Heterogeneous Resource Slot Optimization in Multi-Dimensional Recommendation Landscapes: A Submodular Constrained Framework with Cross-Space Spillover Effects

Contemporary large-scale digital platforms face severe challenges in multi-channel resource slot allocation, including cross-channel redundancy, metric fragmentation, fairness-efficiency conflicts, and ignorance of asymmetric cross-space spillover effects, leading to significant losses in revenue and user engagement. This paper proposes AllocOpt, a submodular constrained optimization framework for heterogeneous resource slot allocation in multi-dimensional recommendation landscapes, which explicitly models directed cross-channel spillover effects and integrates efficiency, engagement, and fairness objectives. The framework formalizes cross-channel interactions as a directed acyclic spillover graph, proves the approximate submodularity of the global objective under reasonable constraints, and designs a polynomial-time greedy algorithm with (1−1/e) approximation guarantee. Meanwhile, a contextual Thompson-sampling bandit algorithm is adopted for online learning of spillover parameters, and hierarchical fairness is enforced via stochastic dominance instead of rigid quotas. Validated in 18-month production with over 200 million users, AllocOpt improves allocation efficiency by 38.7%, reduces cross-channel redundancy by 67.4%, enhances user satisfaction by 28.4%, and boosts small merchants’ weekly sales by 128.6%, with only 6.3 ms computational latency per optimization cycle. This framework unifies real-time performance, allocation efficiency and ecosystem fairness, and is generalizable to e-commerce, mobility and other large-scale platforms with heterogeneous recommendation surfaces.