This question concerns online learning in a non-agnostic setting. Recall that at each time-step, a new example is revealed, and a classification algorithm makes a prediction, and then the actual (true) label (which is 0 or 1 based on an unknown hypothesis c*) is revealed. Let n denote the number of variables (features). In your solution, you can refer to any observation/result established in A3 without re-proving it. (a) Prove that there is an online learning algorithm for learning monotone conjunctions that makes at most n mistakes before learning an unknown monotone conjunction c*. (b) Prove that any online learning algorithm for learning monotone conjunction makes at least n mistakes before learning an unknown monotone conjunction c*. (c) Prove that any online learning algorithm for learning decision lists makes at least n + 1 mistakes before learning an unknown decision list c*.

This question concerns online learning in a non-agnostic setting. Recall that at each time-step, a new example is revealed, and a classification algorithm makes a prediction, and then the actual (true) label (which is 0 or 1 based on an unknown hypothesis c) is revealed. Let n denote the number of variables (features). In your solution, you can refer to any observation/result established in A3 without re-proving it. (a) Prove that there is an online learning algorithm for learning monotone conjunctions that makes at most n mistakes before learning an unknown monotone conjunction c. (b) Prove that any online learning algorithm for learning monotone conjunction makes at least n mistakes before learning an unknown monotone conjunction c. (c) Prove that any online learning algorithm for learning decision lists makes at least n + 1 mistakes before learning an unknown decision list c.