# M-HOF-Opt: Multi-Objective Hierarchical Output Feedback Optimization via Multiplier Induced Loss Landscape Scheduling

arXiv: https://arxiv.org/abs/2403.13728 · HTML: https://mlsanity.com/paper/2403.13728/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 65 references that are in the map.
- First posted on arXiv 20 Mar 2024.

## Builds on (most cited first, 30 of 31)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivation](https://mlsanity.com/paper/1604.06057/) (2016)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization](https://mlsanity.com/paper/2109.02934/) (2021)
- [DIVA: Domain Invariant Variational Autoencoders](https://mlsanity.com/paper/1905.10427/) (2019)
- [Tunability: Importance of Hyperparameters of Machine Learning Algorithms](https://mlsanity.com/paper/1802.09596/) (2018)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [Learning Hierarchical Priors in VAEs](https://mlsanity.com/paper/1905.04982/) (2019)
- [Domain Adversarial Neural Networks for Domain Generalization: When It Works and How to Improve](https://mlsanity.com/paper/2102.03924/) (2021)
- [Scalable Pareto Front Approximation for Deep Multi-Objective Learning](https://mlsanity.com/paper/2103.13392/) (2021)
- [Pareto Invariant Risk Minimization: Towards Mitigating the Optimization Dilemma in Out-of-Distribution Generalization](https://mlsanity.com/paper/2206.07766/) (2022)
- [Piecewise Strong Convexity of Neural Networks](https://mlsanity.com/paper/1810.12805/) (2018)
- [Optimization Algorithms as Robust Feedback Controllers](https://mlsanity.com/paper/2103.11329/) (2021)
- [Domain Invariant Adversarial Learning](https://mlsanity.com/paper/2104.00322/) (2021)
- [High Dimensional Restrictive Federated Model Selection with multi-objective Bayesian Optimization over shifted distributions](https://mlsanity.com/paper/1902.08999/) (2019)
- [Hierarchical Variational Auto-Encoding for Unsupervised Domain Generalization](https://mlsanity.com/paper/2101.09436/) (2021)
- [Variational Resampling Based Assessment of Deep Neural Networks under Distribution Shift](https://mlsanity.com/paper/1906.02972/) (2019)
- [Tutorial and Survey on Probabilistic Graphical Model and Variational Inference in Deep Reinforcement Learning](https://mlsanity.com/paper/1908.09381/) (2019)
- [Closing the Loop: Dynamic State Estimation and Feedback Optimization of Power Grids](https://mlsanity.com/paper/1909.02753/) (2019)

## Abstract (arXiv)

A probabilistic graphical model is proposed, modeling the joint model parameter and multiplier evolution, with a hypervolume based likelihood, promoting multi-objective descent in structural risk minimization. We address multi-objective model parameter optimization via a surrogate single objective penalty loss with time-varying multipliers, equivalent to online scheduling of loss landscape. The multi-objective descent goal is dispatched hierarchically into a series of constraint optimization sub-problems with shrinking bounds according to Pareto dominance. The bound serves as setpoint for the low-level multiplier controller to schedule loss landscapes via output feedback of each loss term. Our method forms closed loop of model parameter dynamic, circumvents excessive memory requirements and extra computational burden of existing multi-objective deep learning methods, and is robust against controller hyperparameter variation, demonstrated on domain generalization tasks with multi-dimensional regularization losses.