Learning to Allocate Resources with Censored Feedback

In many applications, evaluating the effectiveness of different alternatives comes with varying costs or resource usage. Motivated by such heterogeneity, we study the Best Arm Identification with Resource Constraints (BAIwRC) problem, where an agent seeks to identify the best alternative (aka arm) in the presence of resource constraints. Each arm pull consumes one or more types of limited resources. We make two key contributions. First, we propose the Successive Halving with Resource Rationing (SH-RR) algorithm, which integrates resource-aware allocation into the classical successive halving framework on best arm identification. The SH-RR algorithm unifies the theoretical analysis for both the stochastic and deterministic consumption settings, with a new \textit{effective consumption measure

We establish near-optimal regret bounds for budget-constrained online learning against arbitrary classes of budget-pacing experts in the adversarial setting. In particular, given any class of $F$ experts and a candidate budget pacing schedule, we provide a full-information algorithm which obtains regret $O(D \sqrt{\log F}+ \sqrt{T\log F})$ against all experts whose cumulative spending stays within distance $D$ of this schedule, matching lower bounds established by Braverman et al. (2025). We additionally show that our technique extends to various problems in online resource allocation, where the learner gets to see the rewards and costs of the current options available to them, and establish $O(D\sqrt{\log F})$ regret bounds when fractional allocation is allowed. This is the first algorithm we are aware of which can achieve $o(\sqrt{T})$ guarantees for such tasks.

A matching platform is a system that matches participants of different types, such as companies and job-seekers. In such a platform, maximizing matches may concentrate assignments on popular participants, increasing dissatisfaction among others, and eventually causing churn, which reduces the platform's profit opportunities. To address this issue, we propose a novel online learning problem, Combinatorial Allocation Bandits (CAB), which incorporates the notion of arm satisfaction. In CAB, at each round, the learner observes feature vectors for $K$ arms and $N$ users, assigns users to arms, and observes feedback following a generalized linear model (GLM). Unlike prior work, the objective is to maximize arm satisfaction rather than the number of positive feedback. For CAB, we develop an upper confidence bound algorithm that uses an approximate optimization oracle and achieves an approximate regret upper bound, whose dependence on $d$, $T$, and $N$ matches the known lower bound for contextual combinatorial linear bandits up to logarithmic factors. We also analyze a Thompson sampling algorithm with a standard regret bound under an exact optimization oracle, and propose a cheaper one-pass variant retaining sublinear approximate regret under a self-concordance assumption. Experiments on synthetic data support the objective and show that CAB-UCB achieves higher cumulative satisfaction than baselines.