论文标题
通过贪婪的部署和寻求代理商的共识的多代理表演预测
Multi-agent Performative Prediction with Greedy Deployment and Consensus Seeking Agents
论文作者
论文摘要
我们考虑了一个场景，其中多个代理商正在从数据中学习一个共同的决策向量，该数据可能受代理的决策影响。这导致了多代理性能预测（多PFD）的问题。在本文中，我们将多PFD提出为分散的优化问题，该问题最小化了损失函数的总和，其中每个损失函数基于受本地决策向量影响的分布。我们首先证明了多PFD问题的必要条件，可以接受独特的多代理性能稳定（多PS）解决方案。我们表明，与单一剂量相比，实施共识会导致具有多PS解决方案的兰克斯条件。然后，我们研究了贪婪部署计划的分散扩展[Mendler-Dünner等，2020]，称为DSGD-GD方案。我们表明，DSGD-GD会收敛到多PS溶液并分析其非反应收敛速率。数值结果验证了我们的分析。
We consider a scenario where multiple agents are learning a common decision vector from data which can be influenced by the agents' decisions. This leads to the problem of multi-agent performative prediction (Multi-PfD). In this paper, we formulate Multi-PfD as a decentralized optimization problem that minimizes a sum of loss functions, where each loss function is based on a distribution influenced by the local decision vector. We first prove the necessary and sufficient condition for the Multi-PfD problem to admit a unique multi-agent performative stable (Multi-PS) solution. We show that enforcing consensus leads to a laxer condition for the existence of Multi-PS solution with respect to the distributions' sensitivities, compared to the single agent case. Then, we study a decentralized extension to the greedy deployment scheme [Mendler-Dünner et al., 2020], called the DSGD-GD scheme. We show that DSGD-GD converges to the Multi-PS solution and analyze its non-asymptotic convergence rate. Numerical results validate our analysis.
