Auction learning as a two-player game

Abstract

Designing an incentive compatible auction that maximizes expected revenue is a central problem in Auction Design. While theoretical approaches to the problem have hit some limits, a recent research direction initiated by Duetting et al. (2019) consists in building neural network architectures to find optimal auctions. We propose two conceptual deviations from their approach which result in enhanced performance. First, we use recent results in theoretical auction design (Rubinstein and Weinberg, 2018) to introduce a time-independent Lagrangian. This not only circumvents the need for an expensive hyper-parameter search (as in prior work), but also provides a principled metric to compare the performance of two auctions (absent from prior work). Second,the optimization procedure in previous work uses an inner maximization loop to compute optimal misreports. We amortize this process through the introduction of an additional neural network. We demonstrate the effectiveness of our approach by learning competitive or strictly improved auctions compared to prior work. Both results together further imply a novel formulation of Auction Design as a two-player game with stationary utility functions.

Adversarial Constrained Bidding via Minimax Regret Optimization with Causality-Aware Reinforcement Learning

“…While it is well agreed recently that online ad markets dynamically changes [27,41], we emphasize that the bidding environment can be essentially adversarial [26,33] because online auctions involve multiple parties with conflicting objectives. For instance, the sellers may update their mechanism towards maximal revenue, e.g., by learning personalized reserve prices [14,18], or even automatically learn mechanisms from data [16,37]. On the other hand, rival bidders can employ data-driven auto-bidding algorithms to optimize their own utilities.…”

“…For instance, sellers may learn the distribution of bidders' private values and set personalized reserved prices in auctions [14,18,35]. Recent studies [16,37] have introduced neural network-based selling mechanisms learned from data. In addition, rival bidders can also employ complex bidding strategies to optimize their long-term utility [15], leading to a complex distribution of competing bids that can affect the performance of our bidding agent [26].…”

Generative Adversarial Equilibrium Solvers

“…Our contributions generally relate to a line of work on differentiable economics, which seeks to use methods of neural computation for problems of economic design and equilibrium computation. In regard to finding optimal economic designs, deep learning has been used for problems of auction design (Dütting et al, 2019;Curry et al, 2022c;Tacchetti et al, 2019;Curry et al, 2022a;Gemp et al, 2022;Rahme et al, 2020) and matching (Ravindranath et al, 2021). In regard to solving for equilibria, some recent works have tried to solve for Nash equilibria in auctions (Heidekrüger et al, 2019;Bichler et al, 2021), and dynamic stochastic general equilibrium models (Curry et al, 2022b;Chen et al, 2021;Hill et al, 2021).…”

ProportionNet: Balancing Fairness and Revenue for Auction Design with Deep Learning

“…Additionally, results for the 4 x 6 and 5 x 5 auctions significantly exceed the itemwise Myerson, but their regret and unfairness values are also high. However, prior success in applying the augmented Lagrangian to higher-complexity auctions (3 x 10, 5 x 10) in addition to RegretNet's sensitivity to hyperparameter search [35] suggest that these problems can be resolved at the cost of greater computational resources. 2: Revenue for Setting D -a 3 bidder x 4 item auction with items 1 and 2 valued at 𝑈 [0, 1] and items 3 and 4 at 𝑈 [0, 1] + 𝑏.…”

“…Future work might include incorporating improvements to the training procedure as in [35], or making use of techniques that can exactly evaluate the degree to which strategyproofness is violated, as in [11]. Additionally, the theoretical question of characterizing which fair, strategyproof mechanisms maximize revenue is an interesting one.…”