Applications such as employees sharing office spaces over a workweek can be
modeled as problems where agents are matched to resources over multiple rounds.
Agents' requirements limit the set of compatible resources and the rounds in
which they want to be matched. Viewing such an application as a multi-round
matching problem on a bipartite compatibility graph between agents and
resources, we show that a solution (i.e., a set of matchings, with one matching
per round) can be found efficiently if one exists. To cope with situations
where a solution does not exist, we consider two extensions. In the first
extension, a benefit function is defined for each agent and the objective is to
find a multi-round matching to maximize the total benefit. For a general class
of benefit functions satisfying certain properties (including diminishing
returns), we show that this multi-round matching problem is efficiently
solvable. This class includes utilitarian and Rawlsian welfare functions. For
another benefit function, we show that the maximization problem is NP-hard. In
the second extension, the objective is to generate advice to each agent (i.e.,
a subset of requirements to be relaxed) subject to a budget constraint so that
the agent can be matched. We show that this budget-constrained advice
generation problem is NP-hard. For this problem, we develop an integer linear
programming formulation as well as a heuristic based on local search. We
experimentally evaluate our algorithms on synthetic networks and apply them to
two real-world situations: shared office spaces and matching courses to
classrooms.

针对多轮匹配问题，我们在普遍应用实践中探究了解决资源与代理人之间的配对问题的方法，并研究了不同类型的收益函数的解决策略，同时针对不同的场景，我们提出了整数线性规划和基于局部搜索的启发式算法。

多轮匹配实现资源共享

Resource Sharing Through Multi-Round Matchings

The unit selection problem is to identify a group of individuals who are most
likely to exhibit a desired mode of behavior, for example, selecting
individuals who would respond one way if incentivized and a different way if
not. The unit selection problem consists of evaluation and search subproblems.
Li and Pearl defined the "benefit function" to evaluate the average payoff of
selecting a certain individual with given characteristics. The search
subproblem is then to design an algorithm to identify the characteristics that
maximize the above benefit function. The hardness of the search subproblem
arises due to the large number of characteristics available for each individual
and the sparsity of the data available in each cell of characteristics. In this
paper, we present a machine learning framework that uses the bounds of the
benefit function that are estimable from the finite population data to learn
the bounds of the benefit function for each cell of characteristics. Therefore,
we could easily obtain the characteristics that maximize the benefit function.

本论文提出了一种机器学习框架，利用可估算的有限人口数据上的福利函数范围来学习特征单元格的福利函数范围，以便轻松获得最大化福利函数的特征。

单位选择：从有限人口数据中学习受益函数

Unit Selection: Learning Benefit Function from Finite Population Data

The unit selection problem defined by Li and Pearl identifies individuals who
have desired counterfactual behavior patterns, for example, individuals who
would respond positively if encouraged and would not otherwise. Li and Pearl
showed by example that their unit selection model is beyond the A/B test
heuristics. In this paper, we reveal the essence of the A/B test heuristics,
which are exceptional cases of the benefit function defined by Li and Pearl.
Furthermore, We provided more simulated use cases of Li-Pearl's unit selection
model to help decision-makers apply their model correctly, explaining that A/B
test heuristics are generally problematic.

该研究介绍了 Li 和 Pearl 所定义的单元选择问题，针对有所需反事实行为模式的人进行筛选，并且比较了该模型与 A/B 测试的区别和优越性，同时提供了更多模拟用例，并指出 A/B 测试普遍存在问题。

单元选择：案例研究及与 A/B 测试启发式算法的比较

Unit Selection: Case Study and Comparison with A/B Test Heuristic

The unit selection problem aims to identify a set of individuals who are most
likely to exhibit a desired mode of behavior, for example, selecting
individuals who would respond one way if encouraged and a different way if not
encouraged. Using a combination of experimental and observational data, Li and
Pearl derived tight bounds on the "benefit function", which is the payoff/cost
associated with selecting an individual with given characteristics. This paper
extends the benefit function to the general form such that the treatment and
effect are not restricted to binary. We propose an algorithm to test the
identifiability of the nonbinary benefit function and an algorithm to compute
the bounds of the nonbinary benefit function using experimental and
observational data.

本论文扩展了利益函数的一般形式，提出了一种算法来测试非二进制利益函数的可识别性，并使用实验和观测数据计算非二进制利益函数的边界。