CIF: Small: Self-Adaptive Optimization Algorithms with Fast Convergence via Geometry-Adapted Hyper-Parameter Scheduling

CIF：小型：通过几何自适应超参数调度实现快速收敛的自适应优化算法

• 批准号: 2106216
• 负责人: Yi Zhou
• 金额: $ 41.12万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2106216&HistoricalAwards=false
• 关键词: CIF; Small; Self; Adaptive; Optimization

Machine-learning and artificial-intelligence techniques have been widely applied in modern society to enhance quality of lifr. In these applications, machine-learning models such as neural networks are trained on a large dataset using various optimization algorithms, which iteratively adjust the model parameters and converge to a good model. In particular, the convergence of these optimization algorithms often relies on choosing a good set of hyper-parameters. For example, one important algorithm hyper-parameter is the step size, which controls the scale of the update applied to the model parameters in every iteration, and it must be carefully chosen to avoid slow convergence and possible divergence. In practice, these algorithm hyper-parameters either are guided by optimization theory or are set through manual fine-tuning. While theory-guided algorithm hyper-parameters often rely on certain unknown geometrical information of the model and are often too conservative, resulting in result in slow convergence, manually fine-tuned algorithm hyper-parameters critically depend on the specific application and algorithm, and often introduce much computation overhead. This project aims to address these issues by developing a principled, computation-light and effective hyper-parameter scheduling scheme for different types of optimization algorithms to achieve fast and stable convergence. The developed adapted hyper-parameter scheduling scheme is intended to facilitate machine-learning practitioners tuning the algorithm hyper-parameters and dynamically adapt them to the ongoing optimization process. This has further positive impact on implementation of large-scale machine learning applications such as autonomous driving, training adversary-robust models, robust decision making in finance and control, etc. In this project, the researchers are developing a principled and efficient algorithm hyper-parameter scheduling framework that jointly adapts different algorithm hyper-parameters to the local geometry of the nonconvex objective function for a variety of popular optimization algorithms, and corroborate them with strong theoretical convergence guarantees in nonconvex machine learning. Specifically, the researchers are developing such geometry-adapted hyper-parameter scheduling scheme for deterministic optimization algorithms, including first-order gradient-based algorithms, accelerated gradient algorithms and second-order Newton-type algorithms. The researchers are developing new analysis tools that advance the understanding of the relation between hyper-parameters and the dynamic optimization process. Iteration and computation complexities of these algorithms is being established in nonconvex optimization. Based on this development, the researchers are extending the adapted hyper-parameter scheduling scheme to stochastic optimization algorithms, which use mini-batch random sampling and therefore necessitate a joint scheduling of step-size and batch size. Analysis of sample complexity and high probability convergence guarantee is being established for these algorithms. Furthermore, these developments are guiding the design of adapted hyper-parameter scheduling scheme for gradient-based minimax optimization algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

机器学习和人工智能技术已在现代社会中广泛应用，以提高LIFR的质量。在这些应用程序中，使用各种优化算法在大型数据集上对机器学习模型进行训练，该算法会迭代地调整模型参数并收敛到良好的模型。特别是，这些优化算法的收敛性通常依赖于选择一组良好的超参数。例如，一个重要的算法超参数是步长，它控制着在每次迭代中应用于模型参数的更新的尺度，并且必须仔细选择它以避免缓慢的收敛性和可能的​​差异。 在实践中，这些算法超参数要么以优化理论为指导，要么是通过手动微调设置的。尽管理论指导算法超参数通常依赖于模型的某些未知几何信息，并且通常过于保守，从而导致趋势缓慢，手动微调算法超参数严重取决于特定的应用和算法，并且通常会引入大量的计算。该项目旨在通过开发针对不同类型的优化算法的原则，计算和有效的超参数调度方案来解决这些问题，以实现快速和稳定的收敛性。开发的适应性参数调度方案旨在促进机器学习实践者调整算法超参数，并动态地使其适应持续的优化过程。这对实施大规模机器学习应用程序（例如自主驾驶，培训对手驾驶模型，财务和控制中的强大决策等）具有进一步的积极影响。在该项目中，研究人员正在开发一个有原则的，有效的算法超参数调度表调度框架，这些计划范围与非算法的范围不合格的范围的范围不同，该框架的范围是多种多样的范围，该算法的范围是多种多样的范围，该算法的范围是多种多样的范围，算法，并在非凸机机器学习中以强大的理论融合来证实它们。具体而言，研究人员正在开发用于确定性优化算法的几何适应性超参数调度方案，包括基于一阶梯度算法，加速梯度算法和二阶牛顿型算法。研究人员正在开发新的分析工具，以提高对超参数和动态优化过程之间关系的理解。这些算法的迭代和计算复杂性正在非convex优化中建立。基于此开发，研究人员将适应性的超参数调度方案扩展到随机优化算法，这些算法使用迷你批次随机抽样，因此需要对步进尺寸和批量尺寸进行联合调度。为这些算法建立了样本复杂性和高概率收敛保证的分析。此外，这些发展正在指导基于梯度的Minimax优化算法的适应性超参数调度方案。该奖项反映了NSF的法定任务，并被认为值得通过基金会的知识分子优点和更广泛的影响标准通过评估来进行评估。

项目成果

Sample Efficient Stochastic Policy Extragradient Algorithm for Zero-Sum Markov Game

• 发表时间: 2022
• 作者: Ziyi Chen;Shaocong Ma;Yi Zhou

Accelerated Proximal Alternating Gradient-Descent-Ascent for Nonconvex Minimax Machine Learning

• DOI: 10.1109/isit50566.2022.9834691
• 发表时间: 2021-12
• 期刊: 2022 IEEE International Symposium on Information Theory (ISIT)
• 作者: Ziyi Chen;Shaocong Ma;Yi Zhou

Greedy-GQ with Variance Reduction: Finite-time Analysis and Improved Complexity

• 发表时间: 2021-03
• 期刊: ArXiv
• 作者: Shaocong Ma;Ziyi Chen;Yi Zhou;Shaofeng Zou

Proximal Gradient Descent-Ascent: Variable Convergence under KŁ Geometry

• 发表时间: 2021-02
• 期刊: ArXiv
• 作者: Ziyi Chen;Yi Zhou;Tengyu Xu;Yingbin Liang

Sample and Communication-Efficient Decentralized Actor-Critic Algorithms with Finite-Time Analysis

• 发表时间: 2021-09
• 作者: Ziyi Chen;Yi Zhou;Rongrong Chen;Shaofeng Zou