2022/01/18 by Kaan Gökcesu, Gokcesu, Kaan, Hakan Gökcesu +1
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2201.07164
openalex publication_date 2022/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we propose a computationally efficient algorithm for the problem of global optimization in univariate loss functions. For the performance evaluation, we study the cumulative regret of the algorithm instead of the simple regret between our best query and the optimal value of the objective function. Although our approach has similar regret results with the traditional lower-bounding algorithms such as the Piyavskii-Shubert method for the Lipschitz continuous or Lipschitz smooth functions, it has a major computational cost advantage. In Piyavskii-Shubert method, for certain types of functions, the query points may be hard to determine (as they are solutions to additional optimization problems). However, this issue is circumvented in our binary sampling approach, where the sampling set is predetermined irrespective of the function characteristics. For a search space of [0,1], our approach has at most Llog (3T) and 2.25H regret for L-Lipschitz continuous and H-Lipschitz smooth functions respectively. We also analytically extend our results for a broader class of functions that covers more complex regularity conditions.