Find a hypothesis class H and a sequence of examples on which Consistent makes |H|−1 mistakes.

1. Find a hypothesis class and a sequence of examples on which Consistent makes |H|−1 mistakes.

2. Find a hypothesis class and a sequence of examples on which the mistake bound the Halving algorithm is tight.

3. Let ≥ 2, = {1, . . .,d} and let = {h j ∈ [d]}, where h j (x) = 1[x=]. Calculate MHalving(H) (i.e., derive lower and upper bounds on MHalving(H), and prove that they are equal).

4 The Doubling Trick:

In Theorem 21.15, the parameter η depends on the time horizon . In this exercise we show how to get rid of this dependence by a simple trick. Consider an algorithm that enjoys a regret bound of the form α √\ , but its

parameters require the knowledge of . The doubling trick, described in the following, enables us to convert such an algorithm into an algorithm that does not need to know the time horizon. The idea is to divide the time into periods of increasing size and run the original algorithm on each period. The Doubling Trick

input: algorithm whose parameters depend on the time horizon for = 0,1,2, . . . run on the 2rounds = 2m, . . .,2m+1 −1 Show that if the regret of on each period of 2rounds is at most α √ 2m, then the total regret is at most

find the cost of your paper

Suggest a modification of the binary search algorithm that emulates this strategy for a list of names.

1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

Explain why insertion sort works well on partially sorted lists.

1. Which configuration of data in a list causes the smallest number of exchanges in a selection sort? Which configuration of data causes the largest number of exchanges? 2. Explain….

Draw a class diagram that shows the relationships among the classes in this new version of the system

Jack decides to rework the banking system, which already includes the classes BankView, Bank, SavingsAccount, and RestrictedSavingsAccount. He wants to add another class for checking accounts. He sees that savings….