arXiv subjects

Gauthier Gidel

Publications and source records attributed to Gauthier Gidel.

At least 73 records · Page 4Linked to original sources

arXiv2022

Optimal Extragradient-Based Bilinearly-Coupled Saddle-Point Optimization

We consider the smooth convex-concave bilinearly-coupled saddle-point problem, $\min_{\mathbf{x}}\max_{\mathbf{y}}~F(\mathbf{x}) + H(\mathbf{x},\mathbf{y}) - G(\mathbf{y})$, where one has access to stochastic first-order oracles for $F$, $G$ as well as the bilinear coupling function $H$. Building upon standard stochastic extragradient analysis for variational inequalities, we present a stochastic \emph{accelerated gradient-extragradient (AG-EG)} descent-ascent algorithm that combines extragradient and Nesterov's acceleration in general stochastic settings. This algorithm leverages scheduled restarting to admit a fine-grained nonasymptotic convergence rate that matches known lower bounds by both \citet{ibrahim2020linear} and \citet{zhang2021lower} in their corresponding settings, plus an additional statistical error term for bounded stochastic noise that is optimal up to a constant prefactor. This is the first result that achieves such a relatively mature characterization of optimality in saddle-point optimization.

math.OC↗

arXiv2022

Generating Diverse Realistic Laughter for Interactive Art

We propose an interactive art project to make those rendered invisible by the COVID-19 crisis and its concomitant solitude reappear through the welcome melody of laughter, and connections created and explored through advanced laughter synthesis approaches. However, the unconditional generation of the diversity of human emotional responses in high-quality auditory synthesis remains an open problem, with important implications for the application of these approaches in artistic settings. We developed LaughGANter, an approach to reproduce the diversity of human laughter using generative adversarial networks (GANs). When trained on a dataset of diverse laughter samples, LaughGANter generates diverse, high quality laughter samples, and learns a latent space suitable for emotional analysis and novel artistic applications such as latent mixing/interpolation and emotional transfer.

cs.LG↗

arXiv2022

The ICML 2022 Expressive Vocalizations Workshop and Competition: Recognizing, Generating, and Personalizing Vocal Bursts

The ICML Expressive Vocalization (ExVo) Competition is focused on understanding and generating vocal bursts: laughs, gasps, cries, and other non-verbal vocalizations that are central to emotional expression and communication. ExVo 2022, includes three competition tracks using a large-scale dataset of 59,201 vocalizations from 1,702 speakers. The first, ExVo-MultiTask, requires participants to train a multi-task model to recognize expressed emotions and demographic traits from vocal bursts. The second, ExVo-Generate, requires participants to train a generative model that produces vocal bursts conveying ten different emotions. The third, ExVo-FewShot, requires participants to leverage few-shot learning incorporating speaker identity to train a model for the recognition of 10 emotions conveyed by vocal bursts. This paper describes the three tracks and provides performance measures for baseline models using state-of-the-art machine learning strategies. The baseline for each track is as follows, for ExVo-MultiTask, a combined score, computing the harmonic mean of Concordance Correlation Coefficient (CCC), Unweighted Average Recall (UAR), and inverted Mean Absolute Error (MAE) ($S_{MTL}$) is at best, 0.335 $S_{MTL}$; for ExVo-Generate, we report Fréchet inception distance (FID) scores ranging from 4.81 to 8.27 (depending on the emotion) between the training set and generated samples. We then combine the inverted FID with perceptual ratings of the generated samples ($S_{Gen}$) and obtain 0.174 $S_{Gen}$; and for ExVo-FewShot, a mean CCC of 0.444 is obtained.

eess.AS↗

arXiv2022

Generating Diverse Vocal Bursts with StyleGAN2 and MEL-Spectrograms

We describe our approach for the generative emotional vocal burst task (ExVo Generate) of the ICML Expressive Vocalizations Competition. We train a conditional StyleGAN2 architecture on mel-spectrograms of preprocessed versions of the audio samples. The mel-spectrograms generated by the model are then inverted back to the audio domain. As a result, our generated samples substantially improve upon the baseline provided by the competition from a qualitative and quantitative perspective for all emotions. More precisely, even for our worst-performing emotion (awe), we obtain an FAD of 1.76 compared to the baseline of 4.81 (as a reference, the FAD between the train/validation sets for awe is 0.776).

cs.SD↗

arXiv2022

Only Tails Matter: Average-Case Universality and Robustness in the Convex Regime

The recently developed average-case analysis of optimization methods allows a more fine-grained and representative convergence analysis than usual worst-case results. In exchange, this analysis requires a more precise hypothesis over the data generating process, namely assuming knowledge of the expected spectral distribution (ESD) of the random matrix associated with the problem. This work shows that the concentration of eigenvalues near the edges of the ESD determines a problem's asymptotic average complexity. This a priori information on this concentration is a more grounded assumption than complete knowledge of the ESD. This approximate concentration is effectively a middle ground between the coarseness of the worst-case scenario convergence and the restrictive previous average-case analysis. We also introduce the Generalized Chebyshev method, asymptotically optimal under a hypothesis on this concentration and globally optimal when the ESD follows a Beta distribution. We compare its performance to classical optimization algorithms, such as gradient descent or Nesterov's scheme, and we show that, in the average-case context, Nesterov's method is universally nearly optimal asymptotically.

math.OC↗

arXiv2022

On the Convergence of Stochastic Extragradient for Bilinear Games using Restarted Iteration Averaging

We study the stochastic bilinear minimax optimization problem, presenting an analysis of the same-sample Stochastic ExtraGradient (SEG) method with constant step size, and presenting variations of the method that yield favorable convergence. In sharp contrasts with the basic SEG method whose last iterate only contracts to a fixed neighborhood of the Nash equilibrium, SEG augmented with iteration averaging provably converges to the Nash equilibrium under the same standard settings, and such a rate is further improved by incorporating a scheduled restarting procedure. In the interpolation setting where noise vanishes at the Nash equilibrium, we achieve an optimal convergence rate up to tight constants. We present numerical experiments that validate our theoretical findings and demonstrate the effectiveness of the SEG method when equipped with iteration averaging and restarting.

math.OC↗

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.

cs.LG↗

arXiv2022

Extragradient Method: $O(1/K)$ Last-Iterate Convergence for Monotone Variational Inequalities and Connections With Cocoercivity

Extragradient method (EG) (Korpelevich, 1976) is one of the most popular methods for solving saddle point and variational inequalities problems (VIP). Despite its long history and significant attention in the optimization community, there remain important open questions about convergence of EG. In this paper, we resolve one of such questions and derive the first last-iterate $O(1/K)$ convergence rate for EG for monotone and Lipschitz VIP without any additional assumptions on the operator unlike the only known result of this type (Golowich et al., 2020) that relies on the Lipschitzness of the Jacobian of the operator. The rate is given in terms of reducing the squared norm of the operator. Moreover, we establish several results on the (non-)cocoercivity of the update operators of EG, Optimistic Gradient Method, and Hamiltonian Gradient Method, when the original operator is monotone and Lipschitz.

math.OC↗

arXiv2022

Stochastic Extragradient: General Analysis and Improved Rates

The Stochastic Extragradient (SEG) method is one of the most popular algorithms for solving min-max optimization and variational inequalities problems (VIP) appearing in various machine learning tasks. However, several important questions regarding the convergence properties of SEG are still open, including the sampling of stochastic gradients, mini-batching, convergence guarantees for the monotone finite-sum variational inequalities with possibly non-monotone terms, and others. To address these questions, in this paper, we develop a novel theoretical framework that allows us to analyze several variants of SEG in a unified manner. Besides standard setups, like Same-Sample SEG under Lipschitzness and monotonicity or Independent-Samples SEG under uniformly bounded variance, our approach allows us to analyze variants of SEG that were never explicitly considered in the literature before. Notably, we analyze SEG with arbitrary sampling which includes importance sampling and various mini-batching strategies as special cases. Our rates for the new variants of SEG outperform the current state-of-the-art convergence guarantees and rely on less restrictive assumptions.

math.OC↗

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

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.

cs.LG↗

arXiv2021

Convergence Analysis and Implicit Regularization of Feedback Alignment for Deep Linear Networks

We theoretically analyze the Feedback Alignment (FA) algorithm, an efficient alternative to backpropagation for training neural networks. We provide convergence guarantees with rates for deep linear networks for both continuous and discrete dynamics. Additionally, we study incremental learning phenomena for shallow linear networks. Interestingly, certain specific initializations imply that negligible components are learned before the principal ones, thus potentially negatively affecting the effectiveness of such a learning algorithm; a phenomenon we classify as implicit anti-regularization. We also provide initialization schemes where the components of the problem are approximately learned by decreasing order of importance, thus providing a form of implicit regularization.

cs.LG↗

arXiv2021

Pick Your Battles: Interaction Graphs as Population-Level Objectives for Strategic Diversity

Strategic diversity is often essential in games: in multi-player games, for example, evaluating a player against a diverse set of strategies will yield a more accurate estimate of its performance. Furthermore, in games with non-transitivities diversity allows a player to cover several winning strategies. However, despite the significance of strategic diversity, training agents that exhibit diverse behaviour remains a challenge. In this paper we study how to construct diverse populations of agents by carefully structuring how individuals within a population interact. Our approach is based on interaction graphs, which control the flow of information between agents during training and can encourage agents to specialise on different strategies, leading to improved overall performance. We provide evidence for the importance of diversity in multi-agent training and analyse the effect of applying different interaction graphs on the training trajectories, diversity and performance of populations in a range of games. This is an extended version of the long abstract published at AAMAS.

cs.AI↗

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.

cs.LG↗

arXiv2021

A single gradient step finds adversarial examples on random two-layers neural networks

Daniely and Schacham recently showed that gradient descent finds adversarial examples on random undercomplete two-layers ReLU neural networks. The term "undercomplete" refers to the fact that their proof only holds when the number of neurons is a vanishing fraction of the ambient dimension. We extend their result to the overcomplete case, where the number of neurons is larger than the dimension (yet also subexponential in the dimension). In fact we prove that a single step of gradient descent suffices. We also show this result for any subexponential width random neural network with smooth activation function.

cs.LG↗

arXiv2021

A Limited-Capacity Minimax Theorem for Non-Convex Games or: How I Learned to Stop Worrying about Mixed-Nash and Love Neural Nets

Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in reinforcement learning which have been applied to complex games such as Go or Poker. In practice, a \emph{single} pair of networks is typically trained in order to find an approximate equilibrium of a highly nonconcave-nonconvex adversarial problem. However, while a classic result in game theory states such an equilibrium exists in concave-convex games, there is no analogous guarantee if the payoff is nonconcave-nonconvex. Our main contribution is to provide an approximate minimax theorem for a large class of games where the players pick neural networks including WGAN, StarCraft II, and Blotto Game. Our findings rely on the fact that despite being nonconcave-nonconvex with respect to the neural networks parameters, these games are concave-convex with respect to the actual models (e.g., functions or distributions) represented by these neural networks.

stat.ML↗

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

Linear Lower Bounds and Conditioning of Differentiable Games

Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we approach the question of fundamental iteration complexity by providing lower bounds to complement the linear (i.e. geometric) upper bounds observed in the literature on a wide class of problems. We cast saddle-point and min-max problems as 2-player games. We leverage tools from single-objective convex optimisation to propose new linear lower bounds for convex-concave games. Notably, we give a linear lower bound for $n$-player differentiable games, by using the spectral properties of the update operator. We then propose a new definition of the condition number arising from our lower bound analysis. Unlike past definitions, our condition number captures the fact that linear rates are possible in games, even in the absence of strong convexity or strong concavity in the variables.

cs.LG↗