliability, especially as new user inputs can differ from the training distribution. Here we propose a novel approach, MLDemon, for ML DEployment MONitoring. MLDemon integrates both unlabeled data and a small amount of on-demand labels to produce a real-time estimate of the ML model’s current performance on a given data stream. Subject to budget constraints, MLDemon decides when to acquire additional, potentially costly, expert supervised labels to verify the model. On temporal datasets with diverse distribution drifts and models, MLDemon outperforms existing approaches. Moreover, we provide theoretical analysis to show that MLDemon is minimax rate optimal for a broad class of distribution drifts.

In this paper, we study the sharpness of a deep learning (DL) loss landscape around local minima in order to reveal systematic mechanisms underlying the generalization abilities of DL models. Our analysis is performed across varying network and optimizer hyper-parameters, and involves a rich family of different sharpness measures. We compare these measures and show that the low-pass filter based measure exhibits the highest correlation with the generalization abilities of DL models, has high robustness to both data and label noise, and furthermore can track the double descent behavior for neural networks. We next derive the optimization algorithm, relying on the low-pass filter (LPF), that actively searches the flat regions in the DL optimization landscape using SGD-like procedure. The update of the proposed algorithm, that we call LPF-SGD, is determined by the gradient of the convolution of the filter kernel with the loss function and can be efficiently computed using MC sampling. We empirically show that our algorithm achieves superior generalization performance compared to the common DL training strategies. On the theoretical front we prove that LPF-SGD converges to a better optimal point with smaller generalization error than SGD.

In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped with a measure of "inconsistency". We prove that many standard loss functions arise as the inconsistency of a natural PDG describing the appropriate scenario, and use the same approach to justify a well-known connection between regularizers and priors. We also show that the PDG inconsistency captures a large class of statistical divergences, and detail benefits of thinking of them in this way, including an intuitive visual language for deriving inequalities between them. In variational inference, we find that the ELBO, a somewhat opaque objective for latent variable models, and variants of it arise for free out of uncontroversial modeling assumptions—as do simple graphical proofs of their corresponding bounds. Finally, we observe that inconsistency becomes the log partition function (free energy) in the setting where PDGs are factor graphs.

Level set estimation (LSE) is the problem of identifying regions where an unknown function takes values above or below a specified threshold. Active sampling strategies for efficient LSE have primarily been studied in continuous-valued functions. Motivated by applications in human psychophysics where common experimental designs produce binary responses, we study LSE active sampling with Bernoulli outcomes. With Gaussian process classification surrogate models, the look-ahead model posteriors used by state-of-the-art continuous-output methods are intractable. However, we derive analytic expressions for look-ahead posteriors of sublevel set membership, and show how these lead to analytic expressions for a class of look-ahead LSE acquisition functions, including information-based methods. Benchmark experiments show the importance of considering the global look-ahead impact on the entire posterior. We demonstrate a clear benefit to using this new class of acquisition functions on benchmark problems, and on a challenging real-world task of estimating a high-dimensional contrast sensitivity function.

Second-order methods have shown state-of-the-art performance for optimizing deep neural networks. Nonetheless, their large memory requirement and high computational complexity, compared to first-order methods, hinder their versatility in a typical low-budget setup. This paper introduces a general framework of layerwise loss construction for multilayer neural networks that achieves a performance closer to second-order methods while utilizing first-order optimizers only. Our methodology lies upon a three-component loss, target, and regularizer combination, for which altering each component results in a new update rule. We provide examples using squared loss and layerwise Bregman divergences induced by the convex integral functions of various transfer functions. Our experiments on benchmark models and datasets validate the efficacy of our new approach, reducing the gap between first-order and second-order optimizers.

In this paper we prove that Local (S)GD (or FedAvg) can optimize deep neural networks with Rectified Linear Unit (ReLU) activation function in polynomial time. Despite the established convergence theory of Local SGD on optimizing general smooth functions in communication-efficient distributed optimization, its convergence on non-smooth ReLU networks still eludes full theoretical understanding. The key property used in many Local SGD analysis on smooth function is gradient Lipschitzness, so that the gradient on local models will not drift far away from that on averaged model. However, this decent property does not hold in networks with non-smooth ReLU activation function. We show that, even though ReLU network does not admit gradient Lipschitzness property, the difference between gradients on local models and average model will not change too much, under the dynamics of Local SGD. We validate our theoretical results via extensive experiments. This work is the first to show the convergence of Local SGD on non-smooth functions, and will shed lights on the optimization theory of federated training of deep neural networks.

We study the bilinearly coupled minimax problem: $\min_{x} \max_{y} f(x) + y^\top A x - h(y)$, where $f$ and $h$ are both strongly convex smooth functions and admit first-order gradient oracles. Surprisingly, no known first-order algorithms have hitherto achieved the lower complexity bound of $\Omega((\sqrt{\frac{L_x}{\mu_x}} + \frac{\|A\|}{\sqrt{\mu_x \mu_y}} + \sqrt{\frac{L_y}{\mu_y}}) \log(\frac1{\varepsilon}))$ for solving this problem up to an $\varepsilon$ primal-dual gap in the general parameter regime, where $L_x, L_y,\mu_x,\mu_y$ are the corresponding smoothness and strongly convexity constants. We close this gap by devising the first optimal algorithm, the Lifted Primal-Dual (LPD) method. Our method lifts the objective into an extended form that allows both the smooth terms and the bilinear term to be handled optimally and seamlessly with the same primal-dual framework. Besides optimality, our method yields a desirably simple single-loop algorithm that uses only one gradient oracle call per iteration. Moreover, when $f$ is just convex, the same algorithm applied to a smoothed objective achieves the nearly optimal iteration complexity. We also provide a direct single-loop algorithm, using the LPD method, that achieves the iteration complexity of $O(\sqrt{\frac{L_x}{\varepsilon}} + \frac{\|A\|}{\sqrt{\mu_y \varepsilon}} + \sqrt{\frac{L_y}{\varepsilon}})$. Numerical experiments on quadratic minimax problems and policy evaluation problems further demonstrate the fast convergence of our algorithm in practice.

The lifted junction tree algorithm (LJT) is an inference algorithm that allows for tractable inference regarding domain sizes. To answer multiple queries efficiently, it decomposes a first-order input model into a first-order junction tree. During inference, degrees of belief are propagated through the tree. This propagation significantly contributes to the runtime complexity not just of LJT but of any tree-based inference algorithm. We present a lifted propagation scheme based on the so-called Hugin scheme whose runtime complexity is independent of the degree of the tree. Thereby, lifted Hugin can achieve asymptotic speed improvements over the existing lifted Shafer-Shenoy propagation. An empirical evaluation confirms these results.

Label-scarce, high-dimensional domains such as healthcare present a challenge for modern machine learning techniques. To overcome the difficulties posed by a lack of labeled data, we explore an "order-contrastive" method for self-supervised pre-training on longitudinal data. We sample pairs of time segments, switch the order for half of them, and train a model to predict whether a given pair is in the correct order. Intuitively, the ordering task allows the model to attend to the least time-reversible features (for example, features that indicate progression of a chronic disease). The same features are often useful for downstream tasks of interest. To quantify this, we study a simple theoretical setting where we prove a finite-sample guarantee for the downstream error of a representation learned with order-contrastive pre-training. Empirically, in synthetic and longitudinal healthcare settings, we demonstrate the effectiveness of order-contrastive pre-training in the small-data regime over supervised learning and other self-supervised pre-training baselines. Our results indicate that pre-training methods designed for particular classes of distributions and downstream tasks can improve the performance of self-supervised learning.

Motivated by problems of ranking with partial information, we introduce a variant of the cascading bandit model that considers flexible length sequences with varying rewards and losses. We formulate two generative models for this problem within the generalized linear setting, and design and analyze upper confidence algorithms for it. Our analysis delivers tight regret bounds which, when specialized to standard cascading bandits, results in sharper guarantees than previously available in the literature. We evaluate our algorithms against a representative sample of cascading bandit baselines on a number of real-world datasets and show significantly improved empirical performance.

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers’ actions. This paper formulates a new game theoretic framework for this phenomenon, called multi-player performative prediction. We establish transparent sufficient conditions for strong monotonicity of the game and use them to develop algorithms for finding Nash equilibria. We investigate derivative free methods and adaptive gradient algorithms wherein each player alternates between learning a parametric description of their distribution and gradient steps on the empirical risk. Synthetic and semi-synthetic numerical experiments illustrate the results.

We introduce the “inverse bandit” problem of estimating the rewards of a multi-armed bandit instance from observing the learning process of a low-regret demonstrator. Existing approaches to the related problem of inverse reinforcement learning assume the execution of an optimal policy, and thereby suffer from an identifiability issue. In contrast, we propose to leverage the demonstrator’s behavior en route to optimality, and in particular, the exploration phase, for reward estimation. We begin by establishing a general information-theoretic lower bound under this paradigm that applies to any demonstrator algorithm, which characterizes a fundamental tradeoff between reward estimation and the amount of exploration of the demonstrator. Then, we develop simple and efficient reward estimators for upper-confidence-based demonstrator algorithms that attain the optimal tradeoff, showing in particular that consistent reward estimation—free of identifiability issues—is possible under our paradigm. Extensive simulations on both synthetic and semi-synthetic data corroborate our theoretical results.

Programmatic weak supervision creates models without hand-labeled training data by combining the outputs of heuristic labelers. Existing frameworks make the restrictive assumption that labelers output a single class label. Enabling users to create partial labelers that output subsets of possible class labels would greatly expand the expressivity of programmatic weak supervision. We introduce this capability by defining a probabilistic generative model that can estimate the underlying accuracies of multiple noisy partial labelers without ground truth labels. We show how to scale up learning, for example learning on 100k examples in one minute, a 300$\times$ speed up compared to a naive implementation. We also prove that this class of models is generically identifiable up to label swapping under mild conditions. We evaluate our framework on three text classification and six object classification tasks. On text tasks, adding partial labels increases average accuracy by 8.6 percentage points. On image tasks, we show that partial labels allow us to approach some zero-shot object classification problems with programmatic weak supervision by using class attributes as partial labelers. On these tasks, our framework has accuracy comparable to recent embedding-based zero-shot learning methods, while using only pre-trained attribute detectors.

In supervised learning, it is known that overparameterized neural networks with one hidden layer provably and efficiently learn and generalize, when trained using stochastic gradient descent with a sufficiently small learning rate and suitable initialization. In contrast, the benefit of overparameterization in unsupervised learning is not well understood. Normalizing flows (NFs) constitute an important class of models in unsupervised learning for sampling and density estimation. In this paper, we theoretically and empirically analyze these models when the underlying neural network is a one-hidden-layer overparametrized network. Our main contributions are two-fold: (1) On the one hand, we provide theoretical and empirical evidence that for constrained NFs (this class of NFs underlies most NF constructions) with the one-hidden-layer network, overparametrization hurts training. (2) On the other hand, we prove that unconstrained NFs, a recently introduced model, can efficiently learn any reasonable data distribution under minimal assumptions when the underlying network is overparametrized and has one hidden-layer.

We study the problem of learning a single neuron $\mathbf{x}\mapsto \sigma(\mathbf{w}^T\mathbf{x})$ with gradient descent (GD). All the existing positive results are limited to the case where $\sigma$ is monotonic. However, it is recently observed that non-monotonic activation functions outperform the traditional monotonic ones in many applications. To fill this gap, we establish learnability without assuming monotonicity. Specifically, when the input distribution is the standard Gaussian, we show that mild conditions on $\sigma$ (e.g., $\sigma$ has a dominating linear part) are sufficient to guarantee the learnability in polynomial time and polynomial samples. Moreover, with a stronger assumption on the activation function, the condition of input distribution can be relaxed to a non-degeneracy of the marginal distribution. We remark that our conditions on $\sigma$ are satisfied by practical non-monotonic activation functions, such as SiLU/Swish and GELU. We also discuss how our positive results are related to existing negative results on training two-layer neural networks.

We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different tasks, and do not consider the additional task-specific observable side information. In this work, we model the meta-parameter through an order-$3$ tensor, which can adapt to the observed task features of the task. We propose two methods to estimate the underlying tensor. The first method solves a tensor regression problem and works under natural assumptions on the data generating process. The second method uses the method of moments under additional distributional assumptions and has an improved sample complexity in terms of the number of tasks. We also focus on the meta-test phase, and consider estimating task-specific parameters on a new task. Substituting the estimated tensor from the first step allows us estimating the task-specific parameters with very few samples of the new task, thereby showing the benefits of learning tensor representations for meta-learning. Finally, through simulation and several real-world datasets, we evaluate our methods and show that it improves over previous linear models of shared representations for meta-learning.

Gaussian Bayesian networks are widely used to model causal interactions among continuous variables. In this work, we study the problem of learning a fixed-structure Gaussian Bayesian network up to a bounded error in total variation distance. We analyze the commonly used node-wise least squares regression LeastSquares and prove that it has the near-optimal sample complexity. We also study a couple of new algorithms for the problem: BatchAvgLeastSquares takes the average of several batches of least squares solutions at each node, so that one can interpolate between the batch size and the number of batches. We show that BatchAvgLeastSquares also has near-optimal sample complexity. CauchyEst takes the median of solutions to several batches of linear systems at each node. We show that the algorithm specialized to polytrees, CauchyEstTree, has near-optimal sample complexity. Experimentally, we show that for uncontaminated, realizable data, the LeastSquares algorithm performs best, but in the presence of contamination or DAG misspecification, CauchyEst/CauchyEstTree and BatchAvgLeastSquares respectively perform better.