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cs221-practice-midterm

# cs221-practice-midterm - CS221 Midterm 1 STANFORD...

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CS221 Midterm 1 STANFORD UNIVERSITY CS 221 Midterm, Fall 2007 Question Points 1 Short Answers /18 2 Motion Planning /12 3 Search Space Formulation /14 4 A* /12 5 Supervised Learning /20 6 Markov Decision Processes /16 7 Computer Vision /8 Total /100 Name of Student: Exam policy: This exam is open-book and open-notes. Any printed material that you brought with you is allowed. However, the use of mobile devices is not permitted. This includes laptops, cellular phones and pagers. Time: 3 hours. Length: This midterm contains 21 pages. The last two pages are blank pages that you can use if you need extra space to answer some question. The Stanford University Honor Code: I attest that I have not given or received aid in this examination, and that I have done my share and taken an active part in seeing to it that others as well as myself uphold the spirit and letter of the Honor Code. Signed:

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CS221 Midterm 2 1. Short answers [18 points] The following questions require a true/false accompanied by one sentence of explanation, or a very short answer (also accompanied by a brief explanation). To discourage random guessing, one point will be deducted for a wrong answer on multiple choice (such as yes/no or true/false) questions! Also, no credit will be given for answers without a correct explanation. (a) [3 points] In class, we noted that grid-based discretization for motion planning works well in 2-4 dimensional problems, and studied probabilistic roadmaps for higher di- mensions. However, since we live in a 3-dimensional world, most real motion planning problems in robotics can be solved in a reasonable about of time using grid-based dis- cretization. [True/False] (b) [3 points] Suppose h is an admissible heuristic for a search problem, such that h = 2 h is not admissible. Then A* search with the heuristic function h will never expand more nodes than A* search with the heuristic function h . [True/False] (c) [3 points] Suppose we are interested in finding all solutions to a constraint satisfac- tion problem. Say, for an 8-queens problem, instead of asking for any one solution (i.e., any one arrangement in which the 8 queens lie on different rows, columns and diagonals), we want all possible solutions (i.e., all such arrangements). Which of the following techniques would still be useful for constructing efficient algo- rithms for finding all solutions? i. Forward checking. ii. Choosing the next value to assign a variable using the least constraining value heuristic. iii. Choosing the next variable to instantiate using the minimum remaining values heuristic.
CS221 Midterm 3 (d) [3 points] An MDP has a reward function R , optimal value function V and optimal policy π . Consider new reward functions: i. R 1 ( s ) = R ( s ) + 10. ii. A reward function R 2 such that whenever R ( s 1 ) > R ( s 2 ) for two states s 1 and s 2 , then we also have R 2 ( s 1 ) > R 2 ( s 2 ). (You can assume that the reward R ( s ) is different for each state s .) Consider replacing the reward function R in the original MDP by each of these reward functions. In which of the above two cases (if any) must π still be an optimal policy in the new MDP?

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