Reviews: Multiclass Performance Metric Elicitation

This paper studies the metric elicitation problem, a problem proposed by [7] (AISTATS'19 paper). The authors defined two types of metrics for multi-class classification, Diagonal Linear Performance Metric (DLPM) and Linear Performance Metric (LPM), and designed algorithms for the two type of metrics respectively. The algorithm for DLPM is relatively simple: just use binary-search like [7] and apply it for (k-1) times. The LPM case is much more complicated - the authors proposed a coordinate-wise binary-search style algorithm based on the geometry of the feasible set. Theoretical guarantees for both algorithms are provided.