Final published version, 1.67 MB, PDF document
Available under license: CC BY-NC-ND
Research output: Thesis › Doctoral Thesis
Research output: Thesis › Doctoral Thesis
}
TY - BOOK
T1 - Exploration and exploitation in Bayes sequential decision problems
AU - Edwards, James
PY - 2016
Y1 - 2016
N2 - Bayes sequential decision problems are an extensive problem class with wide application. They involve taking actions in sequence in a system which has characteristics which are unknown or only partially known. These characteristics can be learnt over time as a result of our actions. Therefore we are faced with a trade-off between choosing actions that give desirable short term outcomes (exploitation) and actions that yield useful information about the system which can be used to improve longer term outcomes (exploration).Gittins indices provide an optimal method for a small but important subclass of these problems. Unfortunately the optimality of index methods does not hold generally and Gittins indices can be impractical to calculate for many problems. This has motivated the search for easy-to-calculate heuristics with general application. One such non-index method is the knowledge gradient heuristic. A thorough investigation of the method is made which identifies crucial weaknesses. Index and non-index variants are developed which avoid these weaknesses.The problem of choosing multiple website elements to present to user is an important problem relevant to many major web-based businesses. A Bayesian multi-armed bandit model is developed which captures the interactions between elements and the dual uncertainties of both user preferences and element quality. The problem has many challenging features but solution methods are proposed that are both easy to implement and which can be adapted to particular applications.Finally, easy-to-use software to calculate Gittins indices for Bernoulli and normal rewards has been developed as part of this thesis and has been made publicly available. The methodology used is presented together with a study of accuracy and speed.
AB - Bayes sequential decision problems are an extensive problem class with wide application. They involve taking actions in sequence in a system which has characteristics which are unknown or only partially known. These characteristics can be learnt over time as a result of our actions. Therefore we are faced with a trade-off between choosing actions that give desirable short term outcomes (exploitation) and actions that yield useful information about the system which can be used to improve longer term outcomes (exploration).Gittins indices provide an optimal method for a small but important subclass of these problems. Unfortunately the optimality of index methods does not hold generally and Gittins indices can be impractical to calculate for many problems. This has motivated the search for easy-to-calculate heuristics with general application. One such non-index method is the knowledge gradient heuristic. A thorough investigation of the method is made which identifies crucial weaknesses. Index and non-index variants are developed which avoid these weaknesses.The problem of choosing multiple website elements to present to user is an important problem relevant to many major web-based businesses. A Bayesian multi-armed bandit model is developed which captures the interactions between elements and the dual uncertainties of both user preferences and element quality. The problem has many challenging features but solution methods are proposed that are both easy to implement and which can be adapted to particular applications.Finally, easy-to-use software to calculate Gittins indices for Bernoulli and normal rewards has been developed as part of this thesis and has been made publicly available. The methodology used is presented together with a study of accuracy and speed.
KW - Multi-armed bandit problem
KW - Statistical learning
KW - Operational research
KW - Dynamic optimization
KW - Statistical modelling
KW - Dynamic programming
KW - Gittins index
KW - Bayesian statistics
M3 - Doctoral Thesis
PB - Lancaster University
ER -