Online optimization with memory costs has many real-world applications, where
sequential actions are made without knowing the future input. Nonetheless, the
memory cost couples the actions over time, adding substantial challenges.
Conventionally, this problem has been approached by various expert-designed
online algorithms with the goal of achieving bounded worst-case competitive
ratios, but the resulting average performance is often unsatisfactory. On the
other hand, emerging machine learning (ML) based optimizers can improve the
average performance, but suffer from the lack of worst-case performance
robustness. In this paper, we propose a novel expert-robustified learning (ERL)
approach, achieving {both} good average performance and robustness. More
concretely, for robustness, ERL introduces a novel projection operator that
robustifies ML actions by utilizing an expert online algorithm; for average
performance, ERL trains the ML optimizer based on a recurrent architecture by
explicitly considering downstream expert robustification. We prove that, for
any $\lambda\geq1$, ERL can achieve $\lambda$-competitive against the expert
algorithm and $\lambda\cdot C$-competitive against the optimal offline
algorithm (where $C$ is the expert's competitive ratio). Additionally, we
extend our analysis to a novel setting of multi-step memory costs. Finally, our
analysis is supported by empirical experiments for an energy scheduling
application.

提出一种新的 Expert-Robustified Learning (ERL) 方法，即利用专家在线算法进行投影运算实现对机器学习行为（即 Online Optimization with Memory Costs）的强度鲁棒性，并通过递归神经网络模型进行传递专家在线算法的平均性能训练，从而在内存成本上提高行为竞争性能和稳健性。