Approximate Iterative Algorithms

Dr. Almudevar was born in Halifax and raised in Ontario, Canada. He completed a PhD in Statistics at the University of Toronto, and is currently a faculty member in the Department of Biostatistics and Computational Biology at the University of Rochester. He has a wide range of interests, which include biological network modeling, analysis of genetic data, immunological modeling and clinical applications of technological home monitoring. He has a more general interest in optimization and control theory, with an emphasis on the computational issues associated with Markov decision processes.

1. Introduction. PART I Mathematical background: 2. Real analysis and linear algebra 3. Background – measure theory 4. Background – probability theory 5. Background – stochastic processes 6. Functional analysis 7. Fixed point equations 8. The distribution of a maximum. PART II General theory of approximate iterative algorithms: 9. Background – linear convergence 10. A general theory of approximate iterative algorithms (AIA) 11. Selection of approximation schedules for coarse-to-fine AIAs. PART III Application to Markov decision processes: 12. Markov decision processes (MDP) – background 13. Markov decision processes – value iteration 14. Model approximation in dynamic programming – general theory 15. Sampling based approximation methods 16. Approximate value iteration by truncation 17. Grid approximations of MDPs with continuous state/action spaces 18. Adaptive control of MDPs.