arXiv research

New algorithm AG-OG optimizes separable convex-concave problems efficiently.

Paper improves algorithms for convex-concave minimax optimization problems.

A new algorithm solves minimax problems without needing parameters.

We study the global convergence of generative adversarial imitation learning for linear quadratic regulators, which is posed as minimax optimization. To address the challenges arising from non-convex-concave geometry, we analyze the alternating gradient algorithm and establish its Q-linear rate of convergence to a uniq…

Optimistic method adapted for faster convex-concave min-max problems.

The paper analyzes how optimization algorithms affect the generalization of minimax models.

This paper resolves a longstanding open question pertaining to the design of near-optimal first-order algorithms for smooth and strongly-convex-strongly-concave minimax problems. Current state-of-the-art first-order algorithms find an approximate Nash equilibrium using $\tilde{O}(κ_{\mathbf x}+κ_{\mathbf y})$ or $\tild…

Paper proposes ZO-SMD for MERO, achieving optimal convergence rates.

New algorithms solve nonconvex-nonconcave minimax optimization problems.

New algorithms ensure reproducibility and optimal convergence in convex optimization.

This paper analyzes saddle points and minimax points in non-convex smooth games.

Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate convergence of simultaneous gradient descent (simGD) and its variants under the assump…

This paper tackles convex-submodular minimax problems in mixed continuous-discrete domains.

Improved FTPL algorithm reduces regret in predictable minimax games.

Paper proves Sion's theorem in geodesic spaces and develops a Riemannian extragradient method.

Paper establishes lower bounds for finite-sum optimization problems using novel construction methods.

New saddle network architectures preserve convex-concave geometry in optimization problems.

GAT-GMM improves GANs' performance in learning Gaussian mixture models.

Paper develops efficient algorithms for robust optimization across multiple groups.

This work finds mixed equilibria in machine learning problems using measures and simultaneous gradient ascent-descent.

This paper analyzes OGDA and EG methods for nonconvex minimax problems.

New algorithms solve monotone inclusions and convex-concave minimax problems.

Framework improves policy generalizability under biased training data.

New method finds arbitrage opportunities in fluctuating asset bands.

Riemannian algorithms converge at Euclidean rates for geodesically convex-concave problems.

New method GSAT improves robustness against structured perturbations.

This paper analyzes stability and generalization of Markov chain stochastic gradient methods.

While classic work in convex-concave min-max optimization relies on average-iterate convergence results, the emergence of nonconvex applications such as training Generative Adversarial Networks has led to renewed interest in last-iterate convergence guarantees. Proving last-iterate convergence is challenging because ma…

Proposes a risk parity portfolio optimization method that accounts for uncertainty in asset returns.

In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games. Specifically, \cite{DISZ17, LiangS18} show last iterate convergence of the so called "Optimistic Gradient Descent/Ascent" for the case of \t…

Improved algorithms for convex-concave min-max optimization and monotone variational inequalities.

We consider nonconvex-concave minimax problems, $\min_{\mathbf{x}} \max_{\mathbf{y} \in \mathcal{Y}} f(\mathbf{x}, \mathbf{y})$, where $f$ is nonconvex in $\mathbf{x}$ but concave in $\mathbf{y}$ and $\mathcal{Y}$ is a convex and bounded set. One of the most popular algorithms for solving this problem is the celebrated…

Optimizes bond portfolios to avoid worst-case losses.

We define a class of L-convex-concave subsets of $\Bbb{R}P^n$, where L is a projective subspace of dimension l in $\Bbb{R}P^n$. These are sets whose sections by any (l+1)-dimensional space L' containing L are convex and concavely depend on L'. We introduce an L-duality for these sets, and prove that the L-dual to an L-…

PURE-CD algorithm proves complexity bounds for convex-concave problems.

ICCNLS models complex relationships as convex and concave components.

Gradient Descent Ascent converges to von-Neumann solution in hidden zero-sum games.

We solve a complex optimization problem for Wasserstein barycenters using stochastic methods.

Paper introduces $\ell$-DER for regression tasks using morphological operators and convex-concave procedure.

In this paper we study the smooth convex-concave saddle point problem. Specifically, we analyze the last iterate convergence properties of the Extragradient (EG) algorithm. It is well known that the ergodic (averaged) iterates of EG converge at a rate of $O(1/T)$ (Nemirovski, 2004). In this paper, we show that the last…

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible parallel optimization for large-scale problems. Our method shares the efficiency an…

Optimizes portfolios using CPT utility via convex optimization.

A generalized optimistic method for saddle point problems with improved complexity.

We consider variational inequalities coming from monotone operators, a setting that includes convex minimization and convex-concave saddle-point problems. We assume an access to potentially noisy unbiased values of the monotone operators and assess convergence through a compatible gap function which corresponds to the …

Partial label learning deals with the problem where each training instance is assigned a set of candidate labels, only one of which is correct. This paper provides the first attempt to leverage the idea of self-training for dealing with partially labeled examples. Specifically, we propose a unified formulation with pro…

Generative Adversarial Imitation Learning (GAIL) is a powerful and practical approach for learning sequential decision-making policies. Different from Reinforcement Learning (RL), GAIL takes advantage of demonstration data by experts (e.g., human), and learns both the policy and reward function of the unknown environme…

Framework for worst-case generation using Wasserstein space optimization.

As has been observed by Morse \cite{Mo}, any generic vector field $v$ on a compact smooth manifold $X$ with boundary gives rise to a stratification of the boundary $\d X$ by compact submanifolds $\{\d_j^\pm X(v)\}_{1 \leq j \leq \dim(X)}$, where $\textup{codim}(\d_j^\pm X(v))= j$. Our main observation is that this stra…