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Enabling First-Order Gradient-Based Learning for Equilibrium Computation in Markets

Nils KohringFabian R. PierothMartin Bichler
Mar 2023
Understanding and analyzing markets is crucial, yet analytical equilibriumsolutions remain largely infeasible. Recent breakthroughs in equilibriumcomputation rely on zeroth-order policy gradient estimation. These approachescommonly suffer from high variance and are computationally expensive. The useof fully differentiable simulators would enable more efficient gradientestimation. However, the discrete allocation of goods in economic simulationsis a non-differentiable operation. This renders the first-order Monte Carlogradient estimator inapplicable and the learning feedback systematicallymisleading. We propose a novel smoothing technique that creates a surrogatemarket game, in which first-order methods can be applied. We providetheoretical bounds on the resulting bias which justifies solving the smoothedgame instead. These bounds also allow choosing the smoothing strength a priorisuch that the resulting estimate has low variance. Furthermore, we validate ourapproach via numerous empirical experiments. Our method theoretically andempirically outperforms zeroth-order methods in approximation quality andcomputational efficiency.