# Bilevel optimization with a multi-objective lower-level problem: Risk-neutral and risk-averse formulations

arXiv: https://arxiv.org/abs/2302.05540 · HTML: https://mlsanity.com/paper/2302.05540/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2023.

## Built on by (most cited first, 5 of 5)

- [Optimal Algorithms for Stochastic Bilevel Optimization under Relaxed Smoothness Conditions](https://mlsanity.com/paper/2306.12067/) (2023)
- [A stochastic gradient method for trilevel optimization](https://mlsanity.com/paper/2505.06805/) (2025)
- [On the Stability and Generalization of First-order Bilevel Minimax Optimization](https://mlsanity.com/paper/2604.20115/) (2026)
- [Robust Server Defense Against Unreliable Clients in One-Shot Fair Collaborative Machine Learning](https://mlsanity.com/paper/2605.08616/) (2026)
- [Efficient Hessian-Free Methods for Multi-Objective Bilevel Optimization with Nonconvex Lower Level](https://mlsanity.com/paper/2608.12704/) (2026)

## Abstract (arXiv)

In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective optimization. To solve bilevel problems with a multi-objective lower level, different approaches can be considered depending on the interpretation of the lower-level optimality. An optimistic formulation that was previously introduced for the deterministic case consists of minimizing the upper-level function over all non-dominated lower-level solutions. In this paper, we develop new risk-neutral and risk-averse formulations, address their main computational challenges, and develop the corresponding deterministic and stochastic gradient-based algorithms.