# Hybrid Block Successive Approximation for One-Sided Non-Convex Min-Max Problems: Algorithms and Applications

arXiv: https://arxiv.org/abs/1902.08294 · HTML: https://mlsanity.com/paper/1902.08294/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2019.

## Built on by (most cited first, 30 of 55)

- [Independent Policy Gradient Methods for Competitive Reinforcement Learning](https://mlsanity.com/paper/2101.04233/) (2021)
- [Faster Single-loop Algorithms for Minimax Optimization without Strong Concavity](https://mlsanity.com/paper/2112.05604/) (2021)
- [Federated Minimax Optimization: Improved Convergence Analyses and Algorithms](https://mlsanity.com/paper/2203.04850/) (2022)
- [Complexity Lower Bounds for Nonconvex-Strongly-Concave Min-Max Optimization](https://mlsanity.com/paper/2104.08708/) (2021)
- [Efficiently Escaping Saddle Points in Bilevel Optimization](https://mlsanity.com/paper/2202.03684/) (2022)
- [Proximal Gradient Descent-Ascent: Variable Convergence under KL Geometry](https://mlsanity.com/paper/2102.04653/) (2021)
- [Adversarial Examples can be Effective Data Augmentation for Unsupervised Machine Learning](https://mlsanity.com/paper/2103.01895/) (2021)
- [Nest Your Adaptive Algorithm for Parameter-Agnostic Nonconvex Minimax Optimization](https://mlsanity.com/paper/2206.00743/) (2022)
- [Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization](https://mlsanity.com/paper/2408.11974/) (2024)
- [Accelerating Inexact HyperGradient Descent for Bilevel Optimization](https://mlsanity.com/paper/2307.00126/) (2023)
- [Distributed Distributionally Robust Optimization with Non-Convex Objectives](https://mlsanity.com/paper/2210.07588/) (2022)
- [AdaGDA: Faster Adaptive Gradient Descent Ascent Methods for Minimax Optimization](https://mlsanity.com/paper/2106.16101/) (2021)
- [Asynchronous Distributed Bilevel Optimization](https://mlsanity.com/paper/2212.10048/) (2022)
- [Finding Second-Order Stationary Points in Nonconvex-Strongly-Concave Minimax Optimization](https://mlsanity.com/paper/2110.04814/) (2021)
- [A Single-Loop Gradient Descent and Perturbed Ascent Algorithm for Nonconvex Functional Constrained Optimization](https://mlsanity.com/paper/2207.05650/) (2022)
- [Nonsmooth Nonconvex-Nonconcave Minimax Optimization: Primal-Dual Balancing and Iteration Complexity Analysis](https://mlsanity.com/paper/2209.10825/) (2022)
- [Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problems](https://mlsanity.com/paper/2211.13668/) (2022)
- [Convergence Rates of Two-Time-Scale Gradient Descent-Ascent Dynamics for Solving Nonconvex Min-Max Problems](https://mlsanity.com/paper/2112.09579/) (2021)
- [First-Order Algorithms for Min-Max Optimization in Geodesic Metric Spaces](https://mlsanity.com/paper/2206.02041/) (2022)
- [A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problems](https://mlsanity.com/paper/2106.06075/) (2021)
- [FedMM: Saddle Point Optimization for Federated Adversarial Domain Adaptation](https://mlsanity.com/paper/2110.08477/) (2021)
- [Min-Max Bilevel Multi-objective Optimization with Applications in Machine Learning](https://mlsanity.com/paper/2203.01924/) (2022)
- [On Convergence of Gradient Descent Ascent: A Tight Local Analysis](https://mlsanity.com/paper/2207.00957/) (2022)
- [Minimax Optimization with Smooth Algorithmic Adversaries](https://mlsanity.com/paper/2106.01488/) (2021)
- [Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain](https://mlsanity.com/paper/2110.03950/) (2021)
- [A first-order augmented Lagrangian method for constrained minimax optimization](https://mlsanity.com/paper/2301.02060/) (2023)
- [Federated Minimax Optimization with Client Heterogeneity](https://mlsanity.com/paper/2302.04249/) (2023)
- [Derivative-free Alternating Projection Algorithms for General Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/2108.00473/) (2021)
- [Generalization Bounds of Nonconvex-(Strongly)-Concave Stochastic Minimax Optimization](https://mlsanity.com/paper/2205.14278/) (2022)
- [Tight Analysis of Extra-gradient and Optimistic Gradient Methods For Nonconvex Minimax Problems](https://mlsanity.com/paper/2210.09382/) (2022)

## Abstract (arXiv)

The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal processing and communication (SPCOM) problems. Despite its popularity, most existing theory for this class has been mainly developed for problems with certain special convex-concave structure. Therefore, it cannot be used to guide the algorithm design for many interesting problems in SPCOM, where various kinds of non-convexity arise. In this work, we consider a block-wise one-sided non-convex min-max problem, in which the minimization problem consists of multiple blocks and is non-convex, while the maximization problem is (strongly) concave. We propose a class of simple algorithms named Hybrid Block Successive Approximation (HiBSA), which alternatingly perform gradient descent-type steps for the minimization blocks and gradient ascent-type steps for the maximization problem. A key element in the proposed algorithm is the use of certain regularization and penalty sequences, which stabilize the algorithm and ensure convergence. We show that HiBSA converges to some properly defined first-order stationary solutions with quantifiable global rates. To validate the efficiency of the proposed algorithms, we conduct numerical tests on a number of problems, including the robust learning problem, the non-convex min-utility maximization problems, and certain wireless jamming problem arising in interfering channels.