We study worst-case VCG redistribution mechanism design for the public project problem. For VCG redistribution mechanisms, the mechanism design task is only on setting the payments, subject to strategy-proofness and the non-deficit constraint, while maximizing the worst-case allocative efficiency ratio. We use a multilayer perceptron (MLP) with ReLU activation to model the payment function. We 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. We require a tiny network structure for MIP 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. We train a large network and prune it into a tiny subnetwork (i.e., draw a ticket). We run MIP-based worst-case training on the drawn subnetwork and evaluate the training result's worst-case performance (i.e., scratch the ticket). If the subnetwork can 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 (i.e., redraw from the original ticket pot while avoiding drawing the same ticket twice). With a large enough initial network and a large enough number of draws, we expect to eventually encounter a tiny trainable subnetwork. We find an optimal mechanism for 3 agents that uses only 2 hidden nodes! We also find previously unknown optimal mechanisms for 4 and 5 agents. For up to 20 agents, we derive significantly improved worst-case mechanisms compared to existing manual results.

翻译：我们针对公共项目问题研究最坏情形VCG再分配机制设计。对于VCG再分配机制，机制设计任务仅在于设定支付规则，需满足策略证明性与非赤字约束，同时最大化最坏情形配置效率比。我们采用带ReLU激活函数的多层感知机建模支付函数，并利用混合整数规划求解最大程度违反机制设计约束的最坏情形类型配置。通过收集这些最坏情形类型配置作为训练样本，我们迭代优化以实现更优的最坏情形机制。为使混合整数规划可扩展，我们要求网络结构极简。彩票假说指出，大型网络往往包含中奖彩票——一个因初始化优势而训练效率极高的小型子网络。我们首先训练大型网络，将其剪枝为微型子网络（即抽取彩票），对子网络执行基于混合整数规划的最坏情形训练，并评估训练结果的最坏情形性能（即刮开彩票）。若子网络无法达到理想的最坏情形性能，则记录导致本次抽取失败的类型配置。为重新抽奖，我们将大型网络恢复至初始权重，利用先前抽取中记录的失败类型配置进行剪枝（即从原始奖池中重新抽奖，避免重复抽取相同彩票）。当初始网络规模足够大且抽奖次数足够多时，我们预期最终将获得可训练的小型子网络。仅使用2个隐藏节点，我们便为3个智能体找到最优机制！针对4个和5个智能体，我们还发现了此前未知的最优机制。对于多达20个智能体的场景，相较现有手工设计方案，我们推导出显著提升的最坏情形机制。