PDF-MeanVariance Optimization in Markov Decision Processes Shie Mannor shieee

technionacil Technion Israel Institute of Technology John N Tsitsiklis jntmitedu Massachusetts Institute of Technology Cambridge MA Abstract We consider 64257nite horizon Markov decision processes under performance measures that involve both the mean. T state 8712X action or input 8712U uncertainty or disturbance 8712W dynamics functions XUW8594X w w are independent RVs variation state dependent input space 8712U 8838U is set of allowed actions in state at time brPage 5br Policy action is function Nimantha . Thushan. Baranasuriya. Girisha. . Durrel. De Silva. Rahul . Singhal. Karthik. . Yadati. Ziling. . Zhou. Outline. Random Walks. Markov Chains. Applications. 2SAT. 3SAT. Card Shuffling. Alan Ritter. Markov Networks. Undirected. graphical models. Cancer. Cough. Asthma. Smoking. Potential functions defined over cliques. Smoking. Cancer. . Ф. (S,C). False. False. 4.5. False. True. Network. . Ben . Taskar. ,. . Carlos . Guestrin. Daphne . Koller. 2004. Topics Covered. Main Idea.. Problem Setting.. Structure in classification problems.. Markov Model.. SVM. Combining SVM and Markov Network.. Hao. Wu. Mariyam. Khalid. Motivation. Motivation. How would we model this scenario?. Motivation. How would we model this scenario?. Logical Approach. Motivation. How would we model this scenario?. Logical Approach. First – a . Markov Model. State. . : . sunny cloudy rainy sunny ? . A Markov Model . is a chain-structured process . where . future . states . depend . only . on . the present . state, . Part 4. The Story so far …. Def:. Markov Chain: collection of states together with a matrix of probabilities called transition matrix (. p. ij. ) where . p. ij. indicates the probability of switching from state S. notes for. CSCI-GA.2590. Prof. Grishman. Markov Model . In principle each decision could depend on all the decisions which came before (the tags on all preceding words in the sentence). But we’ll make life simple by assuming that the decision depends on only the immediately preceding decision. Mark Stamp. 1. HMM. Hidden Markov Models. What is a hidden Markov model (HMM)?. A machine learning technique. A discrete hill climb technique. Where are . HMMs. used?. Speech recognition. Malware detection, IDS, etc., etc.. . and Bayesian Networks. Aron. . Wolinetz. Bayesian or Belief Network. A probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG).. TO EVALUATE COST-EFFECTIVENESS. OF CERVICAL CANCER TREATMENTS. Un modelo de . Markov. en un árbol de . decisión para . un análisis . del . coste-efectividad . del tratamientos . de cáncer de cuello uterino. Andrew Sutton. Learning objectives. Understand:. the role of modelling in economic evaluation. the construction and analysis of decision trees. the design and interpretation of a simple Markov model. Gordon Hazen. February 2012. Medical Markov Modeling. We think of Markov chain models as the province of operations research analysts. However …. The number of publications in medical journals . using Markov models. Jurafsky. Outline. Markov Chains. Hidden Markov Models. Three Algorithms for HMMs. The Forward Algorithm. The . Viterbi. Algorithm. The Baum-Welch (EM Algorithm). Applications:. The Ice Cream Task. Part of Speech Tagging.