- Continuous-time dynamic programs
- The HJB equation; a heuristic derivation; and proof of optimality.
- High level idea: Policy Improvement and Policy Evaluation.
- Value Iteration; Policy Iteration.
- Temporal Differences; Q-factors.
- Positive Programming, Negative Programming & Discounted Programming.
- Optimality Conditions.
- Markov Decisions Problems; Bellman’s Equation; Two examples
- Dynamic Programs; Bellman’s Equation; An example.
Lyapunov functions are an extremely convenient device for proving that a dynamical system converges.
Sequentially a player decides to play and his adversary decides . At time , a decision results in a vector payoff . Given is the average vector payoff at time , Blackwell’s Approachability Theorem is a necessary and sufficient condition so that, regardless of the adversary’s decisions, the player makes the sequence of vectors approach a convex set .