You need to be able to define the following terms and answer basic questions about them:

Transcription

1 CS440/ECE448 Sectin Q Fall 2017 Midterm Review Yu need t be able t define the fllwing terms and answer basic questins abut them: Intr t AI, agents and envirnments Pssible definitins f AI, prs and cns f each Turing test: prs and cns, alternatives Ratinality Utility, expected utility PEAS Envirnment characteristics: fully vs. partially bservable, deterministic vs. stchastic, episdic vs. sequential, static vs. dynamic, discrete vs. cntinuus, single-agent vs. multi-agent, knwn vs. unknwn Search Search prblem frmulatin: initial state, actins, transitin mdel, gal state, path cst, state space Tree search algrithm utline, frntier, search strategy, repeated state detectin Evaluatin f search strategies: cmpleteness, ptimality, time cmplexity, space cmplexity Uninfrmed search strategies: breadth-first search, unifrm cst search, depthfirst search, iterative deepening search Infrmed search strategies: greedy best-first, A*, weighted A* Heuristics: admissibility, cnsistency, dminance Optimality f A* Cnstraint satisfactin prblems Backtracking search Heuristics: mst cnstrained/mst cnstraining variable, least cnstraining value Frward checking, cnstraint prpagatin, arc cnsistency Tree-structured CSPs Lcal search SAT prblem, NP-cmpleteness Planning Situatin space vs. plan space planners Interleaved vs. nn-interleaved planners Partial rder plan Cmplexity f planning Games Zer-sum games Game tree Minimax strategy, minimax search Alpha-beta pruning Evaluatin functins Quiescence search, hrizn effect

2 Mnte Carl tree search, AlphaG Stchastic games, expectiminimax Partially bservable games Game thery Nrmal frm representatin Dminant strategy Nash equilibrium (pure and mixed strategy) Paret ptimality Examples f games: Prisner s Dilemma, Stag Hunt, Game f Chicken Mechanism design: auctins, regulatin Example test questins 1. Can an envirnment be bth knwn and unbservable? Give an example. 2. What is the distinctin between a wrld state and a search tree nde? 3. In the tree search frmulatin, why d we restrict step csts t be nn-negative? 4. Fr each type f maze described belw, specify whether breadth-first-search (BFS) r depth-first-search (DFS) will mre efficiently find a slutin in the wrst case, and say why. Assume that bth BFS and DFS return the first slutin path they find. a. The Albuquerque maze has 3 pssible directins that yu can take at each intersectin. N path is lnger than 25 steps. There is nly ne slutin. b. The Belmnt maze has 3 pssible directins that yu can take at each intersectin. N path is lnger than 25 steps. Abut half f all available paths are cnsidered slutins t the maze. c. The Crazytwn maze has 3 pssible directins that yu can take at each intersectin. The maze is infinite in size, s sme paths have infinite length. There is nly ne slutin, which is knwn t require 25 steps. 5. Suppse yu are given a perfect heuristic functin that gives the crrect ptimal distance frm each nde t the gal. Is greedy best-first search with this heuristic ptimal? If nt, give a cunterexample. 6. Explain why it is a gd heuristic t chse the variable that is mst cnstrained but the value that is least cnstraining in a CSP search. 7. What is lcal search fr CSPs? Fr which kinds f CSPs might lcal search be better than backtracking search? What abut the ther way arund?

3 8. Refer t the maze shwn belw. Here, M represents Mari, P represents Peach, and the gal f the game is t get Mari and Peach t find each ther. In each mve, bth Mari and Peach take turns. Fr example, ne mve wuld cnsist f Peach mving a blck t the bttm frm her current psitin, and Mari mving ne blck t the left frm his current psitin. Standing still is als an ptin. a. Describe state and actin representatins fr this prblem. b. What is the branching factr f the search tree? c. What is the size f the state space? d. Describe an admissible heuristic fr this prblem. 9. Cnsider the search prblem with the fllwing state space: S dentes the start state, G dentes the gal state, and step csts are written next t each arc. Assume that ties are brken alphabetically (i.e., if there are tw states with equal pririty n the frntier, the state that cmes first alphabetically shuld be visited first). a. What path wuld BFS return fr this prblem? b. What path wuld DFS return fr this prblem? c. What path wuld UCS return fr this prblem? d. Cnsider the heuristics fr this prblem shwn in the table belw.

4 Is h 1 admissible? Is it cnsistent? Is h 2 admissible? Is it cnsistent? 10. Cnsider the graph-clring prblem n the fllwing tree-structured CSP: We assume there are three available clrs (R,G,B) and sme ndes are cnstrained t use nly a subset f these clrs, as indicated abve. Shw all the steps fr applying the tree-structured CSP algrithm fr finding a slutin t this prblem. 11. Fr each f the fllwing prblems, determine whether an algrithm t ptimally slve the prblem requires wrst-case cmputatin time that is plynmial r expnential in the parameters d and m (assuming that P NP). a. A map has d regins. Clrs have been applied t all d regins, drawing frm a set f m pssible clrs. Yur algrithm needs t decide whether r nt any tw adjacent regins have the same clr. b. A map has d regins. Yur algrithm needs t assign clrs t all d regins, drawing clrs frm a set f m pssible clrs, in rder t guarantee that n tw adjacent regins have the same clr. c. Yur algrithm needs t find its way ut f a maze drawn n a d-by-d grid. d. Yur algrithm needs t find the shrtest path in a d-by-d maze while hitting m waypints (equivalent t dts in MP1 part 1.2). e. Yur algrithm needs t slve a planning prblem in a blcks wrld cnsisting f d blcks. 12. Hw can randmness be incrprated int a game tree? Hw abut partial bservability (imperfect infrmatin)?

5 13. In the lectures, we cvered Nash equilibrium strategies fr simultaneus mve games. We can als cnsider minimax strategies fr such games, defined in the same way as fr alternating games. What wuld be the minimax strategies in the Prisner s Dilemma, Stag Hunt, and Game f Chicken? D they differ frm Nash equilibrium strategies? When/why wuld ne prefer t chse a minimax strategy rather than a Nash equilibrium strategy? 14. Cnsider the fllwing expectiminimax tree: Circle ndes are chance ndes, the tp nde is a min nde, and the bttm ndes are max ndes. a. Fr each circle, calculate the nde values, as per expectiminimax definitin. b. Which actin shuld the min player take? 15. Suppse that bth Alice and Bb want t g frm ne place t anther. There are tw rutes R1 and R2. The utility f a rute is inversely prprtinal t the number f cars n the rad. Fr instance, if bth Alice and Bb chse rute R1, the utility f R1 fr each f them is 1/2. a. Write ut the payff matrix. b. Is this a zer-sum game? c. Find dminant strategies (if any). d. Find pure strategy equilibria (if any). e. Find the mixed strategy equilibrium.