Jacobian Descent for Multi-Objective Optimization
- URL: http://arxiv.org/abs/2406.16232v1
- Date: Sun, 23 Jun 2024 22:06:25 GMT
- Title: Jacobian Descent for Multi-Objective Optimization
- Authors: Pierre Quinton, Valérian Rey,
- Abstract summary: We formalize Jacobian descent (JD) as a generalization of gradient descent for vector-valued functions.
In particular, the update should not conflict with any objective and should scale proportionally to the norm of each gradient.
Most notably, we introduce instance-wise risk minimization (IWRM), a learning paradigm in which the loss of each training example is considered a separate objective.
- Score: 0.6138671548064355
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Many optimization problems are inherently multi-objective. To address them, we formalize Jacobian descent (JD), a direct generalization of gradient descent for vector-valued functions. Each step of this algorithm relies on a Jacobian matrix consisting of one gradient per objective. The aggregator, responsible for reducing this matrix into an update vector, characterizes JD. While the multi-task learning literature already contains a variety of aggregators, they often lack some natural properties. In particular, the update should not conflict with any objective and should scale proportionally to the norm of each gradient. We propose a new aggregator specifically designed to satisfy this. Emphasizing conflict between objectives, we then highlight direct applications for our methods. Most notably, we introduce instance-wise risk minimization (IWRM), a learning paradigm in which the loss of each training example is considered a separate objective. On simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss. The performance of our aggregator in those experiments also corroborates our theoretical findings. Lastly, as speed is the main limitation of JD, we provide a path towards a more efficient implementation.
Related papers
- Self-Exploring Language Models: Active Preference Elicitation for Online Alignment [90.4820014819937]
We propose a bilevel objective optimistically biased towards potentially high-reward responses to actively explore out-of-distribution regions.
Our experimental results demonstrate that when finetuned on Zephyr-7B-SFT and Llama-3-8B-Instruct models, SELM significantly boosts the performance on instruction-following benchmarks.
arXiv Detail & Related papers (2024-05-29T17:59:07Z) - Direction-oriented Multi-objective Learning: Simple and Provable
Stochastic Algorithms [12.776767874217663]
We propose a new direction-oriented multi-objective problem by regularizing the common descent direction within a neighborhood of a direction.
We demonstrate the superior performance of the proposed methods in a series of tasks on multi-task supervised learning and reinforcement learning.
arXiv Detail & Related papers (2023-05-28T16:13:59Z) - Self-Supervised Learning via Maximum Entropy Coding [57.56570417545023]
We propose Maximum Entropy Coding (MEC) as a principled objective that explicitly optimize on the structure of the representation.
MEC learns a more generalizable representation than previous methods based on specific pretext tasks.
It achieves state-of-the-art performance consistently on various downstream tasks, including not only ImageNet linear probe, but also semi-supervised classification, object detection, instance segmentation, and object tracking.
arXiv Detail & Related papers (2022-10-20T17:58:30Z) - CASAPose: Class-Adaptive and Semantic-Aware Multi-Object Pose Estimation [2.861848675707602]
We present a new single-stage architecture called CASAPose.
It determines 2D-3D correspondences for pose estimation of multiple different objects in RGB images in one pass.
It is fast and memory efficient, and achieves high accuracy for multiple objects.
arXiv Detail & Related papers (2022-10-11T10:20:01Z) - Efficient first-order predictor-corrector multiple objective
optimization for fair misinformation detection [5.139559672771439]
Multiple-objective optimization (MOO) aims to simultaneously optimize multiple conflicting objectives and has found important applications in machine learning.
We propose a Gauss-Newton approximation that only scales linearly, and that requires only first-order inner-product per iteration.
The innovations make predictor-corrector possible for large networks.
arXiv Detail & Related papers (2022-09-15T12:32:15Z) - Generative multitask learning mitigates target-causing confounding [61.21582323566118]
We propose a simple and scalable approach to causal representation learning for multitask learning.
The improvement comes from mitigating unobserved confounders that cause the targets, but not the input.
Our results on the Attributes of People and Taskonomy datasets reflect the conceptual improvement in robustness to prior probability shift.
arXiv Detail & Related papers (2022-02-08T20:42:14Z) - Conflict-Averse Gradient Descent for Multi-task Learning [56.379937772617]
A major challenge in optimizing a multi-task model is the conflicting gradients.
We introduce Conflict-Averse Gradient descent (CAGrad) which minimizes the average loss function.
CAGrad balances the objectives automatically and still provably converges to a minimum over the average loss.
arXiv Detail & Related papers (2021-10-26T22:03:51Z) - KL Guided Domain Adaptation [88.19298405363452]
Domain adaptation is an important problem and often needed for real-world applications.
A common approach in the domain adaptation literature is to learn a representation of the input that has the same distributions over the source and the target domain.
We show that with a probabilistic representation network, the KL term can be estimated efficiently via minibatch samples.
arXiv Detail & Related papers (2021-06-14T22:24:23Z) - Learning by Minimizing the Sum of Ranked Range [58.24935359348289]
We introduce the sum of ranked range (SoRR) as a general approach to form learning objectives.
A ranked range is a consecutive sequence of sorted values of a set of real numbers.
We explore two applications in machine learning of the minimization of the SoRR framework, namely the AoRR aggregate loss for binary classification and the TKML individual loss for multi-label/multi-class classification.
arXiv Detail & Related papers (2020-10-05T01:58:32Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.