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 introduce a novel representation: the Discontinuous ReLU (DeLU) network, which models the principal's utility as a discontinuous piecewise affine function of the design of a contract 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建立关于代理行为结果支付报酬的契约协议。本文首次提出利用深度学习实现最优契约的自动化设计。我们引入了一种新颖的表示方法——非连续ReLU(DeLU)网络，该网络将委托人的效用建模为契约设计的非连续分段仿射函数，其中每个分段对应代理采取特定行动。DeLU网络隐式学习代理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每个分段进行并行推理以求解最优契约。实验结果表明，该方法能够以少量训练样本有效逼近委托人效用函数，并在包含大量行动与结果的大规模问题上扩展至近似最优契约。