Extend exact optimization beyond the tested offer-budget regime

Establish an exact and computationally practical optimization method for StoBasket joint upsell-and-cross-sell offer selection when the upsell budget exceeds four offers, where the tested vectorized enumeration becomes increasingly costly and the scalability of the proposed graphical dynamic-programming approach remains unresolved.

Background

The paper provides exact enumeration and tree-decomposition dynamic programming for a structured response model, and reports latency results for budgets up to four displayed upsells and at most twenty upsell groups. Enumeration has growth of order O((GJ)^L), while dynamic programming is intended to become more useful for larger budgets, particularly when the interaction graph has bounded treewidth.

However, the reported experiments do not evaluate budgets above L = 4. Consequently, the practical scalability of the exact methods in the larger-budget regime is left unresolved, despite being identified as the regime in which graphical dynamic programming should matter most.