方法对比

	动态规划	随机优化
领域	优化	优化
方法族	Process / pipeline	Process / pipeline
起源年份	1957	1951 (SGD); 2014 (Adam)
提出者	Richard Bellman	—
类型	Exact combinatorial optimization via recursive decomposition	Gradient-based iterative optimization
开创性文献	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Robbins, H. & Monro, S. (1951). A Stochastic Approximation Method. Annals of Mathematical Statistics, 22(3), 400-407.
别名	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	Stokastik Optimizasyon (SGD & Varyantları), stochastic gradient descent, SGD, Adam
相关	3	3
摘要	Dynamic Programming (DP) is an exact optimization technique introduced by Richard Bellman in 1957 for solving multi-stage decision problems. It decomposes a complex problem into simpler, overlapping subproblems, solves each subproblem once, and stores the results to avoid redundant computation. Grounded in the Principle of Optimality, DP guarantees globally optimal solutions whenever the problem exhibits overlapping subproblems and optimal substructure.	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.