Contract design involves a principal who establishes contractual agreements about payments for outcomes that arise from the actions of an agent. In this paper, we initiate the study of deep learning for the automated design of optimal contracts. We formulate this as an offline learning problem, where a deep network is used to represent the principal's expected utility as a function of the design of a contract. We introduce a novel representation: the Discontinuous ReLU (DeLU) network, which models the principal's utility as a discontinuous piecewise affine function where each piece corresponds to the agent taking a particular action. DeLU networks implicitly learn closed-form expressions for the incentive compatibility constraints of the agent and the utility maximization objective of the principal, and support parallel inference on each piece through linear programming or interior-point methods that solve for optimal contracts. We provide empirical results that demonstrate success in approximating the principal's utility function with a small number of training samples and scaling to find approximately optimal contracts on problems with a large number of actions and outcomes.

翻译：契约设计涉及委托人制定关于代理人行为所产生结果的支付契约协议。本文首次提出利用深度学习自动设计最优契约的研究。我们将此问题形式化为离线学习问题，通过深度网络将委托人的期望效用表示为契约设计的函数。我们引入一种新型表示：非连续ReLU（DeLU）网络，该网络将委托人效用建模为非连续分段仿射函数，其中每一段对应代理人采取特定行为。DeLU网络隐式学习代理人激励相容约束与委托人效用最大化目标的闭式表达式，并通过线性规划或内点法对各段进行并行推理以求解最优契约。实验结果表明，该方法能以少量训练样本成功近似委托人效用函数，并在具有大量行为与结果规模的问题中扩展求解近似最优契约。