Online sellers and advertisers are recommended keyphrases for their listed products, which they bid on to enhance their sales. One popular paradigm that generates such recommendations is Extreme Multi-Label Classification (XMC), which involves tagging/mapping keyphrases to items. We outline the limitations of using traditional item-query based tagging or mapping techniques for keyphrase recommendations on E-Commerce platforms. We introduce GraphEx, an innovative graph-based approach that recommends keyphrases to sellers using extraction of token permutations from item titles. Additionally, we demonstrate that relying on traditional metrics such as precision/recall can be misleading in practical applications, thereby necessitating a combination of metrics to evaluate performance in real-world scenarios. These metrics are designed to assess the relevance of keyphrases to items and the potential for buyer outreach. GraphEx outperforms production models at eBay, achieving the objectives mentioned above. It supports near real-time inferencing in resource-constrained production environments and scales effectively for billions of items.

Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for many agents often remain computationally infeasible and lack theoretical guarantees. Mean Field Games (MFGs) address both of these issues and can be extended to Graphon MFGs (GMFGs) to include network structures between agents. Despite their merits, the real world applicability of GMFGs is limited by the fact that graphons only capture dense graphs. Since most empirically observed networks show some degree of sparsity, such as power law graphs, the GMFG framework is insufficient for capturing these network topologies. Thus, we introduce the novel concept of Graphex MFGs (GXMFGs) which builds on the graph theoretical concept of graphexes. Graphexes are the limiting objects to sparse graph sequences that also have other desirable features such as the small world property. Learning equilibria in these games is challenging due to the rich and sparse structure of the underlying graphs. To tackle these challenges, we design a new learning algorithm tailored to the GXMFG setup. This hybrid graphex learning approach leverages that the system mainly consists of a highly connected core and a sparse periphery. After defining the system and providing a theoretical analysis, we state our learning approach and demonstrate its learning capabilities on both synthetic graphs and real-world networks. This comparison shows that our GXMFG learning algorithm successfully extends MFGs to a highly relevant class of hard, realistic learning problems that are not accurately addressed by current MARL and MFG methods.