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Multi-armed bandit allocation indices [[electronic resource] /] / John Gittins, Kevin Glazebrook, Richard Weber
| Multi-armed bandit allocation indices [[electronic resource] /] / John Gittins, Kevin Glazebrook, Richard Weber |
| Autore | Gittins John C. <1938-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Chichester, : Wiley, 2011 |
| Descrizione fisica | 1 online resource (311 p.) |
| Disciplina |
519.5
519.8 |
| Altri autori (Persone) |
GlazebrookKevin D. <1950->
WeberRichard <1953-> |
| Soggetto topico |
Resource allocation - Mathematical models
Mathematical optimization Programming (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-37409-9
9786613374097 0-470-98004-4 0-470-98003-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multi-armed Bandit Allocation Indices; Contents; Foreword; Foreword to the first edition; Preface; Preface to the first edition; 1 Introduction or exploration; Exercises; 2 Main ideas: Gittins index; 2.1 Introduction; 2.2 Decision processes; 2.3 Simple families of alternative bandit processes; 2.4 Dynamic programming; 2.5 Gittins index theorem; 2.6 Gittins index; 2.6.1 Gittins index and the multi-armed bandit; 2.6.2 Coins problem; 2.6.3 Characterization of the optimal stopping time; 2.6.4 The restart-in-state formulation; 2.6.5 Dependence on discount factor
2.6.6 Myopic and forwards induction policies2.7 Proof of the index theorem by interchanging bandit portions; 2.8 Continuous-time bandit processes; 2.9 Proof of the index theorem by induction and interchange argument; 2.10 Calculation of Gittins indices; 2.11 Monotonicity conditions; 2.11.1 Monotone indices; 2.11.2 Monotone jobs; 2.12 History of the index theorem; 2.13 Some decision process theory; Exercises; 3 Necessary assumptions for indices; 3.1 Introduction; 3.2 Jobs; 3.3 Continuous-time jobs; 3.3.1 Definition; 3.3.2 Policies for continuous-time jobs 3.3.3 The continuous-time index theorem for a SFABP of jobs3.4 Necessary assumptions; 3.4.1 Necessity of an infinite time horizon; 3.4.2 Necessity of constant exponential discounting; 3.4.3 Necessity of a single processor; 3.5 Beyond the necessary assumptions; 3.5.1 Bandit-dependent discount factors; 3.5.2 Stochastic discounting; 3.5.3 Undiscounted rewards; 3.5.4 A discrete search problem; 3.5.5 Multiple processors; Exercises; 4 Superprocesses, precedence constraints and arrivals; 4.1 Introduction; 4.2 Bandit superprocesses; 4.3 The index theorem for superprocesses 4.4 Stoppable bandit processes4.5 Proof of the index theorem by freezing and promotion rules; 4.5.1 Freezing rules; 4.5.2 Promotion rules; 4.6 The index theorem for jobs with precedence constraints; 4.7 Precedence constraints forming an out-forest; 4.8 Bandit processes with arrivals; 4.9 Tax problems; 4.9.1 Ongoing bandits and tax problems; 4.9.2 Klimov's model; 4.9.3 Minimum EWFT for the M/G/1 queue; 4.10 Near optimality of nearly index policies; Exercises; 5 The achievable region methodology; 5.1 Introduction; 5.2 A simple example; 5.3 Proof of the index theorem by greedy algorithm 5.4 Generalized conservation laws and indexable systems5.5 Performance bounds for policies for branching bandits; 5.6 Job selection and scheduling problems; 5.7 Multi-armed bandits on parallel machines; Exercises; 6 Restless bandits and Lagrangian relaxation; 6.1 Introduction; 6.2 Restless bandits; 6.3 Whittle indices for restless bandits; 6.4 Asymptotic optimality; 6.5 Monotone policies and simple proofs of indexability; 6.6 Applications to multi-class queueing systems; 6.7 Performance bounds for the Whittle index policy; 6.8 Indices for more general resource configurations; Exercises 7 Multi-population random sampling (theory) |
| Record Nr. | UNINA-9910133454203321 |
Gittins John C. <1938->
|
||
| Chichester, : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multi-armed bandit allocation indices [[electronic resource] /] / John Gittins, Kevin Glazebrook, Richard Weber
| Multi-armed bandit allocation indices [[electronic resource] /] / John Gittins, Kevin Glazebrook, Richard Weber |
| Autore | Gittins John C. <1938-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Chichester, : Wiley, 2011 |
| Descrizione fisica | 1 online resource (311 p.) |
| Disciplina |
519.5
519.8 |
| Altri autori (Persone) |
GlazebrookKevin D. <1950->
WeberRichard <1953-> |
| Soggetto topico |
Resource allocation - Mathematical models
Mathematical optimization Programming (Mathematics) |
| ISBN |
1-283-37409-9
9786613374097 0-470-98004-4 0-470-98003-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multi-armed Bandit Allocation Indices; Contents; Foreword; Foreword to the first edition; Preface; Preface to the first edition; 1 Introduction or exploration; Exercises; 2 Main ideas: Gittins index; 2.1 Introduction; 2.2 Decision processes; 2.3 Simple families of alternative bandit processes; 2.4 Dynamic programming; 2.5 Gittins index theorem; 2.6 Gittins index; 2.6.1 Gittins index and the multi-armed bandit; 2.6.2 Coins problem; 2.6.3 Characterization of the optimal stopping time; 2.6.4 The restart-in-state formulation; 2.6.5 Dependence on discount factor
2.6.6 Myopic and forwards induction policies2.7 Proof of the index theorem by interchanging bandit portions; 2.8 Continuous-time bandit processes; 2.9 Proof of the index theorem by induction and interchange argument; 2.10 Calculation of Gittins indices; 2.11 Monotonicity conditions; 2.11.1 Monotone indices; 2.11.2 Monotone jobs; 2.12 History of the index theorem; 2.13 Some decision process theory; Exercises; 3 Necessary assumptions for indices; 3.1 Introduction; 3.2 Jobs; 3.3 Continuous-time jobs; 3.3.1 Definition; 3.3.2 Policies for continuous-time jobs 3.3.3 The continuous-time index theorem for a SFABP of jobs3.4 Necessary assumptions; 3.4.1 Necessity of an infinite time horizon; 3.4.2 Necessity of constant exponential discounting; 3.4.3 Necessity of a single processor; 3.5 Beyond the necessary assumptions; 3.5.1 Bandit-dependent discount factors; 3.5.2 Stochastic discounting; 3.5.3 Undiscounted rewards; 3.5.4 A discrete search problem; 3.5.5 Multiple processors; Exercises; 4 Superprocesses, precedence constraints and arrivals; 4.1 Introduction; 4.2 Bandit superprocesses; 4.3 The index theorem for superprocesses 4.4 Stoppable bandit processes4.5 Proof of the index theorem by freezing and promotion rules; 4.5.1 Freezing rules; 4.5.2 Promotion rules; 4.6 The index theorem for jobs with precedence constraints; 4.7 Precedence constraints forming an out-forest; 4.8 Bandit processes with arrivals; 4.9 Tax problems; 4.9.1 Ongoing bandits and tax problems; 4.9.2 Klimov's model; 4.9.3 Minimum EWFT for the M/G/1 queue; 4.10 Near optimality of nearly index policies; Exercises; 5 The achievable region methodology; 5.1 Introduction; 5.2 A simple example; 5.3 Proof of the index theorem by greedy algorithm 5.4 Generalized conservation laws and indexable systems5.5 Performance bounds for policies for branching bandits; 5.6 Job selection and scheduling problems; 5.7 Multi-armed bandits on parallel machines; Exercises; 6 Restless bandits and Lagrangian relaxation; 6.1 Introduction; 6.2 Restless bandits; 6.3 Whittle indices for restless bandits; 6.4 Asymptotic optimality; 6.5 Monotone policies and simple proofs of indexability; 6.6 Applications to multi-class queueing systems; 6.7 Performance bounds for the Whittle index policy; 6.8 Indices for more general resource configurations; Exercises 7 Multi-population random sampling (theory) |
| Record Nr. | UNINA-9910830276503321 |
|
Gittins John C. <1938->
|
||
| Chichester, : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multi-armed bandit allocation indices / / John Gittins, Kevin Glazebrook, Richard Weber
| Multi-armed bandit allocation indices / / John Gittins, Kevin Glazebrook, Richard Weber |
| Autore | Gittins John C. <1938-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Chichester, : Wiley, 2011 |
| Descrizione fisica | 1 online resource (311 p.) |
| Disciplina | 519.5 |
| Altri autori (Persone) |
GlazebrookKevin D. <1950->
WeberRichard <1953-> |
| Soggetto topico |
Resource allocation - Mathematical models
Mathematical optimization Programming (Mathematics) |
| ISBN |
1-283-37409-9
9786613374097 0-470-98004-4 0-470-98003-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multi-armed Bandit Allocation Indices; Contents; Foreword; Foreword to the first edition; Preface; Preface to the first edition; 1 Introduction or exploration; Exercises; 2 Main ideas: Gittins index; 2.1 Introduction; 2.2 Decision processes; 2.3 Simple families of alternative bandit processes; 2.4 Dynamic programming; 2.5 Gittins index theorem; 2.6 Gittins index; 2.6.1 Gittins index and the multi-armed bandit; 2.6.2 Coins problem; 2.6.3 Characterization of the optimal stopping time; 2.6.4 The restart-in-state formulation; 2.6.5 Dependence on discount factor
2.6.6 Myopic and forwards induction policies2.7 Proof of the index theorem by interchanging bandit portions; 2.8 Continuous-time bandit processes; 2.9 Proof of the index theorem by induction and interchange argument; 2.10 Calculation of Gittins indices; 2.11 Monotonicity conditions; 2.11.1 Monotone indices; 2.11.2 Monotone jobs; 2.12 History of the index theorem; 2.13 Some decision process theory; Exercises; 3 Necessary assumptions for indices; 3.1 Introduction; 3.2 Jobs; 3.3 Continuous-time jobs; 3.3.1 Definition; 3.3.2 Policies for continuous-time jobs 3.3.3 The continuous-time index theorem for a SFABP of jobs3.4 Necessary assumptions; 3.4.1 Necessity of an infinite time horizon; 3.4.2 Necessity of constant exponential discounting; 3.4.3 Necessity of a single processor; 3.5 Beyond the necessary assumptions; 3.5.1 Bandit-dependent discount factors; 3.5.2 Stochastic discounting; 3.5.3 Undiscounted rewards; 3.5.4 A discrete search problem; 3.5.5 Multiple processors; Exercises; 4 Superprocesses, precedence constraints and arrivals; 4.1 Introduction; 4.2 Bandit superprocesses; 4.3 The index theorem for superprocesses 4.4 Stoppable bandit processes4.5 Proof of the index theorem by freezing and promotion rules; 4.5.1 Freezing rules; 4.5.2 Promotion rules; 4.6 The index theorem for jobs with precedence constraints; 4.7 Precedence constraints forming an out-forest; 4.8 Bandit processes with arrivals; 4.9 Tax problems; 4.9.1 Ongoing bandits and tax problems; 4.9.2 Klimov's model; 4.9.3 Minimum EWFT for the M/G/1 queue; 4.10 Near optimality of nearly index policies; Exercises; 5 The achievable region methodology; 5.1 Introduction; 5.2 A simple example; 5.3 Proof of the index theorem by greedy algorithm 5.4 Generalized conservation laws and indexable systems5.5 Performance bounds for policies for branching bandits; 5.6 Job selection and scheduling problems; 5.7 Multi-armed bandits on parallel machines; Exercises; 6 Restless bandits and Lagrangian relaxation; 6.1 Introduction; 6.2 Restless bandits; 6.3 Whittle indices for restless bandits; 6.4 Asymptotic optimality; 6.5 Monotone policies and simple proofs of indexability; 6.6 Applications to multi-class queueing systems; 6.7 Performance bounds for the Whittle index policy; 6.8 Indices for more general resource configurations; Exercises 7 Multi-population random sampling (theory) |
| Record Nr. | UNINA-9910876618603321 |
|
Gittins John C. <1938->
|
||
| Chichester, : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||