Multi-objective gradient methods are becoming the standard for solving
multi-objective problems. Among others, they show promising results in
developing multi-objective recommender systems with both correlated and
conflicting objectives. Classic multi-gradient~descent usually relies on the
combination of the gradients, not including the computation of first and second
moments of the gradients. This leads to a brittle behavior and misses important
areas in the solution space. In this work, we create a multi-objective
model-agnostic Adamize method that leverages the benefits of the Adam optimizer
in single-objective problems. This corrects and stabilizes~the~gradients of
every objective before calculating a common gradient descent vector that
optimizes all the objectives simultaneously. We evaluate the benefits of
Multi-objective Adamize on two multi-objective recommender systems and for
three different objective combinations, both correlated or conflicting. We
report significant improvements, measured with three different Pareto front
metrics: hypervolume, coverage, and spacing. Finally, we show that the
\textit{Adamized} Pareto front strictly dominates the previous one on multiple
objective pairs.

本文介绍一种多目标梯度下降算法，利用 Adam optimizer 优化多目标推荐系统，通过多个 Pareto front metrics 得出该算法具有显著的改进，且优于之前的算法。