Robustness to distributional shift is one of the key challenges of
contemporary machine learning. Attaining such robustness is the goal of
distributionally robust optimization, which seeks a solution to an optimization
problem that is worst-case robust under a specified distributional shift of an
uncontrolled covariate. In this paper, we study such a problem when the
distributional shift is measured via the maximum mean discrepancy (MMD). For
the setting of zeroth-order, noisy optimization, we present a novel
distributionally robust Bayesian optimization algorithm (DRBO). Our algorithm
provably obtains sub-linear robust regret in various settings that differ in
how the uncertain covariate is observed. We demonstrate the robust performance
of our method on both synthetic and real-world benchmarks.

本文通过使用最大平均偏差（MMD）来度量分布转移，研究了分布鲁棒优化的问题，在零阶、有噪音的优化设置下，提出了一种新颖的分布鲁棒贝叶斯优化算法（DRBO）。实验证明我们的算法在多个设置下能够获得次线性的稳健后悔的实现。

分布鲁棒贝叶斯优化

Distributionally Robust Bayesian Optimization

We consider an unconstrained problem of minimizing a smooth convex function
which is only available through noisy observations of its values, the noise
consisting of two parts. Similar to stochastic optimization problems, the first
part is of stochastic nature. The second part is additive noise of unknown
nature, but bounded in absolute value. In the two-point feedback setting, i.e.
when pairs of function values are available, we propose an accelerated
derivative-free algorithm together with its complexity analysis. The complexity
bound of our derivative-free algorithm is only by a factor of $\sqrt{n}$ larger
than the bound for accelerated gradient-based algorithms, where $n$ is the
dimension of the decision variable. We also propose a non-accelerated
derivative-free algorithm with a complexity bound similar to the
stochastic-gradient-based algorithm, that is, our bound does not have any
dimension-dependent factor except logarithmic. Notably, if the difference
between the starting point and the solution is a sparse vector, for both our
algorithms, we obtain a better complexity bound if the algorithm uses an
$1$-norm proximal setup, rather than the Euclidean proximal setup, which is a
standard choice for unconstrained problems

本文研究优化问题中目标函数存在不确定的噪声干扰，提出了基于导数的无导数算法，考虑了稀疏向量情况下使用 1 范数正则化的优化模型。