方法对比

	动态规划	深度强化学习	整数规划
领域	优化	深度学习	优化
方法族	Process / pipeline	Machine learning	Process / pipeline
起源年份	1957	2015	1958
提出者	Richard Bellman	Mnih, V. et al. (DQN)	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
类型	Exact combinatorial optimization via recursive decomposition	Sequential decision-making (agent–environment interaction)	Mathematical optimisation — exact combinatorial method
开创性文献	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Mnih, V. et al. (2015). Human-Level Control through Deep Reinforcement Learning. Nature, 518, 529–533.	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669
别名	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	Derin Pekiştirmeli Öğrenme (DQN / PPO / A3C), derin pekiştirmeli öğrenme, deep RL, DRL	IP, MIP, mixed-integer programming, mixed-integer linear programming
相关	3	4	4
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.	Deep Reinforcement Learning combines neural networks with reinforcement learning so an agent learns by interacting with an environment, popularised by Mnih and colleagues' 2015 Nature work on human-level Atari control. Instead of learning from a fixed labelled dataset, the agent takes actions, observes rewards, and gradually shapes a policy that maximises long-run return.	Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems.