Many real-world optimization scenarios involve expensive evaluation with
unknown and heterogeneous costs. Cost-aware Bayesian optimization stands out as
a prominent solution in addressing these challenges. To approach the global
optimum within a limited budget in a cost-efficient manner, the design of
cost-aware acquisition functions (AFs) becomes a crucial step. However,
traditional manual design paradigm typically requires extensive domain
knowledge and involves a labor-intensive trial-and-error process. This paper
introduces EvolCAF, a novel framework that integrates large language models
(LLMs) with evolutionary computation (EC) to automatically design cost-aware
AFs. Leveraging the crossover and mutation in the algorithm space, EvolCAF
offers a novel design paradigm, significantly reduces the reliance on domain
expertise and model training. The designed cost-aware AF maximizes the
utilization of available information from historical data, surrogate models and
budget details. It introduces novel ideas not previously explored in the
existing literature on acquisition function design, allowing for clear
interpretations to provide insights into its behavior and decision-making
process. In comparison to the well-known EIpu and EI-cool methods designed by
human experts, our approach showcases remarkable efficiency and generalization
across various tasks, including 12 synthetic problems and 3 real-world
hyperparameter tuning test sets.

本文介绍了一个新的框架，将大型语言模型与进化计算相结合，自动设计成本感知的采集函数，以在有限预算内高效接近全局最优解。

利用大型语言模型进化成本感知的获取函数

Evolve Cost-aware Acquisition Functions Using Large Language Models

This paper introduces a new formulation that finds the optimum for the
Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a
shortest path for an agent, that starts at a depot, visits a set of moving
targets exactly once within their assigned time-windows, and returns to the
depot. The formulation relies on the key idea that when the targets move along
lines, their trajectories become convex sets within the space-time coordinate
system. The problem then reduces to finding the shortest path within a graph of
convex sets, subject to some speed constraints. We compare our formulation with
the current state-of-the-art Mixed Integer Conic Program (MICP) solver for the
MT-TSP. The experimental results show that our formulation outperforms the MICP
for instances with up to 20 targets, with up to two orders of magnitude
reduction in runtime, and up to a 60\% tighter optimality gap. We also show
that the solution cost from the convex relaxation of our formulation provides
significantly tighter lower bounds for the MT-TSP than the ones from the MICP.

该研究介绍了一个新的公式，用于寻找移动目标旅行推销员问题（MT-TSP）的最佳解，通过在空间 - 时间坐标系中寻找凸集图形内的最短路径，相比现有的混合整数锥规划器（MICP）求解器，该公式在运行时间上减少了两个数量级，同时缩小了高达 60% 的最优性差距。

基于凸集图的移动目标旅行推销员问题的混合整数锥规划

A Mixed-Integer Conic Program for the Moving-Target Traveling Salesman  Problem based on a Graph of Convex Sets

Bayesian optimization (BO) based on Gaussian process models is a powerful
paradigm to optimize black-box functions that are expensive to evaluate. While
several BO algorithms provably converge to the global optimum of the unknown
function, they assume that the hyperparameters of the kernel are known in
advance. This is not the case in practice and misspecification often causes
these algorithms to converge to poor local optima. In this paper, we present
the first BO algorithm that is provably no-regret and converges to the optimum
without knowledge of the hyperparameters. During optimization we slowly adapt
the hyperparameters of stationary kernels and thereby expand the associated
function class over time, so that the BO algorithm considers more complex
function candidates. Based on the theoretical insights, we propose several
practical algorithms that achieve the empirical sample efficiency of BO with
online hyperparameter estimation, but retain theoretical convergence
guarantees. We evaluate our method on several benchmark problems.

本文提出了第一个无后悔的贝叶斯优化算法，它在没有核心参数的先验知识的情况下，可以收敛到最优点。通过在优化过程中逐步调整静态核的超参数并随时间扩展相关函数类，该算法可考虑更复杂的函数候选项。