Minimisation of Quasar-Convex Functions Using Random Zeroth-Order Oracles
Amir Ali Farzin, Yuen-Man Pun, Iman Shames·May 04, 2025
Summary
A Gaussian smoothing zeroth-order algorithm optimizes quasar-convex and strongly quasar-convex functions, outperforming gradient descent in specific scenarios. Inspired by evolutionary strategies, it efficiently estimates gradients, surpassing stochastic gradient descent in learning linear dynamical systems. Future research targets its application in constrained cases and minimax problems.
Introduction
Background
Overview of optimization algorithms
Importance of zeroth-order optimization in scenarios without gradient information
Objective
To present a Gaussian smoothing zeroth-order algorithm for optimizing quasar-convex and strongly quasar-convex functions
Highlighting its superiority over gradient descent in specific contexts
Method
Data Collection
Description of the algorithm's data collection process
How it leverages Gaussian smoothing for function approximation
Data Preprocessing
Techniques for preparing data for optimization
Role of preprocessing in enhancing the algorithm's performance
Gradient Estimation
Methodology for estimating gradients without direct gradient information
Comparison with stochastic gradient descent in gradient estimation efficiency
Applications
Optimization of Quasar-Convex and Strongly Quasar-Convex Functions
Detailed explanation of optimization for these function types
Case studies demonstrating algorithm performance
Learning Linear Dynamical Systems
Application of the algorithm in learning linear dynamical systems
Comparison with traditional methods like stochastic gradient descent
Future Research
Constrained Optimization
Exploration of the algorithm's potential in constrained optimization problems
Challenges and strategies for handling constraints
Minimax Problems
Discussion on the algorithm's applicability to minimax problems
Potential improvements and extensions for handling these problems
Conclusion
Summary of Key Findings
Implications for Future Research
Recommendations for Practitioners
Basic info
papers
optimization and control
numerical analysis
machine learning
artificial intelligence
Advanced features
Insights
How does the Gaussian smoothing zeroth-order algorithm estimate gradients compared to traditional methods?
What are the key implementation differences between the Gaussian smoothing algorithm and stochastic gradient descent?
What are the potential future applications of the Gaussian smoothing algorithm in constrained cases and minimax problems?
In what scenarios does the Gaussian smoothing algorithm outperform gradient descent?