CS 730/830: Intro AI 1 handout: slides Are We Done? Beyond A* - PowerPoint PPT Presentation

CS 730/830: Intro AI 1 handout: slides ■ Are We Done? Beyond A* Suboptimal Search Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 1 / 24

EOLQs ■ Are We Done? Beyond A* Suboptimal Search Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 2 / 24

Are We Done? ■ Are We Done? Beyond A* Suboptimal Search Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 3 / 24

■ Are We Done? Beyond A* ■ GBFS ■ 8-puzzle ■ Evaluating Greedy ■ Beam Search Suboptimal Search Anytime Search Beyond A* Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 4 / 24

Greedy Best-first Search (BGFS) Q ← an ordered list containing just the initial state. ■ Are We Done? Beyond A* Loop ■ GBFS If Q is empty, ■ 8-puzzle ■ Evaluating Greedy then return failure. ■ Beam Search Node ← Pop( Q ). Suboptimal Search If Node is a goal, Anytime Search then return Node (or path to it) Real-time Search else EOLQs Children ← Expand ( Node ). Merge Children into Q , keeping sorted by heuristic . ← Wheeler Ruml (UNH) Lecture 4, CS 730 – 5 / 24

GBFS on the 8-puzzle h ( n ) = number of tiles out of place. (The blank is not a tile.) ■ Are We Done? Beyond A* ■ GBFS 2 8 3 1 2 3 ■ 8-puzzle Start state: 1 6 4 Goal state: 8 4 ⊔ ■ Evaluating Greedy ■ Beam Search 7 5 7 6 5 ⊔ Suboptimal Search Anytime Search Real-time Search Please draw the tree resulting from the first two node expansions. EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 6 / 24

Evaluating Greedy Assume branching factor b and solution at depth d . ■ Are We Done? Beyond A* Completeness: ■ GBFS ■ 8-puzzle Time: ■ Evaluating Greedy ■ Beam Search Space: Suboptimal Search Admissibility: Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 7 / 24

Beam Search Truncate queue to hold the most promising k nodes. ■ Are We Done? k is the beam width . Beyond A* ■ GBFS ■ 8-puzzle ■ Evaluating Greedy ■ Beam Search Suboptimal Search Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 8 / 24

■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Suboptimal Search Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 9 / 24

Problem Settings optimal: minimize solution cost ■ Are We Done? suffer all with f ( n ) = g ( n ) + h ( n ) < f ∗ Beyond A* Suboptimal Search ■ Problem Settings greedy: minimize solving time ■ wA* ■ wA* Behavior ■ Distance-to-go bounded suboptimal: minimize time subject to relative cost ■ EES bound (factor of optimal) Anytime Search Real-time Search bounded cost: minimize time subject to absolute cost bound EOLQs contract: minimize cost subject to absolute time bound anytime: iteratively converge to optimal utility: maximize given function of cost and time Wheeler Ruml (UNH) Lecture 4, CS 730 – 10 / 24

Weighted A* ■ Are We Done? f ′ ( n ) = g ( n ) + w · h ( n ) Beyond A* Suboptimal Search ■ Problem Settings ■ wA* nodes with high h ( n ) look even worse ■ ■ wA* Behavior no infinite rabbit holes ■ ■ Distance-to-go ■ EES suboptimality bounded: within a factor of w of optimal! ■ Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 11 / 24

wA* Behavior ■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs optimal: uniform-cost search Wheeler Ruml (UNH) Lecture 4, CS 730 – 12 / 24

wA* Behavior ■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs optimal: A* Wheeler Ruml (UNH) Lecture 4, CS 730 – 12 / 24

wA* Behavior ■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs bounded suboptimal: Weighted A* Wheeler Ruml (UNH) Lecture 4, CS 730 – 12 / 24

For Speed: Distance-to-go, Not Cost-to-go how to minimize solving time? ■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 13 / 24

For Speed: Distance-to-go, Not Cost-to-go how to minimize solving time? ■ Are We Done? how to minimize number of expansions? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 13 / 24

For Speed: Distance-to-go, Not Cost-to-go how to minimize solving time? ■ Are We Done? how to minimize number of expansions? Beyond A* take the shortest path to a goal Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 13 / 24

For Speed: Distance-to-go, Not Cost-to-go how to minimize solving time? ■ Are We Done? how to minimize number of expansions? Beyond A* take the shortest path to a goal Suboptimal Search ■ Problem Settings for domains with costs, this is not h ( n ) ■ wA* ■ wA* Behavior ■ Distance-to-go new information source: distance-to-go = d ( n ) ■ EES Anytime Search n Real-time Search EOLQs h = 4 h = 5 d = 2 d = 1 Wheeler Ruml (UNH) Lecture 4, CS 730 – 13 / 24

For Speed: Distance-to-go, Not Cost-to-go how to minimize solving time? ■ Are We Done? how to minimize number of expansions? Beyond A* take the shortest path to a goal Suboptimal Search ■ Problem Settings for domains with costs, this is not h ( n ) ■ wA* ■ wA* Behavior ■ Distance-to-go new information source: distance-to-go = d ( n ) ■ EES Anytime Search n Real-time Search EOLQs h = 4 h = 5 d = 2 d = 1 Speedy: best-first search on d Wheeler Ruml (UNH) Lecture 4, CS 730 – 13 / 24

Explicit Estimation Search bounded-suboptimal using h , d , and � h ■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs optimal: uniform-cost Wheeler Ruml (UNH) Lecture 4, CS 730 – 14 / 24

Explicit Estimation Search bounded-suboptimal using h , d , and � h ■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs optimal: A* Wheeler Ruml (UNH) Lecture 4, CS 730 – 14 / 24

Explicit Estimation Search bounded-suboptimal using h , d , and � h ■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs bounded suboptimal: Weighted A* Wheeler Ruml (UNH) Lecture 4, CS 730 – 14 / 24

Explicit Estimation Search bounded-suboptimal using h , d , and � h ■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs bounded suboptimal: Optimistic Search (ICAPS, 2008) Wheeler Ruml (UNH) Lecture 4, CS 730 – 14 / 24

Explicit Estimation Search bounded-suboptimal using h , d , and � h ■ Are We Done? Beyond A* Suboptimal Search ■ Problem Settings ■ wA* ■ wA* Behavior ■ Distance-to-go ■ EES Anytime Search Real-time Search EOLQs bounded suboptimal: Explicit Estimation Search (IJCAI, 2011) Wheeler Ruml (UNH) Lecture 4, CS 730 – 14 / 24

■ Are We Done? Beyond A* Suboptimal Search Anytime Search ■ Anytime A* ■ Break Real-time Search Anytime Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 15 / 24

Anytime A* 1. run weighted A* ■ Are We Done? Beyond A* 2. keep going after finding a goal Suboptimal Search 3. keep best goal found (can test at generation) Anytime Search 4. prune anything with f ( n ) > incumbent ■ Anytime A* ■ Break Real-time Search Anytime Restarting A* (ARA*): lower weight after finding each EOLQs solution Anytime EES Wheeler Ruml (UNH) Lecture 4, CS 730 – 16 / 24

Break asst2 ■ ■ Are We Done? scores and grades ■ Beyond A* AAAI ■ Suboptimal Search Anytime Search ■ Anytime A* ■ Break Real-time Search EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 17 / 24

■ Are We Done? Beyond A* Suboptimal Search Anytime Search Real-time Search ■ RTA* ■ LSS-LRTA* ■ Search Algorithms Real-time Search ■ Other Algorithms EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 18 / 24

RTA* keep hash table of h values for visited states ■ Are We Done? Beyond A* Suboptimal Search 1. for each neighbor of current state s Anytime Search 2. either find h in table or do some lookahead Real-time Search 3. add edge cost to get f ■ RTA* ■ LSS-LRTA* 4. update h ( s ) to second-best f value ■ Search Algorithms ■ Other Algorithms 5. move to best neighbor EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 19 / 24

LSS-LRTA* 1. single A* lookahead (LSS) ■ Are We Done? Beyond A* 2. update all h values in LSS Suboptimal Search 3. move to frontier Anytime Search Real-time Search ■ RTA* ■ LSS-LRTA* ■ Search Algorithms ■ Other Algorithms EOLQs Wheeler Ruml (UNH) Lecture 4, CS 730 – 20 / 24