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We consider a scenario where multiple agents are learning a common decisionvector from data which can be influenced by the agents' decisions. This leadsto the problem of multi-agent performative prediction (Multi-PfD). In thispaper, we formulate Multi-PfD as a decentralized optimization problem thatminimizes a sum of loss functions, where each loss function is based on adistribution influenced by the local decision vector. We first prove thenecessary and sufficient condition for the Multi-PfD problem to admit a uniquemulti-agent performative stable (Multi-PS) solution. We show that enforcingconsensus leads to a laxer condition for the existence of Multi-PS solutionwith respect to the distributions' sensitivities, compared to the single agentcase. Then, we study a decentralized extension to the greedy deployment scheme[Mendler-D\"unner et al., 2020], called the DSGD-GD scheme. We show thatDSGD-GD converges to the Multi-PS solution and analyze its non-asymptoticconvergence rate. Numerical results validate our analysis.

Multi-agent Performative Prediction with Greedy Deployment and Consensus Seeking Agents