We study worst-case VCG redistribution mechanism design for the public project problem. We use a multilayer perceptron (MLP) with ReLU activation to model the payment function and use mixed integer programming (MIP) to solve for the worst-case type profiles that maximally violate the mechanism design constraints. We collect these worst-case type profiles and use them as training samples to train toward better worst-case mechanisms. In practice, we require a tiny network structure for the above approach to scale. The Lottery Ticket Hypothesis states that a large network is likely to contain a "winning ticket" -- a much smaller subnetwork that "won the initialization lottery", which makes its training particularly effective. Motivated by this hypothesis, we train a large network and prune it into a tiny subnetwork. We run MIP-based worst-case training on the drawn subnetwork and evaluate the resulting mechanism's worst-case performance. If the subnetwork does not achieve good worst-case performance, then we record the type profiles that cause the current draw to be bad. To draw again, we restore the large network to its initial weights and prune using recorded type profiles from earlier draws, therefore avoiding drawing the same ticket twice. We expect to eventually encounter a tiny subnetwork that leads to effective training for our worst-case mechanism design task. Lastly, a by-product of multiple ticket draws is an ensemble of mechanisms with different worst cases, which improves the worst-case performance further. Using our approach, we find previously unknown optimal mechanisms for up to 5 agents. Our results confirm the tightness of existing theoretical upper bounds. For up to 20 agents, we derive significantly improved worst-case mechanisms, surpassing a long list of existing manual results.

翻译：我们研究了公共项目问题中的最坏情况VCG再分配机制设计。采用带ReLU激活函数的多层感知机（MLP）对支付函数进行建模，并利用混合整数规划（MIP）求解最大程度违反机制设计约束的最坏类型配置。通过收集这些最坏类型配置作为训练样本，我们迭代优化最坏情况机制。实际应用中，上述方法需依赖极小的网络结构才能有效扩展。彩票假设指出，大型网络中很可能包含一个"中奖彩票"——即一个极小规模的子网络，因其"在初始化时中奖"而具备显著训练效率。受此启发，我们首先训练大型网络，再将其剪枝为微小子网络。对剪枝后的子网络执行基于MIP的最坏情况训练，并评估所得机制的性能。若子网络未能达到优良的最坏情况表现，则记录导致当前剪枝效果不佳的类型配置。通过将大型网络恢复至初始权重，并利用先前剪枝中记录的类型配置进行迭代，我们避免重复选择相同的"彩票"。预期最终能获得一个微小但高效的子网络，成功完成最坏情况机制设计任务。此外，多次彩票抽取的副产品是一组具有不同最坏情况的机制集成，进一步提升了最坏情况性能。基于本方法，我们发现了最多支持5个智能体时此前未知的最优机制，验证了现有理论上界的紧致性。对于多达20个智能体的场景，我们推导出显著改进的最坏情况机制，超越了大量现有的手工设计成果。