Self-Improving Neural Pruning: A Graph Neural Network Framework for Scalable Mixed Bundle Pricing

Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games.

It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit.

Exact mixed-bundling formulations capture this structure but are computationally intractable because the number of possible bundles grows exponentially with the number of products.

We propose a graph neural network (GNN)-guided pruning framework for scalable (non-)additive bundle pricing.

Instead of learning on the exponential bundle-level formulation, we encode each instance as a compact customer-product graph and train an edge-output GNN to learn the product-assignment probabilities from optimal mixed-bundling solutions.

The predicted probabilities are then converted into restricted candidate bundle families through fixed cutoff pruning and progressive cutoff pruning; the final prices and assignments are obtained by solving the mixed bundling formulation over the retained bundles.

We further introduce a GNN-guided local search and an iterative self-improvement procedure for larger instances.

The local search refines the retained bundle family by prioritizing high-confidence add/drop moves, while the iterative self-improvement procedure generates high-quality solutions on larger instances for retraining.

Theoretically, we show that under mild distinguishability conditions the proposed edge-output GNN class is expressive enough to recover the optimal product-assignment mapping.

Experiments show that the proposed policies recover over 98% of the optimal profit on small instances and outperform bundle-size pricing on larger instances with substantial runtime savings.