Minimax Theorem

The minimax theorem, fundamentally, concerns finding saddle points in functions of two variables, representing a balance between minimizing one variable and maximizing another. Current research focuses on extending the theorem's applicability beyond traditional convex-concave settings, exploring its use in diverse areas like robust reinforcement learning, statistical estimation under distribution shifts, and adversarial training in machine learning. This involves developing new theoretical frameworks, such as those based on geodesic metric spaces, and analyzing the properties of resulting algorithms, including their convergence rates and optimality. These advancements improve our understanding of optimization landscapes in complex systems and lead to more robust and reliable algorithms in various applications.

Papers

August 3, 2023

Statistical Estimation Under Distribution Shift: Wasserstein Perturbations and Minimax Theory
Patrick Chao, Edgar Dobriban
Distribution Shift Parameter Estimation Wasserstein Distortion Minimax Theorem

March 23, 2023

Connected Superlevel Set in (Deep) Reinforcement Learning and its Application to Minimax Theorems
Sihan Zeng, Thinh T. Doan, Justin Romberg
Reinforcement Learning Application Proficiency Policy Optimization Robust Reinforcement Learning Level Set Minimax Theorem

September 13, 2022

Calibrated Forecasts: The Minimax Proof
Sergiu Hart
Forecast Utterance Calibration Error Calibrated Prediction Simple Proof Minimax Theorem

June 18, 2022

Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classification
Natalie S. Frank, Jonathan Niles-Weed
Adversarial Attack Adversarial Training Adversarial Robustness Binary Classification Adversarial Risk Minimax Theorem Adversarial Surrogate

February 13, 2022

Sion's Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm
Peiyuan Zhang, Jingzhao Zhang, Suvrit Sra
Riemannian Gradient Minimax Problem Concave Saddle Point Problem Nonconvex Nonconcave Problem Geodesic Metric Space Minimax Theorem

Minimax Theorem

Papers

Statistical Estimation Under Distribution Shift: Wasserstein Perturbations and Minimax Theory

Connected Superlevel Set in (Deep) Reinforcement Learning and its Application to Minimax Theorems

Calibrated Forecasts: The Minimax Proof

Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classification

Sion's Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm