# Multi-Objective Bilevel Learning

arXiv: https://arxiv.org/abs/2511.07824 · HTML: https://mlsanity.com/paper/2511.07824/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 75 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 30 of 38)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [TADAM: Task dependent adaptive metric for improved few-shot learning](https://mlsanity.com/paper/1805.10123/) (2018)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Multi-Task Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.09796/) (2020)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [Coresets via Bilevel Optimization for Continual Learning and Streaming](https://mlsanity.com/paper/2006.03875/) (2020)
- [Truncated Back-propagation for Bilevel Optimization](https://mlsanity.com/paper/1810.10667/) (2018)
- [Efficient Multi-objective Neural Architecture Search via Lamarckian Evolution](https://mlsanity.com/paper/1804.09081/) (2018)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [A Near-Optimal Algorithm for Stochastic Bilevel Optimization via Double-Momentum](https://mlsanity.com/paper/2102.07367/) (2021)
- [Provably Faster Algorithms for Bilevel Optimization](https://mlsanity.com/paper/2106.04692/) (2021)
- [A framework for bilevel optimization that enables stochastic and global variance reduction algorithms](https://mlsanity.com/paper/2201.13409/) (2022)
- [A Fully First-Order Method for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2301.10945/) (2023)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Multi-Objective Deep Reinforcement Learning](https://mlsanity.com/paper/1610.02707/) (2016)
- [A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singleton](https://mlsanity.com/paper/2006.04045/) (2020)
- [learn2learn: A Library for Meta-Learning Research](https://mlsanity.com/paper/2008.12284/) (2020)
- [A Single-Timescale Method for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2102.04671/) (2021)
- [Amortized Implicit Differentiation for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2111.14580/) (2021)
- [Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization](https://mlsanity.com/paper/2006.04655/) (2020)
- [Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHF](https://mlsanity.com/paper/2402.06886/) (2024)
- [PARL: A Unified Framework for Policy Alignment in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2308.02585/) (2023)
- [Multi-Objective Meta Learning](https://mlsanity.com/paper/2102.07121/) (2021)
- [Multi-Objective Hyperparameter Optimization in Machine Learning -- An Overview](https://mlsanity.com/paper/2206.07438/) (2022)
- [On the Convergence Theory for Hessian-Free Bilevel Algorithms](https://mlsanity.com/paper/2110.07004/) (2021)

## Built on by (most cited first, 2 of 2)

- [A Tale of Two Problems: Multi-Task Bilevel Learning Meets Equality Constrained Multi-Objective Optimization](https://mlsanity.com/paper/2605.09094/) (2026)
- [Efficient Hessian-Free Methods for Multi-Objective Bilevel Optimization with Nonconvex Lower Level](https://mlsanity.com/paper/2608.12704/) (2026)

## Abstract (arXiv)

As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a compelling need for multi-objective bilevel learning (MOBL). So far, however, the field of MOBL remains in its infancy and many important problems remain under-explored. This motivates us to fill this gap and systematically investigate the theoretical and algorithmic foundation of MOBL. Specifically, we consider MOBL problems with multiple conflicting objectives guided by preferences at the upper-level subproblem, where part of the inputs depend on the optimal solution of the lower-level subproblem. Our goal is to develop efficient MOBL optimization algorithms to (1) identify a preference-guided Pareto-stationary solution with low oracle complexity; and (2) enable systematic Pareto front exploration. To this end, we propose a unifying algorithmic framework called weighted-Chebyshev multi-hyper-gradient-descent (WC-MHGD) for both deterministic and stochastic settings with finite-time Pareto-stationarity convergence rate guarantees, which not only implies low oracle complexity but also induces systematic Pareto front exploration. We further conduct extensive experiments to confirm our theoretical results.