Bandit Algorithms

1.2 Applications 12 rewards accumulated over those rounds are unimportant. We will see examples of this shortly. 1.1.2 Limitatio ...

1.2 Applications 13 a standard multi-armed bandit problem, where in each round a policy chooses At∈ Aand the reward isXt= 1 if t ...

1.2 Applications 14 obviously be applied to more physical networks such as transportation systems used in operations research. D ...

1.3 Bibliographic remarks 15 Tree search The UCT algorithm is a tree search algorithm commonly used in perfect- information game ...

1.3 Bibliographic remarks 16 mobile health: In the typical application the user is prompted with the intention of inducing a lon ...

This material will be published by Cambridge University Press as Bandit Algorithms by Tor Lattimore and Csaba Szepesvari. This p ...

2.1 Probability spaces and random elements 18 X 1 := throw() X 1 = 4? X 21 := throw() X 21 := throw() X 22 := throw() No Yes Fig ...

2.1 Probability spaces and random elements 19 Figure 2.2A key idea in probability theory is the separation of sources of randomn ...

2.1 Probability spaces and random elements 20 with any predicate (an expression evaluating to true or false) whereU,V,...are fun ...

2.1 Probability spaces and random elements 21 The significance of the pushforward measurePXis that any probabilistic question co ...

2.1 Probability spaces and random elements 22 krandom variables on the same domain (Ω,F), thenX(ω) = (X 1 (ω),...,Xk(ω)) is anRk ...

2.1 Probability spaces and random elements 23 prevents us from definingF= 2Ω. There are two justifications not to do this, the f ...

2.1 Probability spaces and random elements 24 collectionX 1 ,...,Xkof random variables. For this to make sense, the constraints ...

2.2σ-algebras and knowledge 25 2.2 σ-algebras and knowledge One of the conceptual advantages of measure-theoretic probability is ...

2.2σ-algebras and knowledge 26 but cannot be extracted in a measurable way. These problems only occur when Xmaps measurable sets ...

2.3 Conditional probabilities 27 is also adapted. Afiltered probability spaceis the tuple (Ω,F,F,P), where (Ω,F,P) is a probabil ...

2.4 Independence 28 the case quite often, explaining why this simple formula has quite a status in probability and statistics. E ...

2.5 Integration and expectation 29 to bemutually independentif for anyn >0 integer andA 1 ,...,Andistinct elements ofG,P(A 1 ...

2.5 Integration and expectation 30 that ∫ X 1 dPand ∫ X 2 dPare defined, ∫ (α 1 X 1 +α 2 X 2 )dPis defined and satisfies ∫ (α 1 ...

2.5 Integration and expectation 31 the unique measure onB(R)) such thatλ((a,b)) =b−afor anya≤b. In this scenario, iff:R→Ris a Bo ...