Mode Connectivity in Auction Design

Optimal auction design is a fundamental problem in algorithmic game theory. This problem is notoriously difficult already in very simple settings. Recent work in differentiable economics showed that neural networks can efficiently learn known optimal auction mechanisms and discover interesting new ones. In an attempt to theoretically justify their empirical success, we focus on one of the first such networks, RochetNet, and a generalized version for affine maximizer auctions. We prove that they satisfy mode connectivity, i.e., locally optimal solutions are connected by a simple, piecewise linear path such that every solution on the path is almost as good as one of the two local optima. Mode connectivity has been recently investigated as an intriguing empirical and theoretically justifiable property of neural networks used for prediction problems. Our results give the first such analysis in the context of differentiable economics, where neural networks are used directly for solving non-convex optimization problems.

[1]  David C. Parkes,et al.  The AI Economist: Taxation policy design via two-level deep multiagent reinforcement learning , 2022, Science advances.

[2]  Michael J. Curry,et al.  Differentiable Economics for Randomized Affine Maximizer Auctions , 2022, IJCAI.

[3]  M. Zaheer,et al.  A Context-Integrated Transformer-Based Neural Network for Auction Design , 2022, ICML.

[4]  Tom Goldstein,et al.  Learning Revenue-Maximizing Auctions With Differentiable Matching , 2021, AISTATS.

[5]  Tom Goldstein,et al.  ProportionNet: Balancing Fairness and Revenue for Auction Design with Deep Learning , 2020, ArXiv.

[6]  Marco Mondelli,et al.  Landscape Connectivity and Dropout Stability of SGD Solutions for Over-parameterized Neural Networks , 2019, ICML.

[7]  Sanjeev Arora,et al.  Explaining Landscape Connectivity of Low-cost Solutions for Multilayer Nets , 2019, NeurIPS.

[8]  Quynh Nguyen,et al.  On Connected Sublevel Sets in Deep Learning , 2019, ICML.

[9]  Liwei Wang,et al.  Gradient Descent Finds Global Minima of Deep Neural Networks , 2018, ICML.

[10]  Yuanzhi Li,et al.  A Convergence Theory for Deep Learning via Over-Parameterization , 2018, ICML.

[11]  Pingzhong Tang,et al.  Automated Mechanism Design via Neural Networks , 2018, AAMAS.

[12]  Paul Dütting,et al.  Optimal auctions through deep learning , 2017, ICML.

[13]  David C. Parkes,et al.  Deep Learning for Revenue-Optimal Auctions with Budgets , 2018, AAMAS.

[14]  David C. Parkes,et al.  Deep Learning for Multi-Facility Location Mechanism Design , 2018, IJCAI.

[15]  Fred A. Hamprecht,et al.  Essentially No Barriers in Neural Network Energy Landscape , 2018, ICML.

[16]  Andrew Gordon Wilson,et al.  Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs , 2018, NeurIPS.

[17]  Yi Zhang,et al.  Stronger generalization bounds for deep nets via a compression approach , 2018, ICML.

[18]  Elias Koutsoupias,et al.  Duality and optimality of auctions for uniform distributions , 2014, SIAM J. Comput..

[19]  Moshe Babaioff,et al.  The menu-size complexity of revenue approximation , 2016, STOC.

[20]  Constantinos Daskalakis,et al.  Multi-item auctions defying intuition? , 2015, SECO.

[21]  Tuomas Sandholm,et al.  Automated Design of Revenue-Maximizing Combinatorial Auctions , 2015, Oper. Res..

[22]  Christos Tzamos,et al.  Strong Duality for a Multiple-Good Monopolist , 2014, EC.

[23]  Noam Nisan,et al.  Sampling and Representation Complexity of Revenue Maximization , 2014, WINE.

[24]  Christos Tzamos,et al.  The Complexity of Optimal Mechanism Design , 2012, SODA.

[25]  Christos Tzamos,et al.  Mechanism design via optimal transport , 2013, EC '13.

[26]  Yang Cai,et al.  Understanding Incentives: Mechanism Design Becomes Algorithm Design , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.

[27]  Kamesh Munagala,et al.  Optimal auctions via the multiplicative weight method , 2012, EC '13.

[28]  Yang Cai,et al.  Optimal Multi-dimensional Mechanism Design: Reducing Revenue to Welfare Maximization , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[29]  Yang Cai,et al.  An algorithmic characterization of multi-dimensional mechanisms , 2011, STOC '12.

[30]  Alejandro M. Manelli,et al.  Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly , 2004, J. Econ. Theory.

[31]  Vincent Conitzer,et al.  Self-interested automated mechanism design and implications for optimal combinatorial auctions , 2004, EC '04.

[32]  J. Rochet,et al.  The Economics of Multidimensional Screening , 2003 .

[33]  Vincent Conitzer,et al.  Complexity of Mechanism Design , 2002, UAI.

[34]  J. Rochet.  A necessary and sufficient condition for rationalizability in a quasi-linear context , 1987 .

[35]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[36]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[37]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[38]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .