arXiv research

Paper proposes an algorithm to solve complex minimax problems efficiently.

The paper analyzes generalization bounds for NC-SC/NC-C stochastic minimax optimization.

A new decentralized method solves minimax problems with reduced communication and sample complexity.

We study online convex optimization under stochastic sub-gradient observation faults, where we introduce adaptive algorithms with minimax optimal regret guarantees. We specifically study scenarios where our sub-gradient observations can be noisy or even completely missing in a stochastic manner. To this end, we propose…

Two algorithms solve nonconvex minimax problems with linear constraints, achieving complexity guarantees.

New analysis improves understanding of bilevel optimization stability and generalization.

Paper improves risk bounds for nonconvex-strongly-concave minimax problems.

New research shows existing information-theoretic methods can't establish minimax rates for gradient descent in stochastic convex optimization.

Choquet and minimax expectations are equivalent in European option pricing.

New algorithm solves federated minimax optimization problems.

The paper identifies network bottlenecks using minimax paths in stochastic networks.

Paper explores generalization of minimax learners, proposing a new metric.

Proves minimax sample complexity for turn-based stochastic games.

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

Optimal multistage method solves noisy minimax problems.

New methods solve complex optimization problems without strong convexity assumptions.

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

We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the number of stochastic subgradient evaluations needed to optimize either the functi…

This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply characterizing the stationary covariance matrix of this process. The…

Optimal algorithm for high-dimensional stochastic linear bandits with sparse parameters.

Study minimax-optimal rates for offline decision-making with function approximation.

In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately due to their applications in modern machine learning tasks. We first consider a …

Paper presents an efficient algorithm for learning minimax risk classifiers with large-scale data.

We propose the kl-UCB ++ algorithm for regret minimization in stochastic bandit models with exponential families of distributions. We prove that it is simultaneously asymptotically optimal (in the sense of Lai and Robbins' lower bound) and minimax optimal. This is the first algorithm proved to enjoy these two propertie…

New framework for DP-SMO with near-optimal privacy-loss trade-off.

Stochastic optimization improves semi-discrete OT map estimation with a minimax rate.

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…

We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and adaptive-gradient methods are (minimax) optimal and, conversely, when nonlinear updates -- su…

This paper analyzes neural networks for solving complex optimization problems.

AGDA and variance-reduced methods solve nonconvex-nonconcave minimax problems globally and faster.

VRPG algorithm optimizes convex constraints with non-asymptotic guarantees.

There are various parametric models for analyzing pairwise comparison data, including the Bradley-Terry-Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this work, we study a flexible model for pairwise comparisons, under which the probabilities of outcomes are requir…

Bayesian methods suffer from the problem of how to specify prior beliefs. One interesting idea is to consider worst-case priors. This requires solving a stochastic zero-sum game. In this paper, we extend well-known results from bandit theory in order to discover minimax-Bayes policies and discuss when they are practica…

We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for both arbitrary noise and stochastic noise settings. We also give matching minimax …

Paper tackles gradient-free minimax optimization with variance reduction for faster convergence.

New algorithms minimize regret in SSP with optimal sparse updates.

Paper proposes algorithms for solving nonconvex-nonconcave problems with complexity guarantees.

New random forest variants achieve optimal performance in high dimensions.

New algorithms ensure reproducibility and optimal convergence in convex optimization.

TiAda adapts adaptive gradient methods for nonconvex minimax optimization.

Study finds optimal regret bound for multi-armed bandit problem with expert advice.

New algorithm reduces worst-case regret for heavy-tailed bandits.

We consider nonconvex-concave minimax optimization problems of the form $\min_{\bf x}\max_{\bf y\in{\mathcal Y}} f({\bf x},{\bf y})$, where $f$ is strongly-concave in $\bf y$ but possibly nonconvex in $\bf x$ and ${\mathcal Y}$ is a convex and compact set. We focus on the stochastic setting, where we can only access an…

Develops high-probability minimax quantile bounds for statistical problems.

New algorithms improve convergence of minimax optimization.

New algorithm reduces bandit regret to log^3(T).

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

Kernel estimator optimally recovers function from noisy exponential Radon transform.