Bandit Algorithms

3.5 Bibliographic remarks 52 version exists can be found in [Halmos, 1950, p210]. Regular versions play a role in a very useful ...

3.6 Exercises 53 (d)Show that (Xm,t)t≥ 1 is also an independent sequence of Bernoulli random variables, that are uniformly distr ...

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

4.2 The learning objective 55 valuable because they teach us important lessons about equivalent models. For now, however, we mov ...

4.3 Knowledge and environment classes 56 4.3 Knowledge and environment classes Even if the horizon is known in advance and we co ...

4.3 Knowledge and environment classes 57 Name Symbol Definition Bernoulli EBk {(B(μi))i:μ∈[0,1]k} Uniform EUk {(U(ai,bi))i:a,b∈R ...

4.4 The regret 58 their destination if all the edges in their chosen path are present. This problem can be formalized by letting ...

4.4 The regret 59 The regret is always nonnegative and for every banditνthere exists a policyπ for which the regret vanishes. Le ...

4.5 Decomposing the regret 60 prior probability measure onE(which must be equipped with aσ-algebraF), then the Bayesian regret i ...

4.6 The canonical bandit model ( ) 61 Lemma 4.5 tells us that a learner should aim to use an arm with a larger suboptimality gap ...

4.6 The canonical bandit model ( ) 62 choose a specific probability space, which we call thecanonical bandit model. Finite horiz ...

4.6 The canonical bandit model ( ) 63 the measure in terms of a distribution. Letpi(0) =Pi({ 0 }) andpi(1) = 1−pi(0) and define ...

4.7 The canonical bandit model for uncountable action sets ( ) 64 interest (usually the regret) only depends on the law ofA 1 ,X ...

4.8 Notes 65 occasionally distributionBmay incur a very small (even negative) reward. Risk-seeking decision makers, if they exis ...

4.9 Bibliographical remarks 66 4 We defined the regret as an expectation, which makes it unusable in conjunction with measures o ...

4.10 Exercises 67 considers so-called coherence risk measures (CVaR, is one example of such a risk measure), and with an approac ...

4.10 Exercises 68 def K(self): pass # Accepts a parameter 0 <= a <= K-1 and returns the # realisation of random variable X ...

4.10 Exercises 69 0 2 4 6 8 10 0 100 200 300 400 500 Regret Frequency Follow-the-Leader Figure 4.2Histogram of regret for Follow ...

4.10 Exercises 70 200 400 600 800 1 , 000 10 20 30 40 50 n Expected Regret Follow-the-Leader Figure 4.3The regret for Follow-the ...

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