arXiv research

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

ICCNLS models complex relationships as convex and concave components.

Optimizes bond portfolios to avoid worst-case losses.

Improved Frank-Wolfe algorithm solves saddle point problems efficiently.

Paper tackles partial label learning with self-guided retraining.

Optimizes portfolios using CPT utility via convex optimization.

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-…

Paper tackles fairness in automated decision-making systems.

OMWU shows last iterate convergence in convex-concave games.

The paper extends convexity results for translating solitons in higher dimensions.

Last iterate of Extragradient algorithm converges slower than averaged iterates in saddle point problems.

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

Faster rates achieved for computing equilibria in convex-concave games.

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

We reformulate LIPs as min-max problems for easier solution.

New method finds arbitrage opportunities in fluctuating asset bands.

Convex-constrained sparse additive models improve regression performance.

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…

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

Gradient method achieves linear convergence for saddle point problems without strong convexity.

Paper improves algorithms for convex-concave minimax optimization problems.

We define a class of $L$-convex-concave subsets of $\mathbb{R}P^3$, where $L$ is a projective line in $\mathbb{R}P^3$. These are sets whose sections by any plane containing $L$ are convex and concavely depend on this plane. We prove a version of Arnold hypothesis for these sets, namely we prove that each such set conta…

The paper tackles dictionary learning with almost sure error constraints.

Efficient method solves large-scale saddle point problems with parallel updates.

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

New analysis shows convergence rate of 1/k for gradient and extra-gradient methods.

New algorithms prove fast convergence in complex min-max problems.

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

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

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

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

A new algorithm solves minimax problems without needing parameters.

A new algorithm speeds up multi-agent reinforcement learning.

New algorithms solve convex-concave problems faster than previous methods.

Solves signal recovery from few linear measurements using convex duality.

DualIV simplifies non-linear IV regression via dual formulation.

Study shows a linear quadratic regulator's imitation learning converges globally.

APAC-Net solves high-dimensional stochastic MFGs using neural networks.

The paper relaxes assumptions for analyzing stochastic optimization algorithms.

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

Universal algorithm for variational inequalities adapts to smoothness and noise.

GradientDICE improves offline estimation for reinforcement learning policies.

This work analyzes how overparameterization aids GANs in reaching global saddle points.

The paper analyzes the GTD policy evaluation algorithms in Markov settings, providing finite sample bounds.

We prove a priori interior $C^{2,α}$ estimates for solutions of fully nonlinear elliptic equations of twisted type. For example, our estimates apply to equations of the type convex + concave. These results are particularly well suited to equations arising from elliptic regularization. As application, we obtain a new pr…

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

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

Paper tackles AUC maximization with deep neural networks for better classification of imbalanced data.