Differentiable economics—the use of deep learning for auction design—has driven progress in multi-item auction design with additive and unit-demand valuations. However, there has been little progress for combinatorial auctions (CAs), even in the simplest and yet important single bidder case, due to exponential growth of the bundle space with the number of items. We address this challenge by introducing a deep network architecture for a menu-based CA, which supports the first dominant-strategy incentive compatible (DSIC), revenue-optimizing single-bidder CA. Our idea is to generate a bundle distribution through an ordinary differential equation (ODE) applied to a tractable initial distribution. The BundleFlow method learns suitable ODE-based transforms, one for each menu element, to optimize expected revenue. BundleFlow achieves up to 2.23$\times$ higher revenue than baselines on standard CA testbeds and scales up to 500 items. Compared with other menu-learning baselines, BundleFlow also reduces training iterations by 3.6-9.5$\times$ and cuts training time by about 80% in settings with 50 and 100 items.

Differentiable economics uses deep learning for automated mechanism design. Despite strong progress, it has remained an open problem to learn multi-bidder, general, and fully strategy-proof (SP) auctions. We introduce GEneral Menu-based NETwork (GemNet), which significantly extends the menu-based approach of RochetNet [Dütting et al., 2024] to the multi-bidder setting. The challenge in achieving SP is to learn bidder-independent menus that are feasible, so that the optimal menu choices for each bidder do not over-allocate items when taken together (we call this menu compatibility). GemNet penalizes the failure of menu compatibility during training, and transforms learned menus after training through price changes, by considering a set of discretized bidder values and reasoning about Lipschitz smoothness to guarantee menu compatibility on the entire value space. This approach is general, leaving undisturbed trained menus that already satisfy menu compatibility and reducing to RochetNet for a single bidder. Mixed-integer linear programs are used for menu transforms and through a number of optimizations enabled by deep learning, including adaptive grids and methods to skip menu elements, we scale to large auction design problems. GemNet learns auctions with better revenue than affine maximization methods, achieves exact SP whereas previous general multi-bidder methods are approximately SP, and offers greatly enhanced interpretability. The full version of this paper is available at https://arxiv.org/abs/2406.07428.

The _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. 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. 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, we must learn signaling schemes rather than allocation rules and handle _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.