Assignment 3 1. Using linear approximation for demand learning, (1) why the algorithm converges given that it uses a linear mction to estimate a nonlinear function? (2) If for stage i, the length of half stage is I i=l6, the estimated function is d(p)=lO-5p, what will be the two prices for next stage? 2. Using bisection for demand learning, 19} = 1,191-2 = 2,17? = 3, revenue observed at p} is 5, revenue observed at pf is 4, revenue observed at p? is 4.25, I ,- is 2. What to do next? 3. (1) Using UCB for demand learning, select arm with indexj = argmaxj 2 + i what role nix/\"7" does i play here and why? yr,- (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