This paper leverages machine-learned predictions to design competitive algorithms for online conversion problems with the goal of improving the competitive ratio when predictions are accurate (i.e., consistency), while also guaranteeing a worst-case competitive ratio regardless of the prediction quality (i.e., robustness). We unify the algorithmic design of both integral and fractional conversion problems, which are also known as the 1-max-search and one-way trading problems, into a class of online threshold-based algorithms (OTA). By incorporating predictions into design of OTA, we achieve the Pareto-optimal trade-off of consistency and robustness, i.e., no online algorithm can achieve a better consistency guarantee given for a robustness guarantee. We demonstrate the performance of OTA using numerical experiments on Bitcoin conversion.

The study of online algorithms with machine-learned predictions has gained considerable prominence in recent years. One of the common objectives in the design and analysis of such algorithms is to attain (Pareto) optimal tradeoffs between the consistency of the algorithm, i.e., its performance assuming perfect predictions, and its robustness, i.e., the performance of the algorithm under adversarial predictions. In this work, we demonstrate that this optimization criterion can be extremely brittle, in that the performance of Pareto-optimal algorithms may degrade dramatically even in the presence of imperceptive prediction error. To remedy this drawback, we propose a new framework in which the smoothness in the performance of the algorithm is enforced by means of a user-specified profile. This allows us to regulate the performance of the algorithm as a function of the prediction error, while simultaneously maintaining the analytical notion of consistency/robustness tradeoffs, adapted to the profile setting. We apply this new approach to a well-studied online problem, namely the one-way trading problem. For this problem, we further address another limitation of the state-of-the-art Pareto-optimal algorithms, namely the fact that they are tailored to worst-case, and extremely pessimistic inputs. We propose a new Pareto-optimal algorithm that leverages any deviation from the worst-case input to its benefit, and introduce a new metric that allows us to compare any two Pareto-optimal algorithms via a dominance relation.