Blackwell Approachability

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Multinomial Subset Routing with Sum-Max Rewards and Operational Constraints
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Feb 24, 2026Teodor Vanislavov Marinov, Mehryar Mohri, Princewill Okoroafor +2Blackwell Approachability Repeated Games
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Feb 22, 2026Jiahao Zhang, Lujing Zhang, Keltin Grimes +3Blackwell Approachability Preference Optimization
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Feb 19, 2026Lunjia Hu, Kevin Tian, Chutong YangBlackwell Approachability Online Learning
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Adaptive Conformal Inference through the Lens of Blackwell Approachability
Oct 17, 2025Guillaume Principato, Gilles StoltzBlackwell Approachability Conformal Prediction
Universit´e Paris-Saclay, CNRS, Inria, Laboratoire de math´ematiques d’Orsay, 91405, Orsay, France · EDF R&D, Palaiseau, France · HEC Paris, Jouy-en-Josas, France

Aug 17, 2026J/K move · Enter open · S save

Multinomial Subset Routing with Sum-Max Rewards and Operational Constraints

Quan Zhou, Yiyan Huang

Blackwell Approachability Online Resource Allocation Combinatorial Multi-Armed Bandits

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We study online routing to subsets of experts under aggregate bandit feedback and long-run operational constraints. Expert contributions can be complementary: for each task dimension, the best selected expert determines the contribution, and the total reward aggregates these dimension-wise maxima. At the same time, capacity, budget, and fairness requirements impose lower and upper bounds on long-run expert activation frequencies. A fixed deterministic subset cannot generally satisfy such heterogeneous requirements, motivating a stochastic routing policy. We formalize this problem as Multinomial Subset Routing (MSR). The learner maintains a distribution

q

over

K

experts, samples an expert independently

M

times from

q

, and routes each task to the distinct sampled experts. We propose OMD-Approachability, which combines online mirror descent with Blackwell's approachability to optimize MSR under two-sided operational constraints. We establish

O(T^{-1/2})

average reward regret and expected constraint violation. We also quantify the approximation gap induced by a linear surrogate, and evaluate the approach on a real-world crowdsourcing dataset.