[Paper Review] Data Market Design through Deep Learning

Sai Srivatsa Ravindranath, Yanchen Jiang+1 more|arXiv (Cornell University)|Oct 31, 2023

Auction Theory and Applications4 citations

TL;DR

This paper introduces a deep learning framework for designing revenue-optimal data markets by learning signaling schemes (statistical experiments) that maximize seller revenue while ensuring incentive compatibility and obedience constraints. The approach extends neural architectures like RochetNet and RegretNet to model buyer behavior and actions, successfully replicating known theoretical solutions and discovering new optimal designs in complex multi-buyer settings.

ABSTRACT

The $ extit{data market design}$ problem is a problem in economic theory to find a set of signaling schemes (statistical experiments) to maximize expected revenue to the information seller, where each experiment reveals some of the information known to a seller and has a corresponding price [Bergemann et al., 2018]. Each buyer has their own decision to make in a world environment, and their subjective expected value for the information associated with a particular experiment comes from the improvement in this decision and depends on their prior and value for different outcomes. In a setting with multiple buyers, a buyer's expected value for an experiment may also depend on the information sold to others [Bonatti et al., 2022]. We introduce the application of deep learning for the design of revenue-optimal data markets, looking to expand the frontiers of what can be understood and achieved. Relative to earlier work on deep learning for auction design [Dütting et al., 2023], we must learn signaling schemes rather than allocation rules and handle $ extit{obedience constraints}$ $-$ these arising from modeling the downstream actions of buyers $-$ in addition to incentive constraints on bids. Our experiments demonstrate that this new deep learning framework can almost precisely replicate all known solutions from theory, expand to more complex settings, and be used to establish the optimality of new designs for data markets and make conjectures in regard to the structure of optimal designs.

Motivation & Objective

• To develop a deep learning framework for designing revenue-optimal data markets where information is sold as statistical experiments.
• To extend neural network architectures to handle both incentive compatibility and obedience constraints in signaling schemes.
• To replicate known theoretical solutions and discover new optimal designs in complex, multi-buyer data market settings.
• To investigate the structure of optimal mechanisms under ex post incentive compatibility and individual rationality.
• To explore the scalability and interpretability of learned mechanisms in high-dimensional or symmetric settings.

Proposed method

• Adapts the RochetNet architecture for single-buyer data markets to learn parameterized menus of priced experiments with guaranteed incentive compatibility.
• Extends the RegretNet framework to multi-buyer settings, learning mechanisms with approximate incentive alignment while minimizing deviations in reporting and action choices.
• Imposes obedience constraints by modeling downstream buyer actions and ensuring no profitable double deviations (misreporting + disobeying recommendations).
• Uses gradient-based optimization to train neural networks on synthetic data drawn from known distributions of buyer types, priors, and values.
• Employs a differentiable simulation of buyer decision-making to backpropagate revenue gradients and refine signaling schemes.
• Validates results by comparing learned mechanisms against theoretical benchmarks and proving optimality via Myerson’s framework in specific settings.

Experimental results

Research questions

• RQ1 Can deep learning be used to design revenue-optimal data markets with signaling schemes that satisfy both incentive compatibility and obedience constraints?
• RQ2 How well can neural networks replicate known theoretical solutions in binary state and binary action settings with single and multiple buyers?
• RQ3 What structural properties emerge in optimal data market designs under ex post incentive compatibility, especially in symmetric multi-buyer environments?
• RQ4 To what extent can the framework discover new optimal mechanisms beyond known theoretical results?
• RQ5 How does the framework scale with the number of buyers, states, or actions, and what limitations arise in the Bayesian incentive compatibility (BIC) setting?

Key findings

• The framework successfully replicates all known theoretical solutions from Bergemann et al. (2018) and Bonatti et al. (2022) in binary state and binary action settings with high accuracy.
• In multi-buyer settings with common priors, the model learns a mechanism that sells a fully informative experiment to buyer i if their virtual value exceeds a threshold based on others’ virtual values, achieving near-optimal revenue.
• For Setting G with α=0.5, the model achieved a test revenue of 0.405 and regret below 0.001, closely matching the theoretical optimum.
• For Setting H with α=2.0, the model achieved a test revenue of 0.270 and regret of 0.001, again aligning with theoretical predictions.
• The framework enabled the conjecture and subsequent proof of optimality for a new mechanism structure in the ex post IC setting, demonstrating its ability to generate novel theoretical insights.
• Despite non-convexity, the training process consistently converged to optimal or near-optimal solutions when theoretical optima were known, suggesting robustness to local optima.