Recently proposed gradient estimators enable gradient descent over stochastic
programs with discrete jumps in the response surface, which are not covered by
automatic differentiation (AD) alone. Although these estimators' capability to
guide a swift local search has been shown for certain problems, their
applicability to models relevant to real-world applications remains largely
unexplored. As the gradients governing the choice in candidate solutions are
calculated from sampled simulation trajectories, the optimization procedure
bears similarities to metaheuristics such as particle swarm optimization, which
puts the focus on the different methods' calibration progress per function
evaluation. Here, we consider the calibration of force-based crowd evacuation
models based on the popular Social Force model augmented by discrete decision
making. After studying the ability of an AD-based estimator for branching
programs to capture the simulation's rugged response surface, calibration
problems are tackled using gradient descent and two metaheuristics. As our main
insights, we find 1) that the estimation's fidelity benefits from disregarding
jumps of large magnitude inherent to the Social Force model, and 2) that the
common problem of calibration by adjusting a simulation input distribution
obviates the need for AD across the Social Force calculations, allowing
gradient descent to excel.

该研究探讨了用于模拟交通疏散的基于力的模型的校准问题，研究了梯度下降和元启发式方法，在分析中发现梯度估计的精度受到模型特性和参数分布的影响。

用于离散决策众包模型校准的自动梯度估计

Automatic Gradient Estimation for Calibrating Crowd Models with Discrete  Decision Making

We study stochastic programs where the decision-maker cannot observe the
distribution of the exogenous uncertainties but has access to a finite set of
independent samples from this distribution. In this setting, the goal is to
find a procedure that transforms the data to an estimate of the expected cost
function under the unknown data-generating distribution, i.e., a predictor, and
an optimizer of the estimated cost function that serves as a near-optimal
candidate decision, i.e., a prescriptor. As functions of the data, predictors
and prescriptors constitute statistical estimators. We propose a
meta-optimization problem to find the least conservative predictors and
prescriptors subject to constraints on their out-of-sample disappointment. The
out-of-sample disappointment quantifies the probability that the actual
expected cost of the candidate decision under the unknown true distribution
exceeds its predicted cost. Leveraging tools from large deviations theory, we
prove that this meta-optimization problem admits a unique solution: The best
predictor-prescriptor pair is obtained by solving a distributionally robust
optimization problem over all distributions within a given relative entropy
distance from the empirical distribution of the data.

本文研究随机程序的优化问题，其中决策者不能观察到外生不确定性的分布，但可以访问此分布的有限样本。作者提出了一种元优化问题来找到最不保守的预测器和处方器，以及遵守它们的样本外失望约束。利用大偏差理论的工具，作者证明了该元优化问题有唯一解。最佳预测器 - 处方器对可以通过在距离数据的经验分布一定的相对熵距离内的所有分布上求解一个分布的鲁棒优化问题来获得。

从数据到决策：分布鲁棒优化是最优的

From Data to Decisions: Distributionally Robust Optimization is Optimal

We consider stochastic programs where the distribution of the uncertain
parameters is only observable through a finite training dataset. Using the
Wasserstein metric, we construct a ball in the space of (multivariate and
non-discrete) probability distributions centered at the uniform distribution on
the training samples, and we seek decisions that perform best in view of the
worst-case distribution within this Wasserstein ball. The state-of-the-art
methods for solving the resulting distributionally robust optimization problems
rely on global optimization techniques, which quickly become computationally
excruciating. In this paper we demonstrate that, under mild assumptions, the
distributionally robust optimization problems over Wasserstein balls can in
fact be reformulated as finite convex programs---in many interesting cases even
as tractable linear programs. Leveraging recent measure concentration results,
we also show that their solutions enjoy powerful finite-sample performance
guarantees. Our theoretical results are exemplified in mean-risk portfolio
optimization as well as uncertainty quantification.

研究使用 Wasserstein metric 中有限训练数据集，构建球形分布空间来解决分布鲁棒优化问题，并阐述其在投资组合优化和不确定性量化等领域的实用性和性能保证。