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

• Projection Optimization: A General Framework for Multi-Objective and Multi-Group RLHF [13.612504157832708]
  Reinforcement Learning with Human Feedback (RLHF) is a widely used fine-tuning approach that aligns machine learning model with human preferences. In this work, we transform the non-linear aggregation problem into a series of sub-problems and extend our framework to handle multi-group scenarios. We demonstrate that our algorithmic framework achieves sublinear regret and can be easily adapted to a reward-free algorithm.
  arXiv  Detail & Related papers  (2025-02-21T01:56:52Z)
• Modeling Multi-Task Model Merging as Adaptive Projective Gradient Descent [72.10987117380584]
  Merging multiple expert models offers a promising approach for performing multi-task learning without accessing their original data.<n>We find existing methods discard task-specific information that, while causing conflicts, is crucial for performance.<n>Our approach consistently outperforms previous methods, achieving state-of-the-art results across diverse architectures and tasks in both vision and NLP domains.
  arXiv  Detail & Related papers  (2025-01-02T12:45:21Z)
• Enhancing Generalization of Universal Adversarial Perturbation through Gradient Aggregation [40.18851174642427]
  Deep neural networks are vulnerable to universal adversarial perturbation (UAP) In this paper, we examine the serious dilemma of UAP generation methods from a generalization perspective. We propose a simple and effective method called Gradient Aggregation (SGA) SGA alleviates the gradient vanishing and escapes from poor local optima at the same time.
  arXiv  Detail & Related papers  (2023-08-11T08:44:58Z)
• 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)
• Scalable Bayesian Meta-Learning through Generalized Implicit Gradients [64.21628447579772]
  Implicit Bayesian meta-learning (iBaML) method broadens the scope of learnable priors, but also quantifies the associated uncertainty. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one.
  arXiv  Detail & Related papers  (2023-03-31T02:10:30Z)
• Global and Preference-based Optimization with Mixed Variables using Piecewise Affine Surrogates [0.6083861980670925]
  This paper proposes a novel surrogate-based global optimization algorithm to solve linearly constrained mixed-variable problems. We assume the objective function is black-box and expensive-to-evaluate, while the linear constraints are quantifiable unrelaxable a priori known. We introduce two types of exploration functions to efficiently search the feasible domain via mixed-integer linear programming solvers.
  arXiv  Detail & Related papers  (2023-02-09T15:04:35Z)
• Supervised Contrastive Learning as Multi-Objective Optimization for Fine-Tuning Large Pre-trained Language Models [3.759936323189417]
  Supervised Contrastive Learning (SCL) has been shown to achieve excellent performance in most classification tasks. In this work, we formulate the SCL problem as a Multi-Objective Optimization problem for the fine-tuning phase of RoBERTa language model.
  arXiv  Detail & Related papers  (2022-09-28T15:13:58Z)
• Provable Stochastic Optimization for Global Contrastive Learning: Small Batch Does Not Harm Performance [53.49803579981569]
  We consider a global objective for contrastive learning, which contrasts each positive pair with all negative pairs for an anchor point. Existing methods such as SimCLR requires a large batch size in order to achieve a satisfactory result. We propose a memory-efficient optimization algorithm for solving the Global Contrastive Learning of Representations, named SogCLR.
  arXiv  Detail & Related papers  (2022-02-24T22:16:53Z)
• Distribution-aware Margin Calibration for Semantic Segmentation in Images [78.65312390695038]
  Jaccard index, also known as Intersection-over-Union (IoU), is one of the most critical evaluation metrics in image semantic segmentation. Direct optimization of IoU score is very difficult because the learning objective is neither differentiable nor decomposable. We propose a margin calibration method, which can be directly used as a learning objective, for an improved generalization of IoU over the data-distribution.
  arXiv  Detail & Related papers  (2021-12-21T22:38:25Z)
• 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)
• Follow the bisector: a simple method for multi-objective optimization [65.83318707752385]
  We consider optimization problems, where multiple differentiable losses have to be minimized. The presented method computes descent direction in every iteration to guarantee equal relative decrease of objective functions.
  arXiv  Detail & Related papers  (2020-07-14T09:50:33Z)
• Cogradient Descent for Bilinear Optimization [124.45816011848096]
  We introduce a Cogradient Descent algorithm (CoGD) to address the bilinear problem. We solve one variable by considering its coupling relationship with the other, leading to a synchronous gradient descent. Our algorithm is applied to solve problems with one variable under the sparsity constraint.
  arXiv  Detail & Related papers  (2020-06-16T13:41:54Z)

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.