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MIT 6.231

MIT 6.231：Dynamic Programming and Stochastic Control（2015 秋）

学习动态规划和随机控制的模型与求解方法。

打开官方课程
难度
中阶
形式
大学课程
语言
英文
规模
23 个课节
内容费用
免费
动手
需要动手环境

第一次学这门课？先完成学前准备，把课程目录搭好。

每节课这样学

  1. 发提示词把下面的每课提示词发给 AI Agent，它会准备这一课的练习文件。
  2. 学官方课节打开对应课节学习，按提示从第一道练习做起；它不会替你写答案。
  3. 记进度学完让 AI Agent 在 progress.md 勾选，并把疑问整理到 questions.md。
每课提示词 · 每次学习前用
继续学习「MIT 6.231：Dynamic Programming and Stochastic Control（2015 秋）」。课程目录是 mit-6231-fall2015/（不知道完整路径就先问我）。
1. 读 progress.md，找到下一课；如果我指定了第几课，就准备那一课。
2. 打开这一课的官方页面和本地讲义，列出本课练习要用的工具、文件和样例数据。缺少的先告诉我，等我同意再安装或下载。
3. 在 lessons/ 对应的课节文件夹里准备好练习：exercises/ 里给每道题建一个文件，写上题号和题目原文链接，不写答案；已有文件保留，样例数据放到 data/。拿不到官方题目或起始代码时记录限制，不编造替代品。
4. 按 README 运行开课时生成的自检脚本或在线检查清单，并检查本课新增工具能否正常使用。
5. 告诉我：本课先读哪几节、从哪道练习开始、大约需要多久。我学完后，帮我在 progress.md 勾选并把问题整理到 questions.md。

边界：
- 需要管理员权限、会产生费用或需要填写密钥的操作，先告诉我原因，等我同意。密钥由我在本机配置，不发到聊天，不写进笔记或版本库；原项目需要 .env 时确认已被 Git 忽略。
- 不替我写练习或作业答案，也不替我提交。我卡住时只给提示；我明确要求时才给解答。
- 只下载许可允许个人保存的材料；其余只放链接。不把未运行的命令说成成功。

课节共 23 节 · 官方顺序

  1. 01Lecture 1：Introduction to Dynamic Programming Examples of Dynamic Programming Significance of Feedback
  2. 02Lecture 2：The Basic Problem Principle of Optimality The General Dynamic Programming Algorithm State Augmentation
  3. 03Lecture 3：Deterministic Finite-State Problem Backward Shortest Path Algorithm Forward Shortest Path Algorithm Alternative Shortest Path Algorithms
  4. 04Lecture 4：Examples of Stochastic Dynamic Programming Problems Linear-Quadratic Problems Inventory Control
  5. 05Lecture 5：Stopping Problems Scheduling Problems Minimax Control
  6. 06Lecture 6：Problems with Imperfect State Info Reduction to the Perfect State Info Cas Linear Quadratic Problems Separation of Estimation and Control
  7. 07Lecture 7：Imperfect State Information Sufficient Statistics Conditional State Distribution as a Sufficient Statistic Finite-State Analysis
  8. 08Lecture 8：Suboptimal Control Cost Approximation Methods: Classification Certainty Equivalent Control Limited Lookahead Policies Performance Bounds Problem Approximation Approach Parametric Cost-To-Go Approximation
  9. 09Lecture 9：Rollout Algorithms Cost Improvement Property Discrete Deterministic Problems Approximations to Rollout Algorithms Model Predictive Control (MPS) Discretization of Continuous Time Discretization of Continuous Space Other Suboptimal Approaches
  10. 10Lecture 10：Infinite Horizon Problems Stochastic Shortest Path (SSP) Problems Bellman’s Equation Dynamic Programming – Value Iteration Discounted Problems as a Special Case of SSP
  11. 11Lecture 11：Review of Stochastic Shortest Path Problems Computation Methods for SSP Computational Methods for Discounted Problems
  12. 12Lecture 12：Average Cost Per Stage Problems Connection With Stochastic Shortest Path Problems Bellman’s Equation Value Iteration, Policy Iteration
展开其余 11 节
  1. 13Lecture 13：Control of Continuous-Time Markov Chains: Semi-Markov Problems Problem Formulation: Equivalence to Discrete-Time Problems Discounted Problems Average Cost Problems
  2. 14Lecture 14：Introduction to Advanced Infinite Horizon Dynamic Programming and Approximation Methods
  3. 15Lecture 15：Review of Basic Theory of Discounted Problems Monotonicity of Contraction Properties Contraction Mappings in Dynamic Programming Discounted Problems: Countable State Space with Unbounded Costs Generalized Discounted Dynamic Programming An Introduction to Abstract Dynamic Programming
  4. 16Lecture 16：Review of Computational Theory of Discounted Problems Value Iteration (VI) Policy Iteration (PI) Optimistic PI Computational Methods for Generalized Discounted Dynamic Programming Asynchronous Algorithms
  5. 17Lecture 17：Undiscounted Problems Stochastic Shortest Path Problems Proper and Improper Policies Analysis and Computational Methods for SSP Pathologies of SSP SSP Under Weak Conditions
  6. 18Lecture 18：Undiscounted Total Cost Problems Positive and Negative Cost Problems Deterministic Optimal Cost Problems Adaptive (Linear Quadratic) Dynamic Programming Affine Monotomic and Risk Sensitive Problems
  7. 19Lecture 19：Introduction to approximate Dynamic Programming Approximation in Policy Space Approximation in Value Space, Rollout / Simulation-based Single Policy Iteration Approximation in Value Space Using Problem Approximation
  8. 20Lecture 20：Discounted Problems Approximate (fitted) VI Approximate PI The Projected Equation Contraction Properties: Error Bounds Matrix Form of the Projected Equation Simulation-based Implementation LSTD, LSPE, and TD Methods
  9. 21Lecture 21：Review of Approximate Policy Iteration Projected Equation Methods for Policy Evaluation Simulation-Based Implementation Issues, Multistep Projected Equation Methods Bias-Variance Tradeoff Exploration-Enhanced Implementations, Oscillations
  10. 22Lecture 22：Aggregation as an Approximation Methodology Aggregate Problem Simulation-based Aggregation Q-Learning
  11. 23Lecture 23：Additional Topics in Advanced Dynamic Programming Stochastic Shortest Path Problems Average Cost Problems Generalizations Basis Function Adaptation Gradient-based Approximation in Policy Space An Overview

来源与使用须知

原始资源
MIT 6.231 收录版本：2015 秋
收录时间
本站首次收录 2026-10-10

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