This work studies the multitasking principal-agent problem. I first show a
``uniformity'' result. Specifically, when the tasks are perfect substitutes,
and the agent's cost function is homogeneous to a certain degree, then the
optimal contract only depends on the marginal utility of each task and the
degree of homogeneity. I then study a setting where the marginal utility of
each task is unknown so that the optimal contract must be learned or estimated
with observational data. I identify this problem as a regression problem with
measurement errors and observe that this problem can be cast as an instrumental
regression problem. The current works observe that both the contract and the
repeated observations (when available) can act as valid instrumental variables,
and propose using the generalized method of moments estimator to compute an
approximately optimal contract from offline data. I also study an online
setting and show how the optimal contract can be efficiently learned in an
online fashion using the two estimators. Here the principal faces an
exploration-exploitation tradeoff: she must experiment with new contracts and
observe their outcome whilst at the same time ensuring her experimentations are
not deviating too much from the optimal contract. This work shows when repeated
observations are available and agents are sufficiently ``diverse", the
principal can achieve a very low $\widetilde{O}(d)$ cumulative utility loss,
even with a ``pure exploitation" algorithm.

这项研究探讨了多任务委托 - 代理问题，通过研究成本函数、边际效用和在线学习方法等，寻求了最优合约的解决方案。

主体 - 代理多任务：最优合同的统一性及其通过仪器回归的高效学习

Principal-Agent Multitasking: the Uniformity of Optimal Contracts and  its Efficient Learning via Instrumental Regression

We study principal-agent problems in which a principal commits to an
outcome-dependent payment scheme -- called contract -- in order to induce an
agent to take a costly, unobservable action leading to favorable outcomes. We
consider a generalization of the classical (single-round) version of the
problem in which the principal interacts with the agent by committing to
contracts over multiple rounds. The principal has no information about the
agent, and they have to learn an optimal contract by only observing the outcome
realized at each round. We focus on settings in which the size of the agent's
action space is small. We design an algorithm that learns an
approximately-optimal contract with high probability in a number of rounds
polynomial in the size of the outcome space, when the number of actions is
constant. Our algorithm solves an open problem by Zhu et al.[2022]. Moreover,
it can also be employed to provide a $\tilde{\mathcal{O}}(T^{4/5})$ regret
bound in the related online learning setting in which the principal aims at
maximizing their cumulative utility, thus considerably improving
previously-known regret bounds.

研究主体 - 代理问题中的主体为了引导代理采取成本高且不可观察的行动以获得有利结果而承诺一种与结果相关的支付方案，考虑了与代理进行多轮合同承诺的问题的推广，设计了一种算法，在观察到每轮的结果后，能够以高概率学习到近似最优的合同，对于行动空间较小的情景，在最优合同学习方面取得了突破性进展，并在相关在线学习环境下用于最大化主体累积效用以提供近似为 O (T^4/5) 的遗憾上界，从而明显改善了之前已知的遗憾上界。

学习最优合同：如何利用小的行动空间

Learning Optimal Contracts: How to Exploit Small Action Spaces

We consider the classic principal-agent model of contract theory, in which a
principal designs an outcome-dependent compensation scheme to incentivize an
agent to take a costly and unobservable action. When all of the model
parameters---including the full distribution over principal rewards resulting
from each agent action---are known to the designer, an optimal contract can in
principle be computed by linear programming. In addition to their demanding
informational requirements, such optimal contracts are often complex and
unintuitive, and do not resemble contracts used in practice.
This paper examines contract theory through the theoretical computer science
lens, with the goal of developing novel theory to explain and justify the
prevalence of relatively simple contracts, such as linear (pure commission)
contracts. First, we consider the case where the principal knows only the first
moment of each action's reward distribution, and we prove that linear contracts
are guaranteed to be worst-case optimal, ranging over all reward distributions
consistent with the given moments. Second, we study linear contracts from a
worst-case approximation perspective, and prove several tight parameterized
approximation bounds.

本文探讨通过理论计算机科学的角度研究契约理论，旨在解释和证明简单契约的普遍性，并通过证明线性契约保证是极端情况下的最佳选择，揭示了 NN 这种简单契约的特征。

简单与最优合同

Simple versus Optimal Contracts

This paper analyzes and compares different incentive mechanisms for a master
to motivate the collaboration of smartphone users on both data acquisition and
distributed computing applications. To collect massive sensitive data from
users, we propose a reward-based collaboration mechanism, where the master
announces a total reward to be shared among collaborators, and the
collaboration is successful if there are enough users wanting to collaborate.
We show that if the master knows the users' collaboration costs, then he can
choose to involve only users with the lowest costs. However, without knowing
users' private information, then he needs to offer a larger total reward to
attract enough collaborators. Users will benefit from knowing their costs
before the data acquisition. Perhaps surprisingly, the master may benefit as
the variance of users' cost distribution increases.
To utilize smartphones' computation resources to solve complex computing
problems, we study how the master can design an optimal contract by specifying
different task-reward combinations for different user types. Under complete
information, we show that the master involves a user type as long as the
master's preference characteristic outweighs that type's unit cost. All
collaborators achieve a zero payoff in this case. If the master does not know
users' private cost information, however, he will conservatively target at a
smaller group of users with small costs, and has to give most benefits to the
collaborators.

本文研究了为鼓励智能手机用户在数据采集和分布式计算应用上合作而设计的不同激励机制，并提出一种基于奖励的协作机制，以及如何针对不同的用户类型设计最优契约。