提出自适应曲率感知的贝叶斯优化获取函数，提升学习与优化效率。
Curvature-aware Expected Free Energy as an Acquisition Function for Bayesian Optimization
- 基于期望自由能设计曲率感知更新律，动态调整搜索策略。
- 在范德波尔振子系统上验证，最终简单后悔值最低，学习误差小。
- 理论保证凹函数无偏收敛，适合高维复杂函数优化任务。
我们提出一种基于期望自由能的贝叶斯优化获取函数，用于同时完成函数优化与学习。在特定假设下，该函数退化为上限置信界、下限置信界和期望信息增益。我们证明了期望自由能在凹函数上的无偏收敛性。基于推导结果，引入曲率感知更新律，并在范德波尔振子系统识别问题上验证其有效性。通过严格的仿真实验表明，所提出的自适应期望自由能获取函数在最小化最终简单后悔值和学习误差方面优于现有最优获取函数。
原文摘要 · Abstract (English)
We propose an Expected Free Energy-based acquisition function for Bayesian optimization to solve the joint learning and optimization problem, i.e., optimize and learn the underlying function simultaneously. We show that, under specific assumptions, Expected Free Energy reduces to Upper Confidence Bound, Lower Confidence Bound, and Expected Information Gain. We prove that Expected Free Energy has unbiased convergence guarantees for concave functions. Using the results from these derivations, we introduce a curvature-aware update law for Expected Free Energy and show its proof of concept using a system identification problem on a Van der Pol oscillator. Through rigorous simulation experiments, we show that our adaptive Expected Free Energy-based acquisition function outperforms state-of-the-art acquisition functions with the least final simple regret and error in learning the Gaussian process.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。