Efficient Lipschitzian Global Optimization of Hölder Continuous Multivariate Functions
This study presents an effective global optimization technique designed for multivariate functions that are H\"older 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 $O(T^{-\frac{\alpha}{n}})$ for optimizing a H\"older continuous target function with H\"older exponent $\alpha$ in an $n$-dimensional space within a given time horizon $T$. We demonstrate that this bound is minimax optimal.
Code (0)
등록된 구현이 없습니다.
Tasks
global-optimizationSimilar Papers 제목 키워드 기반
Adaptive proximal gradient methods are universal without approximation
We show that adaptive proximal gradient methods for convex problems are not restricted to traditional Lipschitzian assumptions. Our analysis reveals that a class of linesearch-free methods is still convergent under mere …
Derivative-Free Global Optimization Algorithms: Bayesian Method and Lipschitzian Approaches
In this paper, we will provide an introduction to the derivative-free optimization algorithms which can be potentially applied to train deep learning models. Existing deep learning model training is mostly based on the b…
Deep Learningglobal-optimizationCumulative Regret Analysis of the Piyavskii--Shubert Algorithm and Its Variants for Global Optimization
We study the problem of global optimization, where we analyze the performance of the Piyavskii--Shubert algorithm and its variants. For any given time duration $T$, instead of the extensively studied simple regret (which…
global-optimizationEfficient Minimax Optimal Global Optimization of Lipschitz Continuous Multivariate Functions
In this work, we propose an efficient minimax optimal global optimization algorithm for multivariate Lipschitz continuous functions. To evaluate the performance of our approach, we utilize the average regret instead of t…
global-optimizationRobust Validation to Geometric Perturbations for Autonomous Pose Estimation
Deploying autonomous systems in safety-critical domains demands guaranteed robustness against physically plausible geometric perturbations rather than abstract pixel-wise noise. In vision-based navigation and autonomous …
Object DetectionPose Estimation