arXiv subjects

Simon Lacoste-Julien

Publications and source records attributed to Simon Lacoste-Julien.

At least 55 records · Page 3Linked to original sources

arXiv2022

Online Adversarial Attacks

Adversarial attacks expose important vulnerabilities of deep learning models, yet little attention has been paid to settings where data arrives as a stream. In this paper, we formalize the online adversarial attack problem, emphasizing two key elements found in real-world use-cases: attackers must operate under partial knowledge of the target model, and the decisions made by the attacker are irrevocable since they operate on a transient data stream. We first rigorously analyze a deterministic variant of the online threat model by drawing parallels to the well-studied $k$-secretary problem in theoretical computer science and propose Virtual+, a simple yet practical online algorithm. Our main theoretical result shows Virtual+ yields provably the best competitive ratio over all single-threshold algorithms for $k<5$ -- extending the previous analysis of the $k$-secretary problem. We also introduce the \textit{stochastic $k$-secretary} -- effectively reducing online blackbox transfer attacks to a $k$-secretary problem under noise -- and prove theoretical bounds on the performance of Virtual+ adapted to this setting. Finally, we complement our theoretical results by conducting experiments on MNIST, CIFAR-10, and Imagenet classifiers, revealing the necessity of online algorithms in achieving near-optimal performance and also the rich interplay between attack strategies and online attack selection, enabling simple strategies like FGSM to outperform stronger adversaries.

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arXiv2022

Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA

This work introduces a novel principle we call disentanglement via mechanism sparsity regularization, which can be applied when the latent factors of interest depend sparsely on past latent factors and/or observed auxiliary variables. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors and the sparse causal graphical model that relates them. We develop a rigorous identifiability theory, building on recent nonlinear independent component analysis (ICA) results, that formalizes this principle and shows how the latent variables can be recovered up to permutation if one regularizes the latent mechanisms to be sparse and if some graph connectivity criterion is satisfied by the data generating process. As a special case of our framework, we show how one can leverage unknown-target interventions on the latent factors to disentangle them, thereby drawing further connections between ICA and causality. We propose a VAE-based method in which the latent mechanisms are learned and regularized via binary masks, and validate our theory by showing it learns disentangled representations in simulations.

stat.ML↗

arXiv2022

Multiset-Equivariant Set Prediction with Approximate Implicit Differentiation

Most set prediction models in deep learning use set-equivariant operations, but they actually operate on multisets. We show that set-equivariant functions cannot represent certain functions on multisets, so we introduce the more appropriate notion of multiset-equivariance. We identify that the existing Deep Set Prediction Network (DSPN) can be multiset-equivariant without being hindered by set-equivariance and improve it with approximate implicit differentiation, allowing for better optimization while being faster and saving memory. In a range of toy experiments, we show that the perspective of multiset-equivariance is beneficial and that our changes to DSPN achieve better results in most cases. On CLEVR object property prediction, we substantially improve over the state-of-the-art Slot Attention from 8% to 77% in one of the strictest evaluation metrics because of the benefits made possible by implicit differentiation.

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arXiv2021

Convergence Rates for the MAP of an Exponential Family and Stochastic Mirror Descent -- an Open Problem

We consider the problem of upper bounding the expected log-likelihood sub-optimality of the maximum likelihood estimate (MLE), or a conjugate maximum a posteriori (MAP) for an exponential family, in a non-asymptotic way. Surprisingly, we found no general solution to this problem in the literature. In particular, current theories do not hold for a Gaussian or in the interesting few samples regime. After exhibiting various facets of the problem, we show we can interpret the MAP as running stochastic mirror descent (SMD) on the log-likelihood. However, modern convergence results do not apply for standard examples of the exponential family, highlighting holes in the convergence literature. We believe solving this very fundamental problem may bring progress to both the statistics and optimization communities.

stat.ML↗

arXiv2021

Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity

Two of the most prominent algorithms for solving unconstrained smooth games are the classical stochastic gradient descent-ascent (SGDA) and the recently introduced stochastic consensus optimization (SCO) [Mescheder et al., 2017]. SGDA is known to converge to a stationary point for specific classes of games, but current convergence analyses require a bounded variance assumption. SCO is used successfully for solving large-scale adversarial problems, but its convergence guarantees are limited to its deterministic variant. In this work, we introduce the expected co-coercivity condition, explain its benefits, and provide the first last-iterate convergence guarantees of SGDA and SCO under this condition for solving a class of stochastic variational inequality problems that are potentially non-monotone. We prove linear convergence of both methods to a neighborhood of the solution when they use constant step-size, and we propose insightful stepsize-switching rules to guarantee convergence to the exact solution. In addition, our convergence guarantees hold under the arbitrary sampling paradigm, and as such, we give insights into the complexity of minibatching.

cs.LG↗

arXiv2021

SVRG Meets AdaGrad: Painless Variance Reduction

Variance reduction (VR) methods for finite-sum minimization typically require the knowledge of problem-dependent constants that are often unknown and difficult to estimate. To address this, we use ideas from adaptive gradient methods to propose AdaSVRG, which is a more robust variant of SVRG, a common VR method. AdaSVRG uses AdaGrad in the inner loop of SVRG, making it robust to the choice of step-size. When minimizing a sum of n smooth convex functions, we prove that a variant of AdaSVRG requires $\tilde{O}(n + 1/ε)$ gradient evaluations to achieve an $O(ε)$-suboptimality, matching the typical rate, but without needing to know problem-dependent constants. Next, we leverage the properties of AdaGrad to propose a heuristic that adaptively determines the length of each inner-loop in AdaSVRG. Via experiments on synthetic and real-world datasets, we validate the robustness and effectiveness of AdaSVRG, demonstrating its superior performance over standard and other "tune-free" VR methods.

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arXiv2021

Parametric Adversarial Divergences are Good Losses for Generative Modeling

Parametric adversarial divergences, which are a generalization of the losses used to train generative adversarial networks (GANs), have often been described as being approximations of their nonparametric counterparts, such as the Jensen-Shannon divergence, which can be derived under the so-called optimal discriminator assumption. In this position paper, we argue that despite being "non-optimal", parametric divergences have distinct properties from their nonparametric counterparts which can make them more suitable for learning high-dimensional distributions. A key property is that parametric divergences are only sensitive to certain aspects/moments of the distribution, which depend on the architecture of the discriminator and the loss it was trained with. In contrast, nonparametric divergences such as the Kullback-Leibler divergence are sensitive to moments ignored by the discriminator, but they do not necessarily correlate with sample quality (Theis et al., 2016). Similarly, we show that mutual information can lead to unintuitive interpretations, and explore more intuitive alternatives based on parametric divergences. We conclude that parametric divergences are a flexible framework for defining statistical quantities relevant to a specific modeling task.

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arXiv2021

Structured Convolutional Kernel Networks for Airline Crew Scheduling

Motivated by the needs from an airline crew scheduling application, we introduce structured convolutional kernel networks (Struct-CKN), which combine CKNs from Mairal et al. (2014) in a structured prediction framework that supports constraints on the outputs. CKNs are a particular kind of convolutional neural networks that approximate a kernel feature map on training data, thus combining properties of deep learning with the non-parametric flexibility of kernel methods. Extending CKNs to structured outputs allows us to obtain useful initial solutions on a flight-connection dataset that can be further refined by an airline crew scheduling solver. More specifically, we use a flight-based network modeled as a general conditional random field capable of incorporating local constraints in the learning process. Our experiments demonstrate that this approach yields significant improvements for the large-scale crew pairing problem (50,000 flights per month) over standard approaches, reducing the solution cost by 17% (a gain of millions of dollars) and the cost of global constraints by 97%.

cs.LG↗

arXiv2021

Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates

Recent works have shown that stochastic gradient descent (SGD) achieves the fast convergence rates of full-batch gradient descent for over-parameterized models satisfying certain interpolation conditions. However, the step-size used in these works depends on unknown quantities and SGD's practical performance heavily relies on the choice of this step-size. We propose to use line-search techniques to automatically set the step-size when training models that can interpolate the data. In the interpolation setting, we prove that SGD with a stochastic variant of the classic Armijo line-search attains the deterministic convergence rates for both convex and strongly-convex functions. Under additional assumptions, SGD with Armijo line-search is shown to achieve fast convergence for non-convex functions. Furthermore, we show that stochastic extra-gradient with a Lipschitz line-search attains linear convergence for an important class of non-convex functions and saddle-point problems satisfying interpolation. To improve the proposed methods' practical performance, we give heuristics to use larger step-sizes and acceleration. We compare the proposed algorithms against numerous optimization methods on standard classification tasks using both kernel methods and deep networks. The proposed methods result in competitive performance across all models and datasets, while being robust to the precise choices of hyper-parameters. For multi-class classification using deep networks, SGD with Armijo line-search results in both faster convergence and better generalization.

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arXiv2021

Stochastic Polyak Step-size for SGD: An Adaptive Learning Rate for Fast Convergence

We propose a stochastic variant of the classical Polyak step-size (Polyak, 1987) commonly used in the subgradient method. Although computing the Polyak step-size requires knowledge of the optimal function values, this information is readily available for typical modern machine learning applications. Consequently, the proposed stochastic Polyak step-size (SPS) is an attractive choice for setting the learning rate for stochastic gradient descent (SGD). We provide theoretical convergence guarantees for SGD equipped with SPS in different settings, including strongly convex, convex and non-convex functions. Furthermore, our analysis results in novel convergence guarantees for SGD with a constant step-size. We show that SPS is particularly effective when training over-parameterized models capable of interpolating the training data. In this setting, we prove that SPS enables SGD to converge to the true solution at a fast rate without requiring the knowledge of any problem-dependent constants or additional computational overhead. We experimentally validate our theoretical results via extensive experiments on synthetic and real datasets. We demonstrate the strong performance of SGD with SPS compared to state-of-the-art optimization methods when training over-parameterized models.

math.OC↗

arXiv2021

Implicit Regularization via Neural Feature Alignment

We approach the problem of implicit regularization in deep learning from a geometrical viewpoint. We highlight a regularization effect induced by a dynamical alignment of the neural tangent features introduced by Jacot et al, along a small number of task-relevant directions. This can be interpreted as a combined mechanism of feature selection and compression. By extrapolating a new analysis of Rademacher complexity bounds for linear models, we motivate and study a heuristic complexity measure that captures this phenomenon, in terms of sequences of tangent kernel classes along optimization paths.

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arXiv2021

Repurposing Pretrained Models for Robust Out-of-domain Few-Shot Learning

Model-agnostic meta-learning (MAML) is a popular method for few-shot learning but assumes that we have access to the meta-training set. In practice, training on the meta-training set may not always be an option due to data privacy concerns, intellectual property issues, or merely lack of computing resources. In this paper, we consider the novel problem of repurposing pretrained MAML checkpoints to solve new few-shot classification tasks. Because of the potential distribution mismatch, the original MAML steps may no longer be optimal. Therefore we propose an alternative meta-testing procedure and combine MAML gradient steps with adversarial training and uncertainty-based stepsize adaptation. Our method outperforms "vanilla" MAML on same-domain and cross-domains benchmarks using both SGD and Adam optimizers and shows improved robustness to the choice of base stepsize.

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arXiv2021

Flight-connection Prediction for Airline Crew Scheduling to Construct Initial Clusters for OR Optimizer

We present a case study of using machine learning classification algorithms to initialize a large-scale commercial solver (GENCOL) based on column generation in the context of the airline crew pairing problem, where small savings of as little as 1% translate to increasing annual revenue by dozens of millions of dollars in a large airline. Under the imitation learning framework, we focus on the problem of predicting the next connecting flight of a crew, framed as a multiclass classification problem trained from historical data, and design an adapted neural network approach that achieves high accuracy (99.7% overall or 82.5% on harder instances). We demonstrate the usefulness of our approach by using simple heuristics to combine the flight-connection predictions to form initial crew-pairing clusters that can be fed in the GENCOL solver, yielding a 10x speed improvement and up to 0.2% cost saving.

cs.LG↗

arXiv2021

Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information

This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a methodology to quickly predict expected tactical descriptions of operational solutions (TDOSs). The problem we address occurs in the context of two-stage stochastic programming where the second stage is demanding computationally. We aim to predict at a high speed the expected TDOS associated with the second stage problem, conditionally on the first stage variables. This may be used in support of the solution to the overall two-stage problem by avoiding the online generation of multiple second stage scenarios and solutions. We formulate the tactical prediction problem as a stochastic optimal prediction program, whose solution we approximate with supervised machine learning. The training dataset consists of a large number of deterministic operational problems generated by controlled probabilistic sampling. The labels are computed based on solutions to these problems (solved independently and offline), employing appropriate aggregation and subselection methods to address uncertainty. Results on our motivating application on load planning for rail transportation show that deep learning models produce accurate predictions in very short computing time (milliseconds or less). The predictive accuracy is close to the lower bounds calculated based on sample average approximation of the stochastic prediction programs.

cs.LG↗

arXiv2021

An Analysis of the Adaptation Speed of Causal Models

Consider a collection of datasets generated by unknown interventions on an unknown structural causal model $G$. Recently, Bengio et al. (2020) conjectured that among all candidate models, $G$ is the fastest to adapt from one dataset to another, along with promising experiments. Indeed, intuitively $G$ has less mechanisms to adapt, but this justification is incomplete. Our contribution is a more thorough analysis of this hypothesis. We investigate the adaptation speed of cause-effect SCMs. Using convergence rates from stochastic optimization, we justify that a relevant proxy for adaptation speed is distance in parameter space after intervention. Applying this proxy to categorical and normal cause-effect models, we show two results. When the intervention is on the cause variable, the SCM with the correct causal direction is advantaged by a large factor. When the intervention is on the effect variable, we characterize the relative adaptation speed. Surprisingly, we find situations where the anticausal model is advantaged, falsifying the initial hypothesis. Code to reproduce experiments is available at https://github.com/remilepriol/causal-adaptation-speed

stat.ML↗

arXiv2021

Adaptive Gradient Methods Converge Faster with Over-Parameterization (but you should do a line-search)

Adaptive gradient methods are typically used for training over-parameterized models. To better understand their behaviour, we study a simplistic setting -- smooth, convex losses with models over-parameterized enough to interpolate the data. In this setting, we prove that AMSGrad with constant step-size and momentum converges to the minimizer at a faster $O(1/T)$ rate. When interpolation is only approximately satisfied, constant step-size AMSGrad converges to a neighbourhood of the solution at the same rate, while AdaGrad is robust to the violation of interpolation. However, even for simple convex problems satisfying interpolation, the empirical performance of both methods heavily depends on the step-size and requires tuning, questioning their adaptivity. We alleviate this problem by automatically determining the step-size using stochastic line-search or Polyak step-sizes. With these techniques, we prove that both AdaGrad and AMSGrad retain their convergence guarantees, without needing to know problem-dependent constants. Empirically, we demonstrate that these techniques improve the convergence and generalization of adaptive gradient methods across tasks, from binary classification with kernel mappings to multi-class classification with deep networks.

cs.LG↗

arXiv2021

Adversarial Example Games

The existence of adversarial examples capable of fooling trained neural network classifiers calls for a much better understanding of possible attacks to guide the development of safeguards against them. This includes attack methods in the challenging non-interactive blackbox setting, where adversarial attacks are generated without any access, including queries, to the target model. Prior attacks in this setting have relied mainly on algorithmic innovations derived from empirical observations (e.g., that momentum helps), lacking principled transferability guarantees. In this work, we provide a theoretical foundation for crafting transferable adversarial examples to entire hypothesis classes. We introduce Adversarial Example Games (AEG), a framework that models the crafting of adversarial examples as a min-max game between a generator of attacks and a classifier. AEG provides a new way to design adversarial examples by adversarially training a generator and a classifier from a given hypothesis class (e.g., architecture). We prove that this game has an equilibrium, and that the optimal generator is able to craft adversarial examples that can attack any classifier from the corresponding hypothesis class. We demonstrate the efficacy of AEG on the MNIST and CIFAR-10 datasets, outperforming prior state-of-the-art approaches with an average relative improvement of $29.9\%$ and $47.2\%$ against undefended and robust models (Table 2 & 3) respectively.

cs.LG↗

arXiv2020

Geometry-Aware Universal Mirror-Prox

Mirror-prox (MP) is a well-known algorithm to solve variational inequality (VI) problems. VI with a monotone operator covers a large group of settings such as convex minimization, min-max or saddle point problems. To get a convergent algorithm, the step-size of the classic MP algorithm relies heavily on the problem dependent knowledge of the operator such as its smoothness parameter which is hard to estimate. Recently, a universal variant of MP for smooth/bounded operators has been introduced that depends only on the norm of updates in MP. In this work, we relax the dependence to evaluating the norm of updates to Bregman divergence between updates. This relaxation allows us to extends the analysis of universal MP to the settings where the operator is not smooth or bounded. Furthermore, we analyse the VI problem with a stochastic monotone operator in different settings and obtain an optimal rate up to a logarithmic factor.

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