Related papers: K-Beam Minimax: Efficient Optimization for Deep Ad…
Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…
This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In…
State-of-the-art adversarial attacks are aimed at neural network classifiers. By default, neural networks use gradient descent to minimize their loss function. The gradient of a classifier's loss function is used by gradient-based…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
We relate the minimax game of generative adversarial networks (GANs) to finding the saddle points of the Lagrangian function for a convex optimization problem, where the discriminator outputs and the distribution of generator outputs play…
Many applications in machine learning can be framed as minimization problems and solved efficiently using gradient-based techniques. However, recent applications of generative models, particularly GANs, have triggered interest in solving…
Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…
From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Learning in multi-player games can model a large variety of practical scenarios, where each player seeks to optimize its own local objective function, which at the same time relies on the actions taken by others. Motivated by the frequent…
We study the $K$-Max combinatorial multi-armed bandits problem with continuous outcome distributions and weak value-index feedback: each base arm has an unknown continuous outcome distribution, and in each round the learning agent selects…
We provide the first oracle efficient sublinear regret algorithms for adversarial versions of the contextual bandit problem. In this problem, the learner repeatedly makes an action on the basis of a context and receives reward for the…
Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…
Adversarial attack has recently become a tremendous threat to deep learning models. To improve the robustness of machine learning models, adversarial training, formulated as a minimax optimization problem, has been recognized as one of the…
We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable,…
We fix a fundamental issue in the stochastic extragradient method by providing a new sampling strategy that is motivated by approximating implicit updates. Since the existing stochastic extragradient algorithm, called Mirror-Prox, of…
Minimax optimization recently is widely applied in many machine learning tasks such as generative adversarial networks, robust learning and reinforcement learning. In the paper, we study a class of nonconvex-nonconcave minimax optimization…
This paper addresses the bilinearly coupled minimax optimization problem: $\min_{x \in \mathbb{R}^{d_x}}\max_{y \in \mathbb{R}^{d_y}} \ f_1(x) + f_2(x) + y^{\top} Bx - g_1(y) - g_2(y)$, where $f_1$ and $g_1$ are smooth convex functions,…