This paper presents a multi-staged approach to nonmyopic adaptive Gaussian
process optimization (GPO) for Bayesian optimization (BO) of unknown, highly
complex objective functions that, in contrast to existing nonmyopic adaptive BO
algorithms, exploits the notion of macro-actions for scaling up to a further
lookahead to match up to a larger available budget. To achieve this, we
generalize GP upper confidence bound to a new acquisition function defined
w.r.t. a nonmyopic adaptive macro-action policy, which is intractable to be
optimized exactly due to an uncountable set of candidate outputs. The
contribution of our work here is thus to derive a nonmyopic adaptive
epsilon-Bayes-optimal macro-action GPO (epsilon-Macro-GPO) policy. To perform
nonmyopic adaptive BO in real time, we then propose an asymptotically optimal
anytime variant of our epsilon-Macro-GPO policy with a performance guarantee.
We empirically evaluate the performance of our epsilon-Macro-GPO policy and its
anytime variant in BO with synthetic and real-world datasets.

提出一种多阶段的方法来针对使用高斯过程噪音模型的复杂目标函数进行非近视自适应贝叶斯优化  (BO)，并利用宏操作来实现针对更大可用预算的进一步前瞻性扩展；通过提出新的求解方法和使用已有技术，建立非近视适应性的 epsilon-Bayes 最优宏操作 GPO（epsilon-Macro-GPO）策略，最后在模拟和真实数据集中对该策略及其任何时候变化进行了实证评估。

宏动作非近视高斯过程优化

Nonmyopic Gaussian Process Optimization with Macro-Actions

In this paper, we consider the problem of Gaussian process (GP) optimization
with an added robustness requirement: The returned point may be perturbed by an
adversary, and we require the function value to remain as high as possible even
after this perturbation. This problem is motivated by settings in which the
underlying functions during optimization and implementation stages are
different, or when one is interested in finding an entire region of good inputs
rather than only a single point. We show that standard GP optimization
algorithms do not exhibit the desired robustness properties, and provide a
novel confidence-bound based algorithm StableOpt for this purpose. We
rigorously establish the required number of samples for StableOpt to find a
near-optimal point, and we complement this guarantee with an
algorithm-independent lower bound. We experimentally demonstrate several
potential applications of interest using real-world data sets, and we show that
StableOpt consistently succeeds in finding a stable maximizer where several
baseline methods fail.

考虑高斯过程优化问题，在最大化函数时增加健壮性，提出基于置信界限的 StableOpt 算法，该算法在真实数据集上的实验表明可以成功找到稳定的极大值点。