ICML 2022 Papers

This paper shows how to adapt several simple and classical sampling-based algorithms for the k-means problem to the setting with outliers. Recently, Bhaskara et al. (NeurIPS 2019) showed how to adapt the classical k-means++ algorithm to the setting with outliers. However, their algorithm needs to output O(log(k)$\cdot$z) outliers, where z is the number of true outliers, to match the O(log k)-approximation guarantee of k-means++. In this paper, we build on their ideas and show how to adapt several sequential and distributed k-means algorithms to the setting with outliers, but with substantially stronger theoretical guarantees: our algorithms output (1 + $\epsilon$)z outliers while achieving an O(1/$\epsilon$)-approximation to the objective function. In the sequential world, we achieve this by adapting a recent algorithm of Lattanzi and Sohler (ICML 2019). In the distributed setting, we adapt a simple algorithm of Guha et al. (IEEE Trans. Know. and Data Engineering 2003) and the popular k-means\|{of} Bahmani et al. (PVLDB2012). A theoretical application of our techniques is an algorithm with running time O(nk^2/z) that achieves an O(1)-approximation to the objective function while outputting O(z) outliers, assuming k << z << n. This is complemented with a matching lower bound of $\Omega$(nk^2/z) for this problem in the oracle model.

Adaptive first-order methods in optimization have widespread ML applications due to their ability to adapt to non-convex landscapes. However, their convergence guarantees are typically stated in terms of vanishing gradient norms, which leaves open the issue of converging to undesirable saddle points (or even local maxima). In this paper, we focus on the AdaGrad family of algorithms - from scalar to full-matrix preconditioning - and we examine the question of whether the method’s trajectories avoid saddle points. A major challenge that arises here is that AdaGrad’s step-size (or, more accurately, the method’s preconditioner) evolves over time in a filtration-dependent way, i.e., as a function of all gradients observed in earlier iterations; as a result, avoidance results for methods with a constant or vanishing step-size do not apply. We resolve this challenge by combining a series of step-size stabilization arguments with a recursive representation of the AdaGrad preconditioner that allows us to employ center-stable techniques and ultimately show that the induced trajectories avoid saddle points from almost any initial condition.

It is well-known that deep learning models are vulnerable to adversarial examples. Existing studies of adversarial training have made great progress against this challenge. As a typical trait, they often assume that the class distribution is overall balanced. However, long-tail datasets are ubiquitous in a wide spectrum of applications, where the amount of head class instances is significantly larger than the tail classes. Under such a scenario, AUC is a much more reasonable metric than accuracy since it is insensitive toward class distribution. Motivated by this, we present an early trial to explore adversarial training methods to optimize AUC. The main challenge lies in that the positive and negative examples are tightly coupled in the objective function. As a direct result, one cannot generate adversarial examples without a full scan of the dataset. To address this issue, based on a concavity regularization scheme, we reformulate the AUC optimization problem as a saddle point problem, where the objective becomes an instance-wise function. This leads to an end-to-end training protocol. Furthermore, we provide a convergence guarantee of the proposed training algorithm. Our analysis differs from the existing studies since the algorithm is asked to generate adversarial examples by calculating the gradient of a min-max problem. Finally, the extensive experimental results show the performance and robustness of our algorithm in three long-tail datasets.

We consider an improper reinforcement learning setting where a learner is given $M$ base controllers for an unknown Markov decision process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. This can be useful in tuning across controllers, learnt possibly in mismatched or simulated environments, to obtain a good controller for a given target environment with relatively few trials. Towards this, we propose two algorithms: (1) a Policy Gradient-based approach; and (2) an algorithm that can switch between a simple Actor-Critic (AC) based scheme and a Natural Actor-Critic (NAC) scheme depending on the available information. Both algorithms operate over a class of improper mixtures of the given controllers. For the first case, we derive convergence rate guarantees assuming access to a gradient oracle. For the AC-based approach we provide convergence rate guarantees to a stationary point in the basic AC case and to a global optimum in the NAC case. Numerical results on (i) the standard control theoretic benchmark of stabilizing an inverted pendulum; and (ii) a constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when the base policies at its disposal are unstable.

We consider the classical problem of multi-class prediction with expert advice, but with an active learning twist. In this new setting the learner will only query the labels of a small number of examples, but still aims to minimize regret to the best expert as usual; the learner is also allowed a very short "burn-in" phase where it can fast-forward and query certain highly-informative examples. We design an algorithm that utilizes Hedge (aka Exponential Weights) as a subroutine, and we show that under a very particular combinatorial constraint on the matrix of expert predictions we can obtain a very strong regret guarantee while querying very few labels. This constraint, which we refer to as $\zeta$-compactness, or just compactness, can be viewed as a non-stochastic variant of the disagreement coefficient, another popular parameter used to reason about the sample complexity of active learning in the IID setting. We also give a polynomial-time algorithm to calculate the $\zeta$-compactness of a matrix up to an approximation factor of 3.

We propose simple active sampling and reweighting strategies for optimizing min-max fairness that can be applied to any classification or regression model learned via loss minimization. The key intuition behind our approach is to use at each timestep a datapoint from the group that is worst off under the current model for updating the model. The ease of implementation and the generality of our robust formulation make it an attractive option for improving model performance on disadvantaged groups. For convex learning problems, such as linear or logistic regression, we provide a fine-grained analysis, proving the rate of convergence to a min-max fair solution.

We introduce an algorithm for active function approximation based on nearest neighbor regression. Our Active Nearest Neighbor Regressor (ANNR) relies on the Voronoi-Delaunay framework from computational geometry to subdivide the space into cells with constant estimated function value and select novel query points in a way that takes the geometry of the function graph into account. We consider the recent state-of-the-art active function approximator called DEFER, which is based on incremental rectangular partitioning of the space, as the main baseline. The ANNR addresses a number of limitations that arise from the space subdivision strategy used in DEFER. We provide a computationally efficient implementation of our method, as well as theoretical halting guarantees. Empirical results show that ANNR outperforms the baseline for both closed-form functions and real-world examples, such as gravitational wave parameter inference and exploration of the latent space of a generative model.

To leverage the power of big data from source domains and overcome the scarcity of target domain samples, representation learning based on multi-task pretraining has become a standard approach in many applications. However, large-scale pretraining is often computationally expensive and not affordable for small organizations. When there is only one target task, most source tasks can be irrelevant, and we can actively sample a subset of source data from the most To leverage the power of big data from source tasks and overcome the scarcity of the target task samples, representation learning based on multi-task pretraining has become a standard approach in many applications. However, up until now, choosing which source tasks to include in the multi-task learning has been more art than science. In this paper, we give the first formal study on resource task sampling by leveraging the techniques from active learning. We propose an algorithm that iteratively estimates the relevance of each source task to the target task and samples from each source task based on the estimated relevance. Theoretically, we show that for the linear representation class, to achieve the same error rate, our algorithm can save up to a textit{number of source tasks} factor in the source task sample complexity, compared with the naive uniform sampling from all source tasks. We also provide experiments on real-world computer vision datasets to illustrate the effectiveness of our proposed method on both linear and convolutional neural network representation classes. We believe our paper serves as an important initial step to bring techniques from active learning to representation learning.

Investigating active learning, we focus on the relation between the number of labeled examples (budget size), and suitable querying strategies. Our theoretical analysis shows a behavior reminiscent of phase transition: typical examples are best queried when the budget is low, while unrepresentative examples are best queried when the budget is large. Combined evidence shows that a similar phenomenon occurs in common classification models. Accordingly, we propose TypiClust – a deep active learning strategy suited for low budgets. In a comparative empirical investigation of supervised learning, using a variety of architectures and image datasets, TypiClust outperforms all other active learning strategies in the low-budget regime. Using TypiClust in the semi-supervised framework, performance gets an even more significant boost. In particular, state-of-the-art semi-supervised methods trained on CIFAR-10 with 10 labeled examples selected by TypiClust, reach 93.2% accuracy – an improvement of 39.4% over random selection. Code is available at https://github.com/avihu111/TypiClust.

Perceived signals in real-world scenarios are usually high-dimensional and noisy, and finding and using their representation that contains essential and sufficient information required by downstream decision-making tasks will help improve computational efficiency and generalization ability in the tasks. In this paper, we focus on partially observable environments and propose to learn a minimal set of state representations that capture sufficient information for decision-making, termed Action-Sufficient state Representations (ASRs). We build a generative environment model for the structural relationships among variables in the system and present a principled way to characterize ASRs based on structural constraints and the goal of maximizing cumulative reward in policy learning. We then develop a structured sequential Variational Auto-Encoder to estimate the environment model and extract ASRs. Our empirical results on CarRacing and VizDoom demonstrate a clear advantage of learning and using ASRs for policy learning. Moreover, the estimated environment model and ASRs allow learning behaviors from imagined outcomes in the compact latent space to improve sample efficiency.

We consider a batch active learning scenario where the learner adaptively issues batches of points to a labeling oracle. Sampling labels in batches is highly desirable in practice due to the smaller number of interactive rounds with the labeling oracle (often human beings). However, batch active learning typically pays the price of a reduced adaptivity, leading to suboptimal results. In this paper we propose a solution which requires a careful trade off between the informativeness of the queried points and their diversity. We theoretically investigate batch active learning in the practically relevant scenario where the unlabeled pool of data is available beforehand (

With the fast development of algorithmic governance, fairness has become a compulsory property for machine learning models to suppress unintentional discrimination. In this paper, we focus on the pre-processing aspect for achieving fairness, and propose a data reweighing approach that only adjusts the weight for samples in the training phase. Different from most previous reweighing methods which usually assign a uniform weight for each (sub)group, we granularly model the influence of each training sample with regard to fairness-related quantity and predictive utility, and compute individual weights based on influence under the constraints from both fairness and utility. Experimental results reveal that previous methods achieve fairness at a non-negligible cost of utility, while as a significant advantage, our approach can empirically release the tradeoff and obtain cost-free fairness for equal opportunity. We demonstrate the cost-free fairness through vanilla classifiers and standard training processes, compared to baseline methods on multiple real-world tabular datasets. Code available at https://github.com/brandeis-machine-learning/influence-fairness.

Approximating a target probability distribution can be cast as an optimization problem where the objective functional measures the dissimilarity to the target. This optimization can be addressed by approximating Wasserstein and related gradient flows. In practice, these are simulated by interacting particle systems, whose stationary states define an empirical measure approximating the target distribution. This approach has been popularized recently to design sampling algorithms, e.g. Stein Variational Gradient Descent, or by minimizing the Maximum Mean or Kernel Stein Discrepancy. However, little is known about quantization properties of these approaches, i.e. how well is the target approximated by a finite number particles. We investigate this question theoretically and numerically. In particular, we prove general upper bounds on the quantization error of MMD and KSD at rates which significantly outperform quantization by i.i.d. samples. We conduct experiments which show that the particle systems at study achieve fast rates in practice, and notably outperform greedy algorithms, such as kernel herding. We compare different gradient flows and highlight their quantization rates. Furthermore we introduce a Normalized Stein Variational Gradient Descent and argue in favor of adaptive kernels, which exhibit faster convergence. Finally we compare the Gaussian and Laplace kernels and argue that the Laplace kernel provides a more robust quantization.

Even though Shapley value provides an effective explanation for a DNN model prediction, the computation relies on the enumeration of all possible input feature coalitions, which leads to the exponentially growing complexity. To address this problem, we propose a novel method SHEAR to significantly accelerate the Shapley explanation for DNN models, where only a few coalitions of input features are involved in the computation. The selection of the feature coalitions follows our proposed Shapley chain rule to minimize the absolute error from the ground-truth Shapley values, such that the computation can be both efficient and accurate. To demonstrate the effectiveness, we comprehensively evaluate SHEAR across multiple metrics including the absolute error from the ground-truth Shapley value, the faithfulness of the explanations, and running speed. The experimental results indicate SHEAR consistently outperforms state-of-the-art baseline methods across different evaluation metrics, which demonstrates its potentials in real-world applications where the computational resource is limited.

Bayesian optimization (BayesOpt) is a gold standard for query-efficient continuous optimization. However, its adoption for drug design has been hindered by the discrete, high-dimensional nature of the decision variables. We develop a new approach (LaMBO) which jointly trains a denoising autoencoder with a discriminative multi-task Gaussian process head, allowing gradient-based optimization of multi-objective acquisition functions in the latent space of the autoencoder. These acquisition functions allow LaMBO to balance the explore-exploit tradeoff over multiple design rounds, and to balance objective tradeoffs by optimizing sequences at many different points on the Pareto frontier. We evaluate LaMBO on two small-molecule design tasks, and introduce new tasks optimizing in silico and in vitro properties of large-molecule fluorescent proteins. In our experiments LaMBO outperforms genetic optimizers and does not require a large pretraining corpus, demonstrating that BayesOpt is practical and effective for biological sequence design.

The Approximate-Proximal Point (APROX) family of model-based stochastic optimization algorithms improve over standard stochastic gradient methods, as they are robust to step size choices, adaptive to problem difficulty, converge on a broader range of problems than stochastic gradient methods, and converge very fast on interpolation problems, all while retaining nice minibatching properties \cite{AsiDu19siopt,AsiChChDu20}. In this paper, we propose an acceleration scheme for the APROX family and provide non-asymptotic convergence guarantees, which are order-optimal in all problem-dependent constants and provide even larger minibatching speedups. For interpolation problems where the objective satisfies additional growth conditions, we show that our algorithm achieves linear convergence rates for a wide range of stepsizes. In this setting, we also prove matching lower bounds, identifying new fundamental constants and showing the optimality of the APROX family. We corroborate our theoretical results with empirical testing to demonstrate the gains accurate modeling, acceleration, and minibatching provide.

We propose computationally tractable accelerated first-order methods for Riemannian optimization, extending the Nesterov accelerated gradient (NAG) method. For both geodesically convex and geodesically strongly convex objective functions, our algorithms are shown to have the same iteration complexities as those for the NAG method on Euclidean spaces, under only standard assumptions. To the best of our knowledge, the proposed scheme is the first fully accelerated method for geodesically convex optimization problems. Our convergence analysis makes use of novel metric distortion lemmas as well as carefully designed potential functions. A connection with the continuous-time dynamics for modeling Riemannian acceleration in (Alimisis et al., 2020) is also identified by letting the stepsize tend to zero. We validate our theoretical results through numerical experiments.

The federated learning (FL) framework enables edge clients to collaboratively learn a shared inference model while keeping privacy of training data on clients. Recently, many heuristics efforts have been made to generalize centralized adaptive optimization methods, such as SGDM, Adam, AdaGrad, etc., to federated settings for improving convergence and accuracy. However, there is still a paucity of theoretical principles on where to and how to design and utilize adaptive optimization methods in federated settings. This work aims to develop novel adaptive optimization methods for FL from the perspective of dynamics of ordinary differential equations (ODEs). First, an analytic framework is established to build a connection between federated optimization methods and decompositions of ODEs of corresponding centralized optimizers. Second, based on this analytic framework, a momentum decoupling adaptive optimization method, FedDA, is developed to fully utilize the global momentum on each local iteration and accelerate the training convergence. Last but not least, full batch gradients are utilized to mimic centralized optimization in the end of the training process to ensure the convergence and overcome the possible inconsistency caused by adaptive optimization methods.

Concurrent algorithmic implementations of Stochastic Gradient Descent (SGD) give rise to critical questions for compute-intensive Machine Learning (ML). Asynchrony implies speedup in some contexts, and challenges in others, as stale updates may lead to slower, or non-converging executions. While previous works showed asynchrony-adaptiveness can improve stability and speedup by reducing the step size for stale updates according to static rules, there is no one-size-fits-all adaptation rule, since the optimal strategy depends on several factors. We introduce (i) $\mathtt{ASAP.SGD}$, an analytical framework capturing necessary and desired properties of staleness-adaptive step size functions and (ii) \textsc{tail}-$\tau$, a method for utilizing key properties of the