Coverage-Maximizing Multinomial Subset Routing under Operational Constraints

Abstract:We introduce Multinomial Subset Routing (MSR), a new online routing framework over $K$ experts in which the learner keeps a multinomial routing policy instead of a deterministic subset of experts. At each round, the learner samples $M$ experts i.i.d. from the multinomial policy, and the resulting set of distinct sampled experts forms the routed subset. The reward depends only on the best-performing expert(s) in the routed subset. This reward structure arises naturally in routing across specialized models but is not captured by standard combinatorial bandits or subset-selection methods, which optimize deterministic subsets and typically assume additive rewards. We require the selection to satisfy several long-term, two-sided operational constraints under bandit feedback, observing only the winner's reward each round. We propose OMD-Approachability, combining online mirror descent with Blackwell's Approachability, and prove it achieves $O(1/\sqrt{T})$ regret in both reward and constraint violation. We ground the framework in practical application domains and validate it empirically on a real-world crowdsourcing dataset.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2608.16375 [cs.LG]

(or arXiv:2608.16375v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.16375 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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