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Artificial Intelligence 15-381 Introduction to AI & Search Methods I Jaime Carbonell [email protected] 28 August 2001 Today’s Topics Are we in the right class? What exactly is AI, anyway? AI = search+knowledge+learning AI application areas Course Outline Administration and grading Basic search methods What is AI: Some Quick Answers From the Media: AI is… …What socially-inept superhackers do …The opposite of natural stupidity …Building useful idiot-savant programs …Deep Blue (IBM’s chess program) …Robots with feelings (Spielberg) What is AI: Some Quick Answers (cont.) From Academia: AI is… …modeling aspects of human cognition by computer …the study of solving ill-formed problems …"nothing more" than advanced algorithms research …cool stuff! Machine learning, data mining, speech, language, vision, web agents…and you can actually get paid a lot for having fun! …what other CS folks don’t yet know how to do, and we AIers aren’t always too sure either Operationally Speaking, AI is: Applied Cognitive Science Computational models of human reasoning • • Problem solving Scientific thinking Models of non-introspective mental processes • Language comprehension, language learning • Human memory organization (STM, LTM) Operationally Speaking, AI is: Knowledge Engineering Codify human knowledge for specific tasks E.g.: Medical diagnosis, Machine Translation Central in 1970s & 80sjust one lecture here Problem-Solving Methods How to encode and use knowledge to find answer E.g. HS, MEA, A*, Logic resolution Always at the very core of AImany lectures Operationally Speaking, AI is: Machine Learning Learning as the hallmark of intelligence…but it is already practical in multiple applications E.g.: D-trees, rule-induction, reinforcement, NNets Discredited in 1960s Vibrant core in 1990s Applications: data & text mining, speech, robotics Most active research area in AI many lectures AI “Application” Areas Rule-Based Expert Systems Medical Diagnosis: MYCIN, INTERNIST, PUFF CSP Scheduling: ISIS, Airline scheduling Data Mining Financial: Fraud detection, credit scoring Sales: Customer preferences, inventory Science: NASA galaxy DB, genome analysis AI “Application” Areas (cont.) Language Processing Speech: dictation, HCI Language: Machine Translation ML & NLP: Fact Extraction ML & words: Information Retrieval Robotics Machine Vision Mobile Robots & “agents” Manipulation AI-Based Problem Solving State-Space <{S}, S0, {SGj}, {Oi}> S0: SG: Oi: Initial State Goal State (to achieve) Operators O: {S} => {S} AI-Based Problem Solving (cont.) State-Space Navigation Forward Search: BFS, DFS, HS,… Backward Search: BFS-1, Backchaining,… Bi-Directional Search: BFS2,… Goal Reduction: Island-S, MEA… Transformation: {S} {S’} Abstraction: {S} {SA} + MEA ({SA})… Analogy: If Sim(P,P’) then Sol(P) Sol’(P’) … More on the State Space Useful Functions: Succ(si) = {sk | oj(si) = sk} Reachable(si) = {U{sk} | Succ *(si)} Succ-1(si) = {sk | oj(sk) = si) Reachable-1(si) = {U{sk} | (Succ-1)*(si)} s-Path(sa0, san) = (sa0, sa1,…, san) …such that for all sa1 exists oj(sai) = sai+1 o-Path(sa0, san) = (oj0, oj1,…, ojn-1) …such that for all sa1 exists oj(sai) = sai+1 More on the State Space (cont.) Useful Concepts: Solution = o-Path(s0, sG) [or s-Path] Cost(Solution) = cost(oj) … (often cost(oj) = 1) P is solvable if at least one o-Path(s0, sG) exists Solutions may be constructed forward, backward or any which way State spaces may be finite, infinite, implicit or explicit Zero-Knowledge Search Simple Depth-First Search DFS(Scurr, Sgoal, S-queue) IF Scurr = Sgoal, SUCCESS ELSE Append(Succ(Scurr), S-queue) IF Null(S-queue), FAILURE ELSE DFS(First(S-queue), Sgoal, Trail(S-queue)) Depth First Search 1 SI 2 7 3 5 4 6 8 … SG DFS (cont.) Problems with DFS Deep (possibly infinite) rat holes depth-bounded DFS, D = max depth Loops: Succ(Succ(..Succ(S))) = S Keep s-Path and always check Scurr Non-Optimality: Other paths may be less costly No fix here for DFS Worst-case time complexity (O(bmax(D,d)) DFS (cont.) When is DFS useful? Very-high solution density Satisficing vs. optimizing Memory-limited search: O(d) space Solution at Known-depth (then D=d) Zero Knowledge Search (cont.) Simple Breadth-First Search BFS(Scurr, Sgoal, S-queue) IF Scurr = Sgoal, SUCCESS ELSE Append(Succ(Scurr), S-queue) IF Null(S-queue), FAILURE ELSE BFS(Last(S-queue), Sgoal, All-ButLast(S-queue)) Breadth-First Search 1 2 5 12 6 3 7 4 8 9 10 … SG 11 Simple BFS cont. Problems with BFS: Loops: Succ(Succ(…Succ(S)))=S Pseudo-loops: Revisiting old states off-path Keep full visited prefix tree Worst case time complexity O(bd) Worst case space complexity O(bd) When is BFS Useful? Guarantee shortest path Very sparse solution space (better if some solution is close to SI) Zero Knowledge Search (cont.) Backwards Breadth-First Search BFS(Scurr, Sinit, S-queue) IF Scurr = Sinit, SUCCESS ELSE Append(Succ-1(Scurr), S-queue) IF Null(S-queue), FAILURE ELSE BFS(Last(S-queue), Sinit, All-But-Last(Squeue)) Backwards Breadth-First Search 9 SI … 4 5 6 7 2 8 3 1 SG Backward-BFS (cont.) Problems with Backward-BFS All the ones for BFS Succ(Scurr) must be invertible: Succ-1(Scurr) When is Backward-BFS useful? In general, same as BFS If backward branching<forward branching Bi-Directional Search Algorithm: 1. 2. 3. 4. 5. 6. 7. Initialize Fboundary:= {Sinit} Initialize Bboundary:= {Sgoal} Initialize treef:= Sinit Initialize treeb:= Sgoal For every Sf in Fboundary IF Succ(Sf) intersects Bboundary THEN return APPEND(Path(treef), Path-1(treeb)) ELSE Replace Sf by Succ(Sf) & UPDATE (treef) For every Sb in Bboundary IF Succ(Sb) intersects Fboundary THEN return APPEND(Path(treef), Path-1(treeb)) ELSE Replace Sb by Succ-1(Sb) & UPDATE (treeb) o to 5. Note: where’s the bug? Bi-Directional Breadth-First Search 1 SI 3 4 8 9 10 13 … 5 6 2 S G 7 11 12 Bi-Directional Search (cont.) Problems with Bi-BFS Loops: Succ(Succ(…Succ(S))) = S Loops: Succ-1(Succ-1(… Succ-1(S)))) = S Pseudo-loops: Revisiting old states off-path Keep full visited prefix treef, trees -1 Succ(Scurr)must be invertible: Succ (Scurr) When is Bi-BFS useful? Space and time complexity: O(bfd/2) + O(bbd/2) = O(bd/2) if bf = bb Island-Driven BFS Definition: An island is a state known a-priori to be on the solution path between Sinit and Sgoal. If there are k sequential islands: BFS(Sinit, S-(goal)= APPEND(BFS(Sinit, Sk1), BFS(Sk1, Sk2),…BFS(SIk, Sgoal)) Upper bound complexity: O(k*maxi=0:k[bdki,ki+1]) Complexity if islands are evenly spaced: O((k+1)*bd/(k+1)) Island-Driven Search 1 SI … SIsland SG