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：我们引入并研究了具有转换成本的在线转换问题，这是一类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，在线玩家在固定时间区间（长度为$T$）内尝试购买（或等价地，出售）某种资产的小数份额。在每个时间步，成本函数（或价格函数）被揭示，玩家必须不可撤销地决定转换的资产数量。此外，当玩家的决策在连续时间步之间发生变化时（即增加或减少购买量），他们还需承担转换成本。针对该问题的最小化和最大化变体，我们提出了基于阈值的竞争性（鲁棒）算法，并证明这些算法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，该算法利用不可信的黑盒建议（如机器学习模型的预测）来显著提升平均情况性能，同时不牺牲最坏情况下的竞争保证。最后，我们通过碳感知电动汽车充电案例研究对所提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。