Discrete optimal transportation problems arise in various contexts in
engineering, the sciences and the social sciences. Often the underlying cost
criterion is unknown, or only partly known, and the observed optimal solutions
are corrupted by noise. In this paper we propose a systematic approach to infer
unknown costs from noisy observations of optimal transportation plans. The
algorithm requires only the ability to solve the forward optimal transport
problem, which is a linear program, and to generate random numbers. It has a
Bayesian interpretation, and may also be viewed as a form of stochastic
optimization.
We illustrate the developed methodologies using the example of international
migration flows. Reported migration flow data captures (noisily) the number of
individuals moving from one country to another in a given period of time. It
can be interpreted as a noisy observation of an optimal transportation map,
with costs related to the geographical position of countries. We use a
graph-based formulation of the problem, with countries at the nodes of graphs
and non-zero weighted adjacencies only on edges between countries which share a
border. We use the proposed algorithm to estimate the weights, which represent
cost of transition, and to quantify uncertainty in these weights.

该论文提出了一种通过噪声数据推断未知成本的方法，利用了前向最优传输问题和随机数生成方法作为基础，探讨了其在国际迁移流问题上的应用和不确定性量化。

逆最优输运

Inverse optimal transport

Accelerated algorithms have broad applications in large-scale optimization,
due to their generality and fast convergence. However, their stability in the
practical setting of noise-corrupted gradient oracles is not well-understood.
This paper provides two main technical contributions: (i) a new accelerated
method AGDP that generalizes Nesterov's AGD and improves on the recent method
AXGD (Diakonikolas & Orecchia, 2018), and (ii) a theoretical study of
accelerated algorithms under noisy and inexact gradient oracles, which is
supported by numerical experiments. This study leverages the simplicity of AGDP
and its analysis to clarify the interaction between noise and acceleration and
to suggest modifications to the algorithm that reduce the mean and variance of
the error incurred due to the gradient noise.

本文提出了一个新的加速方法 AGDP, 并对噪声和不精确梯度预言机下的加速算法进行了理论研究，研究结果支持了通过 AGDP 方法的简单性及其分析，梯度噪声的交互关系以及提示改进算法以减少梯度噪声引起的误差的平均值和方差。