Nonpreemptive Scheduling While Learning Context-Dependent Service Rates

Wansoo Choi, Seoungbin Bae, Dabeen Lee

We study nonpreemptive contextual queueing bandits in a single-server system. Each job is represented by a $d$-dimensional context vector; in each round, a job may arrive with its context drawn from an unknown distribution $\mathcal{D}$, and its departure probability is determined by a logistic model of that context vector with an unknown parameter $θ^*$. The server learns from service outcomes while deciding which waiting job to serve and whether to idle, aiming to minimize queue-length regret, the gap between its expected terminal queue length and the minimum achievable by an admissible policy. Once selected, a job must be served until completion, and we refer to this as the nonpreemptive setting. A central challenge is that, even with full model knowledge, the optimal policy cannot in general be characterized by a simple myopic rule, since the optimal action can change with the remaining horizon at the same queue state. Nevertheless, when the model and horizon are known, the optimal action can be obtained through a finite-horizon Bellman recursion. Motivated by this, we propose Learn--Clear--Plan (LCP), which estimates the system and uses the resulting Bellman recursion to…