Decision-Theoretic Approaches in Learning-Augmented Algorithms

In this work, we initiate the systemic study of decision-theoretic metrics in the design and analysis of algorithms with machine-learned predictions. We introduce approaches based on both deterministic measures such as distance-based evaluation, that help us quantify how close the algorithm is to an ideal solution, as well as stochastic measures that allow us to balance the trade-off between the algorithm's performance and the risk associated with the imperfect oracle. These approaches help us quantify the algorithmic performance across the entire spectrum of prediction error, unlike several previous works that focus on few, and often extreme values of the error. We apply these techniques to two well-known problems from resource allocation and online decision making, namely contract scheduling and 1-max search.