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6.231 | Fall 2015 | Graduate

Dynamic Programming and Stochastic Control

Lecture Notes

6.231 Fall 2015 Complete Lecture Notes
6.231 Fall 2015 Lecture 1: Introduction to Dynamic Programming, Examples of Dynamic Programming, Significance of Feedback
6.231 Fall 2015 Lecture 10: Infinite Horizon Problems, Stochastic Shortest Path (SSP) Problems, Bellman’s Equation, Dynamic Programming – Value Iteration, Discounted Problems as a Special Case of SSP
6.231 Fall 2015 Lecture 11: Review of Stochastic Shortest Path Problems, Computation Methods for SSP, Computational Methods for Discounted Problems
6.231 Fall 2015 Lecture 12: Average Cost Per Stage Problems, Connection With Stochastic Shortest Path Problems, Bellman’s Equation, Value Iteration, Policy Iteration
6.231 Fall 2015 Lecture 13: Control of Continuous-Time Markov Chains: Semi-Markov Problems, Problem Formulation: Equivalence to Discrete-Time Problems, Problem Formulation: Equivalence to Discrete-Time Problems, Average Cost Problems
6.231 Fall 2015 Lecture 14: Introduction to Advanced Infinite Horizon Dynamic Programming and Approximation Methods
6.231 Fall 2015 Lecture 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
6.231 Fall 2015 Lecture 16: Review of Computational Theory of Discounted Problems, Value Iteration (VI), Optimistic PI, Computational Methods for Generalized Discounted Dynamic Programming, Asynchronous Algorithms
6.231 Fall 2015 Lecture 17: Undiscounted Problems, Stochastic Shortest Path Problems, Proper and Improper Policies, Analysis and Computational Methods for SSP, Pathologies of SSP, SSP Under Weak Conditions
6.231 Fall 2015 Lecture 18: Undiscounted Total Cost Problems, Positive and Negative Cost Problems, Proper and Improper Policies, Adaptive (Linear Quadratic) Dynamic Programming, Affine Monotomic and Risk Sensitive Problems
6.231 Fall 2015 Lecture 19: Introduction to affirmative Dynamic Programming, Approximation in Policy Space, Approximation in Value Space, Rollout/Simulation-based Single Policy Iteration, Approximation in Value Space Using Problem Approximation
6.231 Fall 2015 Lecture 2: The Basic Problem, Principle of Optimality, The General Dynamic Programming Algorithm, State Augmentation
6.231 Fall 2015 Lecture 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 and LSPE Methods
6.231 Fall 2015 Lecture 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
6.231 Fall 2015 Lecture 22: Aggregation as an Approximation Methodology, Aggregate Problem, Simulation-based Aggregation, Q-Learning
6.231 Fall 2015 Lecture 23: Additional Topics in Advanced Dynamic Programming, Stochastic Shortest Path Problems, Average Cost Problems, Generalizations, Basis Function Adaption, Gradient-based Approximation in Policy Space, An Overview
6.231 Fall 2015 Lecture 3: Deterministic Finite-State Problem, Backward Shortest Path Algorithm, Forward Shortest Path Algorithm, Alternative Shortest Path Algorithms
6.231 Fall 2015 Lecture 4: Examples of Stochastic Dynamic Programming Problems, Linear-Quadratic Problems, Inventory Control
6.231 Fall 2015 Lecture 5: Stopping Problems, Scheduling Problems, Minimax Control
6.231 Fall 2015 Lecture 6: Problems with Imperfect State Info, Reduction to the Perfect State Info Cast, Linear Quadratic Problems, Separation of Estimation and Control
6.231 Fall 2015 Lecture 7: Imperfect State Information, Sufficient Statistics, Conditional State Distribution as a Sufficient Statistic, Finite-State Analysis
6.231 Fall 2015 Lecture 8: Suboptimal Control, Cost Approximation Methods: Classification, Certainty Equivalent Control, Limited Lookahead Policies, Performance Bounds, Problem Approximation Approach, Parametric Cost-To-Go Approximation
6.231 Fall 2015 Lecture 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

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Fall 2015
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Graduate
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