End-to-End Inventory Prediction and Contract Allocation for Guaranteed Delivery Advertising

Traditional contract advertising systems treat traffic forecasting and inventory allocation as separate stages. This article proposes an end‑to‑end approach called Neural Lagrangian Selling (NLS) that jointly learns traffic prediction and inventory allocation using a differentiable Lagrangian layer and a graph convolutional network (GCN).

The NLS model integrates a differentiable Lagrangian solver into the neural network, allowing gradients to flow through the allocation problem. A GCN extracts features from the bipartite supply‑demand graph, handling complex targeting constraints.

Problem formulation: each supply node represents a minimal inventory unit (e.g., city/device), and demand nodes correspond to contracts. The allocation is modeled as a quadratic program with constraints; the Lagrangian dual is derived and embedded as a trainable layer.

Solution: the Lagrangian layer is implemented with efficient forward and backward passes, compatible with TensorFlow or PyTorch. The GCN processes supply, demand, and edge features (holiday, targeting, competition) to produce enriched node embeddings.

Experiments on offline and online advertising datasets show that NLS outperforms two‑stage baselines and other end‑to‑end methods in normalized deviation, contract fulfillment rate, inventory utilization, and platform revenue. The proposed Lagrangian solver achieves near‑zero allocation error and superior runtime compared with QPTL and IntOpt.

Conclusion: End‑to‑end learning with a neural Lagrangian layer and GCN significantly improves guaranteed‑delivery advertising performance, offering higher accuracy, efficiency, and revenue.