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We introduce and study online conversion with switching costs, a family ofonline problems that capture emerging problems at the intersection of energyand sustainability. In this problem, an online player attempts to purchase(alternatively, sell) fractional shares of an asset during a fixed time horizonwith length $T$. At each time step, a cost function (alternatively, pricefunction) is revealed, and the player must irrevocably decide an amount ofasset to convert. The player also incurs a switching cost whenever theirdecision changes in consecutive time steps, i.e., when they increase ordecrease their purchasing amount. We introduce competitive (robust)threshold-based algorithms for both the minimization and maximization variantsof this problem, and show they are optimal among deterministic onlinealgorithms. We then propose learning-augmented algorithms that take advantageof untrusted black-box advice (such as predictions from a machine learningmodel) to achieve significantly better average-case performance withoutsacrificing worst-case competitive guarantees. Finally, we empirically evaluateour proposed algorithms using a carbon-aware EV charging case study, showingthat our algorithms substantially improve on baseline methods for this problem.

Online Conversion with Switching Costs: Robust and Learning-Augmented Algorithms