# Differentiable Economics for Randomized Affine Maximizer Auctions

arXiv: https://arxiv.org/abs/2202.02872 · HTML: https://mlsanity.com/paper/2202.02872/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 76 references that are in the map.
- First posted on arXiv 6 Feb 2022.

## Builds on (most cited first, 27 of 27)

- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Complexity of Mechanism Design](https://mlsanity.com/paper/1408.1486/) (2014)
- [Automated Mechanism Design via Neural Networks](https://mlsanity.com/paper/1805.03382/) (2018)
- [A Permutation-Equivariant Neural Network Architecture For Auction Design](https://mlsanity.com/paper/2003.01497/) (2020)
- [Auction learning as a two-player game](https://mlsanity.com/paper/2006.05684/) (2020)
- [How much data is sufficient to learn high-performing algorithms? Generalization guarantees for data-driven algorithm design](https://mlsanity.com/paper/1908.02894/) (2019)
- [Sample Complexity of Automated Mechanism Design](https://mlsanity.com/paper/1606.04145/) (2016)
- [PreferenceNet: Encoding Human Preferences in Auction Design with Deep Learning](https://mlsanity.com/paper/2106.03215/) (2021)
- [Certifying Strategyproof Auction Networks](https://mlsanity.com/paper/2006.08742/) (2020)
- [ProportionNet: Balancing Fairness and Revenue for Auction Design with Deep Learning](https://mlsanity.com/paper/2010.06398/) (2020)
- [Towards Efficient Auctions in an Auto-bidding World](https://mlsanity.com/paper/2103.13356/) (2021)
- [A Context-Integrated Transformer-Based Neural Network for Auction Design](https://mlsanity.com/paper/2201.12489/) (2022)
- [Strong Duality for a Multiple-Good Monopolist](https://mlsanity.com/paper/1409.4150/) (2014)
- [Deep Learning for Two-Sided Matching](https://mlsanity.com/paper/2107.03427/) (2021)
- [Learning Revenue-Maximizing Auctions With Differentiable Matching](https://mlsanity.com/paper/2106.07877/) (2021)
- [Deep Learning-powered Iterative Combinatorial Auctions](https://mlsanity.com/paper/1907.05771/) (2019)
- [Machine Learning-powered Iterative Combinatorial Auctions](https://mlsanity.com/paper/1911.08042/) (2019)
- [Understanding Incentives: Mechanism Design becomes Algorithm Design](https://mlsanity.com/paper/1305.4002/) (2013)
- [A Duality-Based Unified Approach to Bayesian Mechanism Design](https://mlsanity.com/paper/1812.01577/) (2018)
- [An n-to-1 Bidder Reduction for Multi-item Auctions and its Applications](https://mlsanity.com/paper/1406.3278/) (2014)
- [Optimal Auctions with Restricted Allocations](https://mlsanity.com/paper/1606.01610/) (2016)
- [Fourier Analysis-based Iterative Combinatorial Auctions](https://mlsanity.com/paper/2009.10749/) (2020)
- [Simple Mechanisms for Subadditive Buyers via Duality](https://mlsanity.com/paper/1611.06910/) (2016)
- [Reinforcement Learning of Sequential Price Mechanisms](https://mlsanity.com/paper/2010.01180/) (2020)
- [Selling Multiple Correlated Goods: Revenue Maximization and Menu-Size Complexity (old title: "The Menu-Size Complexity of Auctions")](https://mlsanity.com/paper/1304.6116/) (2013)
- [Fast Iterative Combinatorial Auctions via Bayesian Learning](https://mlsanity.com/paper/1809.05340/) (2018)
- [Optimizing Affine Maximizer Auctions via Linear Programming: an Application to Revenue Maximizing Mechanism Design for Zero-Day Exploits Markets](https://mlsanity.com/paper/2006.14185/) (2020)

## Built on by (most cited first, 22 of 22)

- [Optimal-er Auctions through Attention](https://mlsanity.com/paper/2202.13110/) (2022)
- [A Scalable Neural Network for DSIC Affine Maximizer Auction Design](https://mlsanity.com/paper/2305.12162/) (2023)
- [GemNet: Menu-Based, Strategy-Proof Multi-Bidder Auctions Through Deep Learning](https://mlsanity.com/paper/2406.07428/) (2024)
- [Data Market Design through Deep Learning](https://mlsanity.com/paper/2310.20096/) (2023)
- [Mode Connectivity in Auction Design](https://mlsanity.com/paper/2305.11005/) (2023)
- [Automated Deterministic Auction Design with Objective Decomposition](https://mlsanity.com/paper/2402.11904/) (2024)
- [Aligned Textual Scoring Rules](https://mlsanity.com/paper/2507.06221/) (2025)
- [Neural Auctions Compromise Bidder Information](https://mlsanity.com/paper/2303.00116/) (2023)
- [Optimal Automated Market Makers: Differentiable Economics and Strong Duality](https://mlsanity.com/paper/2402.09129/) (2024)
- [Bridging the Gap Between Estimated and True Regret Towards Reliable Regret Estimation in Deep Learning based Mechanism Design](https://mlsanity.com/paper/2601.13489/) (2026)
- [Incentive-Aware Multi-Fidelity Optimization for Generative Advertising in Large Language Models](https://mlsanity.com/paper/2604.06263/) (2026)
- [Mechanism Design for Ad Auctions with Display Prices](https://mlsanity.com/paper/2303.13192/) (2023)
- [Statistically Truthful Auctions via Acceptance Rule](https://mlsanity.com/paper/2405.12016/) (2024)
- [Large-Scale Contextual Market Equilibrium Computation through Deep Learning](https://mlsanity.com/paper/2406.15459/) (2024)
- [Learning Fair and Preferable Allocations through Neural Network](https://mlsanity.com/paper/2410.17500/) (2024)
- [Learning Neural Strategy-Proof Matching Mechanism from Examples](https://mlsanity.com/paper/2410.19384/) (2024)
- [Learning Recommender Mechanisms for Bayesian Stochastic Games](https://mlsanity.com/paper/2505.22979/) (2025)
- [Optimal Auction Design in the Joint Advertising](https://mlsanity.com/paper/2507.07418/) (2025)
- [Universal Representation of Generalized Convex Functions and their Gradients](https://mlsanity.com/paper/2509.04477/) (2025)
- [LLM Active Alignment: A Nash Equilibrium Perspective](https://mlsanity.com/paper/2602.06836/) (2026)
- [Enhancing Affine Maximizer Auctions with Correlation-Aware Payment](https://mlsanity.com/paper/2602.09455/) (2026)
- [Duality for Optimal Multi-Item, Multi-Bidder Auction Design: Revenue Certificates through Deep Learning](https://mlsanity.com/paper/2606.10112/) (2026)

## Abstract (arXiv)

A recent approach to automated mechanism design, differentiable economics, represents auctions by rich function approximators and optimizes their performance by gradient descent. The ideal auction architecture for differentiable economics would be perfectly strategyproof, support multiple bidders and items, and be rich enough to represent the optimal (i.e. revenue-maximizing) mechanism. So far, such an architecture does not exist. There are single-bidder approaches (MenuNet, RochetNet) which are always strategyproof and can represent optimal mechanisms. RegretNet is multi-bidder and can approximate any mechanism, but is only approximately strategyproof. We present an architecture that supports multiple bidders and is perfectly strategyproof, but cannot necessarily represent the optimal mechanism. This architecture is the classic affine maximizer auction (AMA), modified to offer lotteries. By using the gradient-based optimization tools of differentiable economics, we can now train lottery AMAs, competing with or outperforming prior approaches in revenue.