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：我们提出并研究带切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问题的在线问题家族。在该问题中，在线玩家需在固定时间范围$T$内，尝试购买（或出售）某项资产的部分份额。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资产转换数量。当玩家在连续时间步中改变决策（即增减购买量）时，还需承担切换成本。针对该问题的最小化与最大化变体，我们提出基于阈值的竞争性（稳健型）算法，并证明其在确定性在线算法中具有最优性。随后，我们设计学习增强型算法，通过利用不可信黑盒建议（例如机器学习模型的预测），在不牺牲最坏情况竞争保证的前提下，显著提升平均表现。最后，我们以碳感知电动汽车充电案例研究对算法进行实证评估，结果表明我们的算法在该问题上显著优于基线方法。