Recursive Best-First Search with Bounded Overhead
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1 Recursive Best-First Search with Bounded Overhead Matthew Hatem and Scott Kiesel and Wheeler Ruml with support from NSF grant IIS Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 1 / 11
2 Problem Summary CR A* remembers every state it visits, often exceeds memory Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 2 / 11
3 Problem Summary CR A* remembers every state it visits, often exceeds memory Motivation for linear-space variants: Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 2 / 11
4 Problem Summary CR A* remembers every state it visits, often exceeds memory Motivation for linear-space variants: Iterative Deepening A* (Korf 1985) Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 2 / 11
5 Problem Summary CR A* remembers every state it visits, often exceeds memory Motivation for linear-space variants: Iterative Deepening A* (Korf 1985) Has bounded overhead Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 2 / 11
6 Problem Summary CR A* remembers every state it visits, often exceeds memory Motivation for linear-space variants: Iterative Deepening A* (Korf 1985) Has bounded overhead Only best-first in some cases! Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 2 / 11
7 Problem Summary CR A* remembers every state it visits, often exceeds memory Motivation for linear-space variants: Iterative Deepening A* (Korf 1985) Has bounded overhead Only best-first in some cases! Recursive Best-First Search (Korf 1993) Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 2 / 11
8 Problem Summary CR A* remembers every state it visits, often exceeds memory Motivation for linear-space variants: Iterative Deepening A* (Korf 1985) Has bounded overhead Only best-first in some cases! Recursive Best-First Search (Korf 1993) Always best-first! Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 2 / 11
9 Problem Summary CR A* remembers every state it visits, often exceeds memory Motivation for linear-space variants: Iterative Deepening A* (Korf 1985) Has bounded overhead Only best-first in some cases! Recursive Best-First Search (Korf 1993) Always best-first! Suffers from thrashing overhead Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 2 / 11
10 Problem Summary CR A* remembers every state it visits, often exceeds memory Motivation for linear-space variants: Iterative Deepening A* (Korf 1985) Has bounded overhead Only best-first in some cases! Recursive Best-First Search (Korf 1993) Always best-first! Suffers from thrashing overhead This is what we fix! Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 2 / 11
11 Iterative Deepening Depth-First Search (IDDFS) CR Depth Bound = 0 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 3 / 11
12 Iterative Deepening Depth-First Search (IDDFS) CR Depth Bound = 1 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 3 / 11
13 Iterative Deepening Depth-First Search (IDDFS) CR Depth Bound = 2 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 3 / 11
14 Iterative Deepening Depth-First Search (IDDFS) CR Depth Bound = 3 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 3 / 11
15 Iterative Deepening Depth-First Search (IDDFS) CR Depth Bound = 4 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 3 / 11
16 Iterative Deepening Depth-First Search (IDDFS) CR Depth Bound = 5 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 3 / 11
17 Iterative Deepening Depth-First Search (IDDFS) CR Depth Bound = 6 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 3 / 11
18 Iterative Deepening A* (IDA*) CR Cost Bound = 6 f(n) = g(n) + h(n) "f layers" Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 4 / 11
19 Iterative Deepening A* (IDA*) CR Cost Bound = 6 f(n) = g(n) + h(n) "f layers" Only best-first if f layers are monotonically increasing! (not the case in, eg, suboptimal variants) Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 4 / 11
20 Recursive Best-First Search (RBFS) CR 3 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
21 Recursive Best-First Search (RBFS) CR best 3 next best bound = 7 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
22 Recursive Best-First Search (RBFS) CR 3 7 next best B=7 best 4 9 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
23 Recursive Best-First Search (RBFS) CR next best B=7 best 4 9 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
24 Recursive Best-First Search (RBFS) CR Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
25 Recursive Best-First Search (RBFS) CR Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
26 Recursive Best-First Search (RBFS) CR next best 3 B=8 8 7 best 9 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
27 Recursive Best-First Search (RBFS) CR B= best 8 next best 1 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
28 Recursive Best-First Search (RBFS) CR Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
29 Recursive Best-First Search (RBFS) CR Strict best-first search order causes thrashing! Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 5 / 11
30 RBFS with Bounded Overhead CR backup min Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 6 / 11
31 RBFS with Bounded Overhead CR min + epsilon Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 6 / 11
32 RBFS with Bounded Overhead CR 3 select value to guarantee at least double! f distribution Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 6 / 11
33 RBFS with Bounded Overhead CR 3 select value to guarantee at least double! f distribution Relaxing best-first search order reduces overhead! See paper for proof Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 6 / 11
34 Sliding Tile Puzzle Tile Puzzle Planning Korf 100 (Korf 1985) A* with Manhattan Distance runs out of memory Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 7 / 11
35 Sliding Tile Puzzle Tile Puzzle Planning Korfs puzzles (unit cost) (w=2) Exp. Avg. Cost Time RBFS 29,253, RBFS ǫ 13,078, RBFS CR 11,695, IDA* 11,136, Relaxing best-first search order gives faster solving times Better solutions but slower than IDA* Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 8 / 11
36 Dockyard Robot Planning Tile Puzzle Planning From Ghallab, Nau, Traverso (2004) All actions have real costs Many duplicate states CR and RBFS CR with transposition tables Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 9 / 11
37 Dockyard Robot Planning Tile Puzzle Planning 5 locations, cranes, piles and 8 containers Exp. Exp./Sec. Time Reopened IDA* CR 2,044m 112k 18,394 2,042m RBFS CR 188m 103k 1,824 87m RBFS ǫ=1 472m 147k 3,222 4m RBFS ǫ=2 251m 140k 1,795 5m RBFS ǫ=3 154m 141k 1,094 14m Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 10 / 11
38 Dockyard Robot Planning Tile Puzzle Planning 5 locations, cranes, piles and 8 containers Exp. Exp./Sec. Time Reopened IDA* CR 2,044m 112k 18,394 2,042m RBFS CR 188m 103k 1,824 87m RBFS ǫ=1 472m 147k 3,222 4m RBFS ǫ=2 251m 140k 1,795 5m RBFS ǫ=3 154m 141k 1,094 14m RBFS CR is faster because it expands 10x fewer nodes Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 10 / 11
39 Summary is depth-first, RBFS is always best-first! Summary Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 11 / 11
40 Summary is depth-first, RBFS is always best-first! Simple modifications reduce overhead (see paper) Summary Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 11 / 11
41 Summary Summary is depth-first, RBFS is always best-first! Simple modifications reduce overhead (see paper) CR gives first provable bounds for overhead Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 11 / 11
42 Summary Summary is depth-first, RBFS is always best-first! Simple modifications reduce overhead (see paper) CR gives first provable bounds for overhead Is it time for IDA* to retire? Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 11 / 11
43 Summary Summary is depth-first, RBFS is always best-first! Simple modifications reduce overhead (see paper) CR gives first provable bounds for overhead Is it time for IDA* to retire? deserves more attention! IDA* citations: 1523 RBFS citations: 310 Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 11 / 11
44 Backup Backup Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 12 / 11
45 Anytime Heuristic Search 15-Puzzle (unit w=4.0) 0.9 Backup Solution Quality RBFS-cr RBFS CPU Time Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 13 / 11
46 Anytime Heuristic Search 15-Puzzle (sqrt w=4.0) 0.9 Backup Solution Quality CPU Time RBFS-cr RBFS Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 13 / 11
47 Anytime Heuristic Search 25 Pancake (sqrt w=1.2) 0.9 Backup Solution Quality RBFS-cr RBFS CPU Time Wheeler Ruml (UNH) Recursive Best-First Search with Bounded Overhead 13 / 11
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