Jacobian Descent for Multi-Objective Optimization
Keywords: multi-objective optimization, optimization, statistical learning theory, machine learning, deep learning, multi-task learning
TL;DR: We propose Jacobian descent, a generalization of gradient descent supporting multi-objective optimization, and we experiment with it on a new learning paradigm called instance-wise risk minimization.
Abstract: Many optimization problems require balancing multiple conflicting objectives.
As gradient descent is limited to single-objective optimization, we introduce its direct generalization: Jacobian descent (JD).
This algorithm iteratively updates parameters using the Jacobian matrix of a vector-valued objective function, in which each row is the gradient of an individual objective.
While several methods to combine gradients already exist in the literature, they are generally hindered when the objectives conflict.
In contrast, we propose projecting gradients to fully resolve conflict while ensuring that they preserve an influence proportional to their norm.
We prove significantly stronger convergence guarantees with this approach, supported by our empirical results.
Our method also enables instance-wise risk minimization (IWRM), a novel learning paradigm in which the loss of each training example is considered a separate objective.
Applied to simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss.
Additionally, we outline an efficient implementation of JD using the Gramian of the Jacobian matrix to reduce time and memory requirements.
Supplementary Material: zip
Primary Area: optimization
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 11709
Loading