2023/03/24 by Kaan Gökcesu, Gokcesu, Kaan, Hakan Gökcesu +1
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Numerical Methods and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2303.14293
openalex publication_date 2023/03/24 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28
This study presents an effective global optimization technique designed for multivariate functions that are Hölder continuous. Unlike traditional methods that construct lower bounding proxy functions, this algorithm employs a predetermined query creation rule that makes it computationally superior. The algorithm's performance is assessed using the average or cumulative regret, which also implies a bound for the simple regret and reflects the overall effectiveness of the approach. The results show that with appropriate parameters the algorithm attains an average regret bound of O(T^-\fracαn) for optimizing a Hölder continuous target function with Hölder exponent α in an n-dimensional space within a given time horizon T. We demonstrate that this bound is minimax optimal.