Learning Optimal Redistribution Mechanisms through Neural Networks
We consider a setting where $p$ public resources are to be allocated among $n$ competing and strategic agents so as to maximize social welfare (the objects should be allocated to those who value them the most). This is called allocative efficiency (AE). We need the agents to report their valuations for obtaining these resources, truthfully referred to as dominant strategy incentive compatibility (DSIC). We use auction-based mechanisms to achieve AE and DSIC yet budget balance cannot be ensured, due to Green-Laffont Impossibility Theorem. That is, the net transfer of money cannot be zero. This problem has been addressed by designing a redistribution mechanism so as to ensure a minimum surplus of money as well as AE and DSIC. The objective could be to minimize surplus in expectation or in the worst case and these $p$ objects could be homogeneous or heterogeneous. Designing redistribution mechanisms which perform well in expectation becomes analytically challenging for heterogeneous settings. In this paper, we take a completely different, data-driven approach. We train a neural network to determine an optimal redistribution mechanism based on given settings with both the objectives, optimal in expectation and optimal in the worst case. We also propose a loss function to train a neural network to optimize worst case. We design neural networks with the underlying rebate functions being linear as well as nonlinear in terms of bids of the agents. Our networks' performances are same as the theoretical guarantees for the cases where it has been solved. We observe that a neural network based redistribution mechanism for homogeneous settings which uses nonlinear rebate functions outperforms linear rebate functions when the objective is optimal in expectation. Our approach also yields an optimal in expectation redistribution mechanism for heterogeneous settings.