方法对比

	随机优化	进化策略（CMA-ES）	鲁棒优化
领域	优化	优化	优化
方法族	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	1951 (SGD); 2014 (Adam)	2001	1970s theoretical roots; modern tractable form from late 1990s–2004
提出者	—	Nikolaus Hansen & Andreas Ostermeier	Ben-Tal, El Ghaoui & Nemirovski (seminal book, 2009); Bertsimas & Sim (tractable polyhedral formulation, 2004)
类型	Gradient-based iterative optimization	Derivative-free continuous black-box optimizer	Mathematical programming framework
开创性文献	Robbins, H. & Monro, S. (1951). A Stochastic Approximation Method. Annals of Mathematical Statistics, 22(3), 400-407.	Hansen, N. & Ostermeier, A. (2001). Completely Derandomized Self-Adaptation in Evolutionary Strategies. Evolutionary Computation, 9(2), 159-195.	Ben-Tal, A., El Ghaoui, L. & Nemirovski, A. (2009). Robust Optimization. Princeton University Press. ISBN: 9780691143682
别名	Stokastik Optimizasyon (SGD & Varyantları), stochastic gradient descent, SGD, Adam	CMA-ES, Evolution Strategy, Evrimsel Strateji (CMA-ES), self-adapting evolution strategy	minimax optimization, worst-case optimization, Gürbüz Optimizasyon (Robust Optimization)
相关	3	5	5
摘要	Stochastic optimization is a family of iterative methods that minimize an objective function by computing gradients on randomly sampled subsets of data — mini-batches — rather than on the entire dataset at once. Pioneered by Robbins and Monro in 1951 as stochastic approximation, the approach became the standard engine for training large-scale machine-learning models through variants such as SGD with momentum, AdaGrad, RMSProp, and Adam.	CMA-ES, short for Covariance Matrix Adaptation Evolution Strategy, is a modern derivative-free optimizer for continuous black-box functions introduced by Hansen and Ostermeier in 2001. It maintains a population of candidate solutions drawn from a multivariate normal distribution and iteratively updates the distribution's mean, step size, and full covariance matrix to steer the search toward better regions of the parameter space. It has become the de-facto standard for continuous black-box optimization and is widely used in neural architecture search and reinforcement-learning policy optimization.	Robust optimization is a mathematical programming framework, formalised by Ben-Tal and Nemirovski in the late 1990s and made broadly tractable by Bertsimas and Sim (2004), that finds decisions guaranteed to perform acceptably under every scenario within a predefined uncertainty set — rather than assuming parameter values are known exactly. Instead of optimising for a single expected outcome, it minimises the worst-case objective across all plausible realisations of uncertain data.