arXiv research

Policy mirror ascent achieves Nash equilibrium in mean field games without a population generative model.

We present a new algorithm based on an gradient ascent for a general Active Exploration bandit problem in the fixed confidence setting. This problem encompasses several well studied problems such that the Best Arm Identification or Thresholding Bandits. It consists of a new sampling rule based on an online lazy mirror …

New algorithm for optimizing statistical utilities in bandits.

MoMA improves model-based RL by using unrestricted policy classes.

Method identifies mixed Nash equilibria in high dimensions for training mixtures of GANs.

A new framework improves reinforcement learning algorithms with policy guarantees.

OMWU shows last iterate convergence in convex-concave games.

Paper proposes MUCS for more reliable TDA in diffusion models.

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estim…

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

Improves posterior approximation speed for Dirichlet process mixture models.

Gradient ascent method successfully removes specific data points from neural networks without retraining.

Sequential coordinate ascent is more robust in high-dimensional linear regression.

Motivated by the pursuit of a systematic computational and algorithmic understanding of Generative Adversarial Networks (GANs), we present a simple yet unified non-asymptotic local convergence theory for smooth two-player games, which subsumes several discrete-time gradient-based saddle point dynamics. The analysis rev…

Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA) method has been implemented in various software packages, it has so far lacked go…

Stochastic dual coordinate ascent (SDCA) is an effective technique for solving regularized loss minimization problems in machine learning. This paper considers an extension of SDCA under the mini-batch setting that is often used in practice. Our main contribution is to introduce an accelerated mini-batch version of SDC…

New algorithm solves federated minimax optimization problems.

We introduce a proximal version of dual coordinate ascent method. We demonstrate how the derived algorithmic framework can be used for numerous regularized loss minimization problems, including $\ell_1$ regularization and structured output SVM. The convergence rates we obtain match, and sometimes improve, state-of-the-…

SoftAD improves classification accuracy with less fine-tuning and fewer computational costs.

Policy gradient aims to maximize expected return using gradient ascent.

New algorithm samples constrained distributions efficiently.

Algorithm improves variational inference in Wasserstein distance.

Paper introduces SGA for barycenter optimization in optimal transport.

Gradient descent-ascent converges to strict local minmax equilibria with a finite timescale separation.

Mirror flows converge to a limiting flow with a convex potential.

New mirror maps improve PMD performance in reinforcement learning.

Lazy neural networks are vulnerable to adversarial attacks.

We study the iteration complexity of the optimistic gradient descent-ascent (OGDA) method and the extra-gradient (EG) method for finding a saddle point of a convex-concave unconstrained min-max problem. To do so, we first show that both OGDA and EG can be interpreted as approximate variants of the proximal point method…

We describe mirror symmetry on higher dimensional tori, paying special attention to the behaviour of D-branes under mirror symmetry. To find the mirror D-branes the description of mirror symmetry on D-branes due to Ooguri, Oz en Yin is used. This method allows us to deal with the coisotropic D-branes recently introduce…

Derives Mirror Descent from gradient flow on a Riemannian manifold.

Paper proposes an algorithm to solve complex minimax problems efficiently.

In machine learning, Feature Selection (FS) is a major part of efficient algorithm. It fuels the algorithm and is the starting block for our prediction. In this paper, we present a new method, called Optimal Coordinate Ascent (OCA) that allows us selecting features among block and individual features. OCA relies on coo…

The stochastic dual coordinate-ascent (S-DCA) technique is a useful alternative to the traditional stochastic gradient-descent algorithm for solving large-scale optimization problems due to its scalability to large data sets and strong theoretical guarantees. However, the available S-DCA formulation is limited to finit…

Motivated by Strominger-Yau-Zaslow's mirror symmetry proposal and Kontsevich's homological mirror symmetry conjecture, we study mirror phenomena (in A-model) of certain results from Donaldson-Thomas theory for Calabi-Yau 4-folds.

Study homological mirror symmetry for Hirzebruch surfaces using Morse homotopy.

This paper deforms complex tori and their mirrors using gerbes.

Constructs mirror pairs for solvmanifolds using Lie groups.

We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups $G_2$ and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to twisted connected sum $G_2$ manifolds, mirrors of such Spin(7) manifolds can be fou…

Random scan CAVI converges linearly under log-concave assumptions.

Homological mirror symmetry for toric Fano surfaces using Morse homotopy.

New analysis shows GMD can converge linearly under PL-like conditions.

We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve state-of-the-art results for various key machine learning optimization problems including …

In this article we explore some finer properties of equi-areal mirrors and introduce techniques for developing new mirror surfaces that simultaneously minimize angular and areal distortion.

Mirror flow optimizes separable data problems, converging to a maximum margin classifier.

Study connects mirror symmetry invariants to K-stability for toric manifolds.

Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax optimization problem to global optimality, but are in practice successfully trained using stochastic gradient descent-ascent.…

Reparameterizes mirror descent as gradient descent for efficient sparse learning.

This paper focuses on a topological version on the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, the SYZ conjecture suggests that mirror pairs of Calabi-Yau manifolds are related by the existence of dual special Lagrangian torus fibrations. We explore this conjecture without reference to the special La…