It is desirable in many multi-objective machine learning applications, such
as multi-task learning and multi-objective reinforcement learning, to find a
Pareto optimal solution that can exactly match a given preference of
decision-makers. These problems are often large-scale with available gradient
information but cannot be handled very well by the existing algorithms. To
tackle this critical issue, this paper proposes a novel predict-and-correct
framework for locating the exact Pareto optimal solutions required by a
decision maker. In the proposed framework, a constraint function is introduced
in the search progress to align the solution with a user-specific preference,
which can be optimized simultaneously with multiple objective functions.
Experimental results show that our proposed method can efficiently find exact
Pareto optimal solutions for standard benchmarks, multi-task, and
multi-objective reinforcement learning problems with more than thousands of
decision variables.
Code is available at: https://github.com/xzhang2523/pmgda.

为了解决多目标机器学习中出现的问题，本文提出了一种新颖的预测和校正框架，用于定位决策者所需的精确 Pareto 最优解。该方法可以高效地在标准基准、多任务和多目标强化学习问题中找到精确的 Pareto 最优解。

PMGDA: 基于偏好的多梯度下降算法

PMGDA: A Preference-based Multiple Gradient Descent Algorithm

Hyperparameter optimization (HPO) is important to leverage the full potential
of machine learning (ML). In practice, users are often interested in
multi-objective (MO) problems, i.e., optimizing potentially conflicting
objectives, like accuracy and energy consumption. To tackle this, the vast
majority of MO-ML algorithms return a Pareto front of non-dominated machine
learning models to the user. Optimizing the hyperparameters of such algorithms
is non-trivial as evaluating a hyperparameter configuration entails evaluating
the quality of the resulting Pareto front. In literature, there are known
indicators that assess the quality of a Pareto front (e.g., hypervolume, R2) by
quantifying different properties (e.g., volume, proximity to a reference
point). However, choosing the indicator that leads to the desired Pareto front
might be a hard task for a user. In this paper, we propose a human-centered
interactive HPO approach tailored towards multi-objective ML leveraging
preference learning to extract desiderata from users that guide the
optimization. Instead of relying on the user guessing the most suitable
indicator for their needs, our approach automatically learns an appropriate
indicator. Concretely, we leverage pairwise comparisons of distinct Pareto
fronts to learn such an appropriate quality indicator. Then, we optimize the
hyperparameters of the underlying MO-ML algorithm towards this learned
indicator using a state-of-the-art HPO approach. In an experimental study
targeting the environmental impact of ML, we demonstrate that our approach
leads to substantially better Pareto fronts compared to optimizing based on a
wrong indicator pre-selected by the user, and performs comparable in the case
of an advanced user knowing which indicator to pick.

我们提出了一种以人为中心的交互式超参数优化方法，旨在从用户中提取优化指标并引导优化，通过学习比较不同帕累托前沿以选择适当的质量指标进行改进，在 ML 环境影响评估中验证了该方法的有效性。