Resource Allocation via Bayesian Optimization in Wasserstein Spaces vs. Semi-Bandit Feedback

Sequential resource allocation has long been a central problem in operations research, yet ongoing technological developments, particularly in cloud and high-performance computing and in multi-channel marketing, are giving rise to new structural constraints that classical methods were not designed to handle. Semi-Bandit Feedback (SBF) has emerged as the dominant framework for these modern settings. This paper introduces an alternative that recasts the allocation problem within the Bayesian Optimization (BO) paradigm. All three proposed BO algorithms consistently outperform SBF, with BORAwSE showing a particularly clear advantage under time-varying budget settings, while CBO achieves comparable rewards under constant budget conditions. The core methodological contribution is a reformulation in which each candidate allocation is represented as a discrete probability distribution over the available options, making the probability simplex the natural search domain. Grounding the search in this space calls for a geometry that respects the structure of distributions: we adopt the optimal transport (Wasserstein) distance, which allows both the Gaussian process surrogate and the acquisition function to be extended as functionals over the simplex. A further practical advantage of the proposed method is its applicability to problem instances where SBF cannot be used without modification. The approach is evaluated on two case studies: the benchmark computing-resource allocation scenario from the original SBF paper, and a budget allocation problem across marketing channels.