We introduce and study a class of online problems called online smoothed demand management $(\texttt{OSDM})$, motivated by paradigm shifts in grid integration and energy storage for large energy consumers such as data centers. In $\texttt{OSDM}$, an operator makes two decisions at each time step: an amount of energy to be purchased, and an amount of energy to be delivered (i.e., used for computation). The difference between these decisions charges (or discharges) the operator's energy storage (e.g., a battery). Two types of demand arrive online: base demand, which must be covered at the current time, and flexible demand, which can be satisfied at any time before a demand-specific deadline $Δ_t$. The operator's goal is to minimize a cost (subject to above constraints) that combines a cost of purchasing energy, a cost for delivering energy (if applicable), and smoothness penalties on the purchasing and delivery rates to discourage fluctuations and encourage ``grid healthy'' decisions. $\texttt{OSDM}$ generalizes several problems in the online algorithms literature while being the first to fully model applications of interest. We propose a competitive algorithm for $\texttt{OSDM}$ called $\texttt{PAAD}$ (partitioned accounting & aggregated decisions) and show it achieves the optimal competitive ratio. To overcome the pessimism typical of worst-case analysis, we also propose a novel learning framework that provides guarantees on the worst-case competitive ratio (i.e., to provide robustness against nonstationarity) while allowing end-to-end differentiable learning of the best algorithm on historical instances of the problem. We evaluate our algorithms in a case study of a grid-integrated data center with battery storage, showing that $\texttt{PAAD}$ effectively solves the problem and end-to-end learning achieves substantial performance improvements compared to $\texttt{PAAD}$.

翻译：本文提出并研究了一类称为在线平滑需求管理（$\texttt{OSDM}$）的在线问题，其动机源于数据中心等大型能源消费者在电网集成和储能方面的范式转变。在 $\texttt{OSDM}$ 中，操作员在每个时间步做出两个决策：采购的能源量，以及交付（即用于计算）的能源量。这两个决策之间的差值会对操作员的储能系统（例如电池）进行充电（或放电）。在线到达两种类型的需求：必须立即满足的基本需求，以及可以在特定需求截止时间 $Δ_t$ 之前的任意时刻满足的弹性需求。操作员的目标是在满足上述约束的条件下最小化总成本，该成本包括能源采购成本、能源交付成本（如适用），以及对采购速率和交付速率的平滑性惩罚，以抑制波动并鼓励“电网友好”的决策。$\texttt{OSDM}$ 概括了在线算法文献中的若干问题，同时首次完整地建模了相关应用。我们为 $\texttt{OSDM}$ 提出了一种名为 $\texttt{PAAD}$（分区计费与聚合决策）的竞争性算法，并证明其达到了最优竞争比。为了克服最坏情况分析中典型的悲观性，我们还提出了一种新颖的学习框架，该框架能在最坏情况竞争比上提供保证（即提供对非平稳性的鲁棒性），同时允许在问题的历史实例上对最佳算法进行端到端的可微分学习。我们通过一个配备电池储能的电网集成数据中心的案例研究评估了我们的算法，结果表明 $\texttt{PAAD}$ 能有效解决该问题，并且端到端学习相比 $\texttt{PAAD}$ 实现了显著的性能提升。