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The goal of multi-objective optimization is to identify a collection ofpoints which describe the best possible trade-offs between the multipleobjectives. In order to solve this vector-valued optimization problem,practitioners often appeal to the use of scalarization functions in order totransform the multi-objective problem into a collection of single-objectiveproblems. This set of scalarized problems can then be solved using traditionalsingle-objective optimization techniques. In this work, we formalise thisconvention into a general mathematical framework. We show how this strategyeffectively recasts the original multi-objective optimization problem into asingle-objective optimization problem defined over sets. An appropriate classof objective functions for this new problem is the R2 utility function, whichis defined as a weighted integral over the scalarized optimization problems. Weshow that this utility function is a monotone and submodular set function,which can be optimised effectively using greedy optimization algorithms. Weanalyse the performance of these greedy algorithms both theoretically andempirically. Our analysis largely focusses on Bayesian optimization, which is apopular probabilistic framework for black-box optimization.

Multi-Objective Optimization Using the R2 Utility