Name: Self-Learning Control of Finite Markov Chains, Vol. 4, , Self-Lea
Brand: Informa PLC
SKU: 9780824794293
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Series Introduction v
Preface vii
1 Controlled Markov Chains 1
1.1 Introduction 1
1.2 Random sequences 1
1.2.1 Random variables 2
1.2.2 Markov sequences and chains 5
1.3 Finite Markov chains 6
1.3.1 State space decomposition 6
1.3.2 Transition matrix 8
1.4 Coefficient of ergodicity 12
1.5 Controlled finite Markov chains 17
1.5.1 Definition of controlled chains 18
1.5.2 Randomized control strategies 19
1.5.3 Transition probabilities 20
1.5.4 Behaviour of random trajectories 22
1.5.5 Classification of controlled chains 24
1.6 Examples of Markov models 26
1.7 Stochastic approximation techniques 31
1.8 Numerical simulations 32
1.9 Conclusions 40
1.10 References 40
I Unconstrained Markov Chains
2 Lagrange Multipliers Approach 47
2.1 Introduction 47
2.2 System description 48
2.3 Problem formulation 51
2.4 Adaptive learning algorithm 52
2.5 Convergence analysis 57
2.6 Conclusions 65
2.7 References 65
3 Penalty Function Approach 69
3.1 Introduction 69
3.2 Adaptive learning algorithm 69
3.3 Convergence analysis 76
3.4 Conclusions 85
3.5 References 85
4 Projection Gradient Method 87
4.1 Introduction 87
4.2 Control algorithm 87
4.3 Estimation of the transition matrix 91
4.4 Convergence analysis 98
4.5 Rate of adaptation and its optimization 107
4.6 On the cost of uncertainty 111
4.7 Conclusions 112
4.8 References 113
II Constrained Markov Chains
5 Lagrange Multipliers Approach 117
5.1 Introduction 117
5.2 System description 118
5.3 Problem formulation 121
5.4 Adaptive learning algorithm 122
5.5 Convergence analysis 129
5.6 Conclusions 137
5.7 References 138
6 Penalty Function Approach 141
6.1 Introduction 141
6.2 System description and problem formulation 142
6.3 Adaptive learning algorithm 144
6.4 Convergence analysis 154
6.5 Conclusions 163
6.6 References 163
7 Nonregular Markov Chains 167
7.1 Introduction 167
7.2 Ergodic Markov chains 167
7.3 General type Markov chains 182
7.4 Conclusions 186
7.5 References 186
8 Practical Aspects 189
8.1 Introduction 189
8.2 Description of controlled Markov chain 190
8.2.1 Equivalent Linear Programming Problem 190
8.3 The unconstrained case (example 1) 192
8.3.1 Lagrange multipliers approach 193
8.3.2 Penalty function approach 202
8.4 The constrained case (example 1) 210
8.4.1 Lagrange multipliers approach 210
8.4.2 Penalty function approach 219
8.5 The unconstrained case (example 2) 228
8.5.1 Lagrange multipliers approach 228
8.5.2 Penalty function approach 237
8.6 The constrained case (example 2) 245
8.6.1 Lagrange multipliers approach 245
8.6.2 Penalty function approach 254
8.7 Conclusions 263
Appendix A 265
Appendix B 281
Index 297

Title: Self-Learning Control of Finite Markov Chains, Vol. 4

Manufacturer:

Informa PLC

Item Number: 9780824794293

Publication Date: January 2000

Number: 1

Product Description: Full Name: Self-Learning Control of Finite Markov Chains, Vol. 4; Short Name:Self-Learning Control of Finite Markov Chains

Universal Product Code (UPC): 9780824794293

WonderClub Stock Keeping Unit (WSKU): 9780824794293

Rating: 3/5 based on 2 Reviews

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Category: Media >> Books

Weight: 0.200 kg (0.44 lbs)

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Depth: 0.000 cm (0.00 inches)

Date Added: August 25, 2020, Added By: Ross

Date Last Edited: August 25, 2020, Edited By: Ross

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Michael Fuchs

reviewed Self-Learning Control of Finite Markov Chains, Vol. 4 on October 25, 2017

Self-Learning Control of Finite Markov Chains

I really like it because it gives clear intuition to the concepts. Great book for an introduction although the formal mathematics definitions are not maintained.

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	Series Introduction	v
	Preface	vii
1	Controlled Markov Chains	1
1.1	Introduction	1
1.2	Random sequences	1
1.2.1	Random variables	2
1.2.2	Markov sequences and chains	5
1.3	Finite Markov chains	6
1.3.1	State space decomposition	6
1.3.2	Transition matrix	8
1.4	Coefficient of ergodicity	12
1.5	Controlled finite Markov chains	17
1.5.1	Definition of controlled chains	18
1.5.2	Randomized control strategies	19
1.5.3	Transition probabilities	20
1.5.4	Behaviour of random trajectories	22
1.5.5	Classification of controlled chains	24
1.6	Examples of Markov models	26
1.7	Stochastic approximation techniques	31
1.8	Numerical simulations	32
1.9	Conclusions	40
1.10	References	40
I	Unconstrained Markov Chains
2	Lagrange Multipliers Approach	47
2.1	Introduction	47
2.2	System description	48
2.3	Problem formulation	51
2.4	Adaptive learning algorithm	52
2.5	Convergence analysis	57
2.6	Conclusions	65
2.7	References	65
3	Penalty Function Approach	69
3.1	Introduction	69
3.2	Adaptive learning algorithm	69
3.3	Convergence analysis	76
3.4	Conclusions	85
3.5	References	85
4	Projection Gradient Method	87
4.1	Introduction	87
4.2	Control algorithm	87
4.3	Estimation of the transition matrix	91
4.4	Convergence analysis	98
4.5	Rate of adaptation and its optimization	107
4.6	On the cost of uncertainty	111
4.7	Conclusions	112
4.8	References	113
II	Constrained Markov Chains
5	Lagrange Multipliers Approach	117
5.1	Introduction	117
5.2	System description	118
5.3	Problem formulation	121
5.4	Adaptive learning algorithm	122
5.5	Convergence analysis	129
5.6	Conclusions	137
5.7	References	138
6	Penalty Function Approach	141
6.1	Introduction	141
6.2	System description and problem formulation	142
6.3	Adaptive learning algorithm	144
6.4	Convergence analysis	154
6.5	Conclusions	163
6.6	References	163
7	Nonregular Markov Chains	167
7.1	Introduction	167
7.2	Ergodic Markov chains	167
7.3	General type Markov chains	182
7.4	Conclusions	186
7.5	References	186
8	Practical Aspects	189
8.1	Introduction	189
8.2	Description of controlled Markov chain	190
8.2.1	Equivalent Linear Programming Problem	190
8.3	The unconstrained case (example 1)	192
8.3.1	Lagrange multipliers approach	193
8.3.2	Penalty function approach	202
8.4	The constrained case (example 1)	210
8.4.1	Lagrange multipliers approach	210
8.4.2	Penalty function approach	219
8.5	The unconstrained case (example 2)	228
8.5.1	Lagrange multipliers approach	228
8.5.2	Penalty function approach	237
8.6	The constrained case (example 2)	245
8.6.1	Lagrange multipliers approach	245
8.6.2	Penalty function approach	254
8.7	Conclusions	263
	Appendix A	265
	Appendix B	281
	Index	297