Using UCB for demand learning, select arm with index = K does play here and...

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Using UCB for demand learning, select arm with index ĵ = K does play here and why? K nj √nj argmaxj + what role (2) Suppose each period you need to choose a price among {3, 4, 5} to maximize revenue, and now you are at the beginning of period 7. You have all the historical data from periods 1-6. Let p(t) and d(t) be the price and demand you observed during period t. You have, p(1)=3, d(1)=10; p(2)=4, d(2)=8; p(3)=5, d(3)=7; p(4)=4, d(4)=5; p(5)=4, d(5)=7; p(6)=4, d(6)=8. Let K=1. What price to pick for period 7 and why? Upper Confidence Bounds (UCB) ● ● Discretize the price interval ● Tj K • At the begging of every period t, compute + for nj √nj ● ● ● amin K I aj Tj is the cumulative revenue when charging aj nj is the number of periods that a; was charged in the past K is a constant I Tj K Select = argmaxj + and set the price for period t to be aĵ. nj √nj is the driver for exploration! amax every price aj, REFERENCE FOR THE QUESTION where Using UCB for demand learning, select arm with index ĵ = K does play here and why? K nj √nj argmaxj + what role (2) Suppose each period you need to choose a price among {3, 4, 5} to maximize revenue, and now you are at the beginning of period 7. You have all the historical data from periods 1-6. Let p(t) and d(t) be the price and demand you observed during period t. You have, p(1)=3, d(1)=10; p(2)=4, d(2)=8; p(3)=5, d(3)=7; p(4)=4, d(4)=5; p(5)=4, d(5)=7; p(6)=4, d(6)=8. Let K=1. What price to pick for period 7 and why? Upper Confidence Bounds (UCB) ● ● Discretize the price interval ● Tj K • At the begging of every period t, compute + for nj √nj ● ● ● amin K I aj Tj is the cumulative revenue when charging aj nj is the number of periods that a; was charged in the past K is a constant I Tj K Select = argmaxj + and set the price for period t to be aĵ. nj √nj is the driver for exploration! amax every price aj, REFERENCE FOR THE QUESTION where

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