We introduce and study online conversion with switching costs, a family of online problems that capture emerging problems at the intersection of energy and sustainability. In this problem, an online player attempts to purchase (alternatively, sell) fractional shares of an asset during a fixed time horizon with length $T$. At each time step, a cost function (alternatively, price function) is revealed, and the player must irrevocably decide an amount of asset to convert. The player also incurs a switching cost whenever their decision changes in consecutive time steps, i.e., when they increase or decrease their purchasing amount. We introduce competitive (robust) threshold-based algorithms for both the minimization and maximization variants of this problem, and show they are optimal among deterministic online algorithms. We then propose learning-augmented algorithms that take advantage of untrusted black-box advice (such as predictions from a machine learning model) to achieve significantly better average-case performance without sacrificing worst-case competitive guarantees. Finally, we empirically evaluate our proposed algorithms using a carbon-aware EV charging case study, showing that our algorithms substantially improve on baseline methods for this problem.

翻译：我们引入并研究了带有切换成本的在线转换问题，这是一个捕捉能源与可持续性交叉领域新兴问题的在线问题族。在该问题中，一位在线参与者在固定时间范围$T$内试图购买（或出售）资产的份额。在每个时间步，成本函数（或价格函数）被揭示，参与者必须不可撤销地决定转换的资产数量。当参与者在连续时间步中的决策发生变化时，即当他们增加或减少购买量时，还会产生切换成本。我们针对该问题的极小化和极大化变体引入了竞争性（鲁棒）阈值算法，并证明其在确定性在线算法中是最优的。随后，我们提出了学习增强算法，这些算法利用不可信的黑盒建议（例如来自机器学习模型的预测）来显著提升平均性能，同时不牺牲最坏情况下的竞争性保证。最后，我们通过一个碳感知电动汽车充电的案例研究对提出的算法进行了实证评估，结果表明我们的算法在该问题上显著优于基线方法。