IEOR 6614, Spring 2016 : Homework 11

Assigned: Thursday, April 14, 2016
Due: Thursday, April 21, 2016

General Instructions

  1. Please review the course information.
  2. You must write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
  3. Numbered problems are all from the textbook Network Flows .

Problems

  1. Here is a variation on the deterministic Weighted Majority algorithm, designed to make it more adaptive.
    1. Each expert begins with weight 1 (as before).
    2. We predict the result of a weighted-majority vote of the experts (as before).
    3. If an expert makes a mistake, we penalize it by dividing its weight by 2, but only if its weight was at least 1/4 of the average weight of experts.
    Prove that in any contiguous block of trials (e.g., the 51st day through the 77th day), the number of mistakes made by the algorithm is at most O(m + log N), where m is the number of mistakes made by the best expert in that block, and N is the total number of experts.
  2. Prove Corollary B on the Multiplicative Weights slide
  3. Problem 17.28. Bounds on concurrent flow.

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