# Momentum-based Gradient Methods in Multi-Objective Recommendation

arXiv: https://arxiv.org/abs/2009.04695 · HTML: https://mlsanity.com/paper/2009.04695/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2020.

## Built on by (most cited first, 4 of 4)

- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art](https://mlsanity.com/paper/2412.01566/) (2024)
- [A multiobjective continuation method to compute the regularization path of deep neural networks](https://mlsanity.com/paper/2308.12044/) (2023)
- [Common pitfalls to avoid while using multiobjective optimization in machine learning](https://mlsanity.com/paper/2405.01480/) (2024)

## Abstract (arXiv)

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 textitAdamized Pareto front strictly dominates the previous one on multiple objective pairs.