Gauthier Gidel

Université de Montréal | UdeM · Department of Computer Science and Operations Research

Deep learning has proven to be effective in a wide variety of loss minimization problems. However, many applications of interest, like minimizing projected Bellman error and min-max optimization, cannot be modelled as minimizing a scalar loss function but instead correspond to solving a variational inequality (VI) problem. This difference in settin...

Given two sets of elements (such as cell types and drug compounds), researchers typically only have access to a limited subset of their interactions. The task of causal imputation involves using this subset to predict unobserved interactions. Squires et al. (2022) have proposed two estimators for this task based on the synthetic interventions (SI)...

Predictions often influence the reality which they aim to predict, an effect known as performativity. Existing work focuses on accuracy maximization under this effect, but model deployment may have important unintended impacts, especially in multiagent scenarios. In this work, we investigate performative prediction in a concrete game-theoretic sett...

The rapid progress in generative models has resulted in impressive leaps in generation quality, blurring the lines between synthetic and real data. Web-scale datasets are now prone to the inevitable contamination by synthetic data, directly impacting the training of future generated models. Already, some theoretical results on self-consuming genera...

The Conditional Gradient (or Frank-Wolfe) method is one of the most well-known methods for solving constrained optimization problems appearing in various machine learning tasks. The simplicity of iteration and applicability to many practical problems helped the method to gain popularity in the community. In recent years, the Frank-Wolfe algorithm r...

Red-teaming, or identifying prompts that elicit harmful responses, is a critical step in ensuring the safe and responsible deployment of large language models (LLMs). Developing effective protection against many modes of attack prompts requires discovering diverse attacks. Automated red-teaming typically uses reinforcement learning to fine-tune an...

Large language models (LLMs) are vulnerable to adversarial attacks that can bypass their safety guardrails. In many domains, adversarial training has proven to be one of the most promising methods to reliably improve robustness against such attacks. Yet, in the context of LLMs, current methods for adversarial training are hindered by the high compu...

Current research in adversarial robustness of LLMs focuses on discrete input manipulations in the natural language space, which can be directly transferred to closed-source models. However , this approach neglects the steady progression of open-source models. As open-source models advance in capability, ensuring their safety also becomes increasing...

The AI4GCC competition presents a bold step forward in the direction of integrating machine learning with traditional economic policy analysis. Below, we highlight two potential areas for improvement that could enhance the competition's ability to identify and evaluate proposed negotiation protocols. Firstly, we suggest the inclusion of an addition...

Stochastic min-max optimization has gained interest in the machine learning community with the advancements in GANs and adversarial training. Although game optimization is fairly well understood in the deterministic setting, some issues persist in the stochastic regime. Recent work has shown that stochastic gradient descent-ascent methods such as t...

Most learning algorithms in machine learning rely on gradient descent to adjust model parameters, and a growing literature in computational neuroscience leverages these ideas to study synaptic plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes (i.e....

Certified defenses against adversarial attacks offer formal guarantees on the robustness of a model, making them more reliable than empirical methods such as adversarial training, whose effectiveness is often later reduced by unseen attacks. Still, the limited certified robustness that is currently achievable has been a bottleneck for their practic...

The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by large datasets for which the computation of the full gradient is prohibitively expensive. In this paper, we prese...

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard convergence results for finding a performatively stable classifier with the method of repeated risk minimization assum...

The past few years have seen impressive progress in the development of deep generative models capable of producing high-dimensional, complex, and photo-realistic data. However, current methods for evaluating such models remain incomplete: standard likelihood-based metrics do not always apply and rarely correlate with perceptual fidelity, while samp...

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity bounds are more accurate and less studied than in-expectation ones. However, SOTA high-probability non-asymptotic...

The extragradient method has recently gained increasing attention, due to its convergence behavior on smooth games. In $n$-player differentiable games, the eigenvalues of the Jacobian of the vector field are distributed on the complex plane, exhibiting more convoluted dynamics compared to classical (i.e., single player) minimization. In this work,...

Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim, 2021, Pethick et al., 2022] aiming at going beyond monotonicity by considering the weaker negative comonotoni...

Adaptive methods are a crucial component widely used for training generative adversarial networks (GANs). While there has been some work to pinpoint the "marginal value of adaptive methods" in standard tasks, it remains unclear why they are still critical for GAN training. In this paper, we formally study how adaptive methods help train GANs; inspi...

Computing the Jacobian of the solution of an optimization problem is a central problem in machine learning, with applications in hyperparameter optimization, meta-learning, optimization as a layer, and dataset distillation, to name a few. Unrolled differentiation is a popular heuristic that approximates the solution using an iterative solver and di...

This is the Proceedings of the ICML Expressive Vocalization (ExVo) Competition. The ExVo competition focuses on understanding and generating vocal bursts: laughs, gasps, cries, and other non-verbal vocalizations that are central to emotional expression and communication. ExVo 2022, included three competition tracks using a large-scale dataset of 59...

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,...

Real-world competitive games, such as chess, go, or StarCraft II, rely on Elo models to measure the strength of their players. Since these games are not fully transitive, using Elo implicitly assumes they have a strong transitive component that can correctly be identified and extracted. In this study, we investigate the challenge of identifying the...

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...

Stochastic first-order methods such as Stochastic Extragradient (SEG) or Stochastic Gradient Descent-Ascent (SGDA) for solving smooth minimax problems and, more generally, variational inequality problems (VIP) have been gaining a lot of attention in recent years due to the growing popularity of adversarial formulations in machine learning. However,...

Byzantine-robustness has been gaining a lot of attention due to the growth of the interest in collaborative and federated learning. However, many fruitful directions, such as the usage of variance reduction for achieving robustness and communication compression for reducing communication costs, remain weakly explored in the field. This work address...

The Past Extragradient (PEG) [Popov, 1980] method, also known as the Optimistic Gradient method, has known a recent gain in interest in the optimization community with the emergence of variational inequality formulations for machine learning. Recently, in the unconstrained case, Golowich et al. [2020] proved that a $O(1/N)$ last-iterate convergence...

We propose a new fast algorithm to estimate any sparse generalized linear model with convex or non-convex separable penalties. Our algorithm is able to solve problems with millions of samples and features in seconds, by relying on coordinate descent, working sets and Anderson acceleration. It handles previously unaddressed models, and is extensivel...

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, min...

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-q...

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, c...

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 der...

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 strateg...

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...

We study the stochastic bilinear minimax optimization problem, presenting an analysis of the Stochastic ExtraGradient (SEG) method with constant step size, and presenting variations of the method that yield favorable convergence. We first note that the last iterate of the basic SEG method only contracts to a fixed neighborhood of the Nash equilibri...

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...

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...

The existence of adversarial examples capable of fooling trained neural network classifiers calls for a much better understanding of possible attacks, in order to guide the development of safeguards against them. It includes attack methods in the highly challenging non-interactive blackbox setting, where adversarial attacks are generated without an...

This paper investigates the geometrical properties of real world games (e.g. Tic-Tac-Toe, Go, StarCraft II). We hypothesise that their geometrical structure resemble a spinning top, with the upright axis representing transitive strength, and the radial axis, which corresponds to the number of cycles that exist at a particular transitive strength, r...

Adversarial training, a special case of multi-objective optimization, is an increasingly useful tool in machine learning. For example, two-player zero-sum games are important for generative modeling (GANs) and for mastering games like Go or Poker via self-play. A classic result in Game Theory states that one must mix strategies, as pure equilibria...

We use matrix iteration theory to characterize acceleration in smooth games. We define the spectral shape of a family of games as the set containing all eigenvalues of the Jacobians of standard gradient dynamics in the family. Shapes restricted to the real line represent well-understood classes of problems, like minimization. Shapes spanning the co...

We study the effect of the stochastic gradient noise on the training of generative adversarial networks (GANs) and show that it can prevent the convergence of standard game optimization methods, while the batch version converges. We address this issue with a novel stochastic variance-reduced extragradient (SVRE) optimization algorithm, which for a...

Gradient descent is arguably one of the most popular online optimization methods with a wide array of applications. However, the standard implementation where agents simultaneously update their strategies yields several undesirable properties; strategies diverge away from equilibrium and regret grows over time. In this paper, we eliminate these neg...

Many recent machine learning tools rely on differentiable game formulations. While several numerical methods have been proposed for these types of games, most of the work has been on convergence proofs or on upper bounds for the rate of convergence of those methods. In this work, we approach the question of fundamental iteration complexity by provi...

We consider differentiable games: multi-objective minimization problems, where the goal is to find a Nash equilibrium. The machine learning community has recently started using extrapolation-based variants of the gradient method. A prime example is the extragradient, which yields linear convergence in cases like bilinear games, where the standard g...

Generative adversarial networks have been very successful in generative modeling, however they remain relatively hard to optimize compared to standard deep neural networks. In this paper, we try to gain insight into the optimization of GANs by looking at the game vector field resulting from the concatenation of the gradient of both players. Based o...

A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This ensures eigenvalues with unit norm and thus stable dynamics and training. However this comes at the cost of redu...

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 the ste...

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces biases that will lead to convergence to specific minimizers of the objective. Consequently, this choice can be cons...

Using large mini-batches when training generative adversarial networks (GANs) has been recently shown to significantly improve the quality of the generated samples. This can be seen as a simple but computationally expensive way of reducing the noise of the gradient estimates. In this paper, we investigate the effect of the noise in this context and...

Games generalize the optimization paradigm by introducing different objective functions for different optimizing agents, known as players. Generative Adversarial Networks (GANs) are arguably the most popular game formulation in recent machine learning literature. GANs achieve great results on generating realistic natural images, however they are kn...

Minimizing a function over an intersection of convex sets is an important task in optimization that is often much more challenging than minimizing it over each individual constraint set. While traditional methods such as Frank-Wolfe (FW) or proximal gradient descent assume access to a linear or quadratic oracle on the intersection, splitting techni...

We propose and analyze a novel adaptive step size variant of the Davis-Yin three operator splitting, a method that can solve optimization problems composed of a sum of a smooth term for which we have access to its gradient and an arbitrary number of potentially non-smooth terms for which we have access to their proximal operator. The proposed metho...

Stability has been a recurrent issue in training generative adversarial networks (GANs). One common way to tackle this issue has been to propose new formulations of the GAN objective. Yet, surprisingly few studies have looked at optimization methods specifically designed for this adversarial training. In this work, we review the "variational inequa...

Generative modeling of high dimensional data like images is a notoriously difficult and ill-defined problem. In particular, how to evaluate a learned generative model is unclear. In this position paper, we argue that adversarial learning, pioneered with generative adversarial networks (GANs), provides an interesting framework to implicitly define m...

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solver over polytopes, thereby par...