One challenge in the optimization and control of societal systems is to handle the unknown and uncertain user behavior. This paper focuses on residential demand response (DR) and proposes a closed-loop learning scheme to address these issues. In particular, we consider DR programs where an aggregator calls upon residential users to change their demand so that the total load adjustment is close to a target value. To learn and select the right users, we formulate the DR problem as a combinatorial multi-armed bandit (CMAB) problem with a reliability objective. We propose a learning algorithm: CUCB-Avg (Combinatorial Upper Confidence Bound-Average), which utilizes both upper confidence bounds and sample averages to balance the tradeoff between exploration (learning) and exploitation (selecting). We consider both a fixed time-invariant target and time-varying targets, and show that CUCB-Avg achieves $O(logT)$ and $O\left(\sqrt{Tlog\left(T\right)}\right)$ regrets respectively. Finally, we numerically test our algorithms using synthetic and real data, and demonstrate that our CUCB-Avg performs significantly better than the classic CUCB and also better than Thompson Sampling.

在优化和控制社会系统中的一项挑战是处理未知和不确定的用户行为。本文着重于住宅需求响应（DR），并提出了一种闭环学习方案来解决这些问题。特别是，我们考虑了DR计划，其中聚合器要求居民用户更改其需求，以使总负载调整接近目标值。为了学习和选择合适的用户，我们将DR问题公式化为具有可靠性目标的组合式多臂匪（CMAB）问题。我们提出一种学习算法：CUCB-Avg（组合上限置信区间平均值），该算法同时利用置信上限和样本平均值来平衡探索（学习）与开发（选择）之间的权衡。$Ø（日志Ť）$ 和 $Ø（\sqrt{Ť日志（Ť）}）$分别感到遗憾。最后，我们使用合成数据和真实数据对算法进行了数值测试，并证明了我们的CUCB-Avg的性能明显优于经典CUCB，也优于汤普森采样。