Related papers: Accelerating Smooth Games by Manipulating Spectral…
The extragradient method has gained popularity due to its robust convergence properties for differentiable games. Unlike single-objective optimization, game dynamics involve complex interactions reflected by the eigenvalues of the game…
Advances in generative modeling and adversarial learning have given rise to renewed interest in smooth games. However, the absence of symmetry in the matrix of second derivatives poses challenges that are not present in the classical…
We investigate different aspects of area convexity [Sherman '17], a mysterious tool introduced to tackle optimization problems under the challenging $\ell_\infty$ geometry. We develop a deeper understanding of its relationship with more…
We design algorithms for minimizing $\max_{i\in[n]} f_i(x)$ over a $d$-dimensional Euclidean or simplex domain. When each $f_i$ is $1$-Lipschitz and $1$-smooth, our method computes an $\epsilon$-approximate solution using $\widetilde{O}(n…
The theory of integral quadratic constraints (IQCs) allows the certification of exponential convergence of interconnected systems containing nonlinear or uncertain elements. In this work, we adapt the IQC theory to study first-order methods…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a…
Box-simplex games are a family of bilinear minimax objectives which encapsulate graph-structured problems such as maximum flow [She17], optimal transport [JST19], and bipartite matching [AJJ+22]. We develop efficient near-linear time,…
The extensive-form game has been studied considerably in recent years. It can represent games with multiple decision points and incomplete information, and hence it is helpful in formulating games with uncertain inputs, such as poker. We…
In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…
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…
We develop primal-dual coordinate methods for solving bilinear saddle-point problems of the form $\min_{x \in \mathcal{X}} \max_{y\in\mathcal{Y}} y^\top A x$ which contain linear programming, classification, and regression as special cases.…
In this work, we establish a frequency-domain framework for analyzing gradient-based algorithms in linear minimax optimization problems; specifically, our approach is based on the Z-transform, a powerful tool applied in Control Theory and…
We present a performant gradient method for smooth convex optimization, drawing inspiration from several recent advances in the field. Our algorithm, the Adaptive Subgame Perfect Gradient Method (ASPGM) is based on the notion of subgame…
We consider differentiable games where the goal is to find a Nash equilibrium. The machine learning community has recently started using variants of the gradient method (GD). Prime examples are extragradient (EG), the optimistic gradient…
The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian methods and provide the first convergence guarantees for certain…
Game Theory studies situations in which multiple agents having conflicting objectives have to reach a collective decision. The question of a compact representation language for agents utility function is of crucial importance since the…
In the first part of this dissertation research, we develop a modular framework that can serve as a recipe for constructing and analyzing iterative algorithms for convex optimization. Specifically, our work casts optimization as iteratively…
Dynamic games are an effective paradigm for dealing with the control of multiple interacting actors. This paper introduces ALGAMES (Augmented Lagrangian GAME-theoretic Solver), a solver that handles trajectory optimization problems with…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…