Selecting the best hyperparameters for a particular optimization instance, such as the learning rate and momentum, is an important but nonconvex problem. As a result, iterative optimization methods such as hypergradient descent lack global optimality guarantees in general.
We propose an online nonstochastic control methodology for mathematical optimization. First, we formalize the setting of meta-optimization, an online learning formulation of learning the best optimization algorithm from a class of methods. The meta-optimization problem over gradient-based methods can be framed as a feedback control problem over the choice of hyperparameters, including the learning rate, momentum, and the preconditioner.
Although the original optimal control problem is nonconvex, we show how recent methods from online nonstochastic control using convex relaxations can be used to overcome the challenge of nonconvexity, and obtain regret guarantees against the best offline solution. This guarantees that in meta-optimization, given a sequence of optimization problems, we can learn a method that attains convergence comparable to that of the best optimization method in hindsight from a class of methods.
An Empirical Study on the Computation Budget of Co-Optimization of Robot Design and Control in Simulation
NTNU Institutt for teknisk kybernetikk（挪威特罗姆瑟大学技术 cybernetics 院）；Department of Game Development - Inland Norway University（内陆挪威大学游戏开发系）；Department of Technology Systems, University of Oslo（奥斯陆大学技术系统系）；RITMO Centre for Interdisciplinary Studies in Rhythm, Time and Motion, University of Oslo（奥斯陆大学节奏、时间与运动跨学科研究中心）；Department of Informatics, University of Oslo（奥斯陆大学信息系）
Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Massachusetts Institute of Technology（麻省理工学院）；University of Maryland, College Park（马里兰大学帕克分校）；Harvard University（哈佛大学）；University of Washington（华盛顿大学）
VABO: Violation-Aware Bayesian Optimization for Closed-Loop Control Performance Optimization with Unmodeled Constraints
Mitsubishi Electric Research Laboratories（三菱电机研究院）；École polytechnique fédérale de Lausanne（洛桑联邦理工学院）；Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科学与技术实验室）
