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Heuristics in Search-Space

This document discusses the basics of heuristics in search space, including temporal considerations, uncertainty, speedup techniques, and weaknesses. It also explores future work and potential improvements in deriving better heuristics and handling incomplete information and temporal constraints.

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Heuristics in Search-Space

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  1. Heuristics in Search-Space CSE 574 April 11, 2003 Dan Weld

  2. Schedule 3. TEMPORAL • Partial-O • Graphplan • Forward-chaining • Stochastic 4. UNCERTAINTY 1. BASICS • Intro • Graphplan • SATplan • State-space • Refinement 2. SPEEDUP • EBL & DDB • Heuristic Gen • Long paper!

  3. More Administrivia • Mailing List • Reviews due by 11am • No class Fri 4/18 • Experimenting with Planners • Context • Basis for Projects

  4. Paper: Main Points • Avoid duplicate work computing heuristics • Pregenerate in forward sweep; search backward • Interpretation of graphplan • Tradeoff for heuristics: admissible?

  5. Regression Search

  6. Experiments • What were they answering? • Weak support for main points • Do you believe GP analysis? • Why is HSPr faster? • Heuristic calculation or backwards search? • Presentation: • Table vs. graph • Speedup ratio (how compared to 85%)

  7. Weaknesses • Experiments • Needed an example • More discussion of mutex tradeoffs • Algo finds “most” mutexes • Memory usage is a problem (but why?) • Hill climbing with w=5

  8. Greedy BFS • F(n) = g(n) + W h(n) • Empirical studies 1979, 1989 on 8 puz, TSP • Increasing W => speeds search • => less optimal solutions • Proof: if W1 • Then |solution|/|optimal|  W • Proof: abstract tree, uniform branch, 1 goal • Then W=1 gives fastest solution • Optimality is a bonus • Contradiction?!

  9. Future Work • Study graphplan in state-space framework • Project idea: Use Hg with IDA* • Recast other planners as HSP • Analysis of where and why HSPr fails • Empirical Comparison • A*, IDA*, BFS, and HSPr

  10. Future Work 2Derivation of better heuristics • Keep some delete effects • Sum vs. max heuristic • Connection to parallel actions • Probabilistic estimate of step reuse • Non admissible, but more accurate? • Can we bound the amount of step sharing?

  11. Bounding Step Sharing • Build bipartite “support” graph • Compute “max non-mutex outdegree” • Good project? A1 A1 A2 A2 Mutex A3 A3 A4 A4 Eff Pre

  12. McDermott’s Grid World

  13. Future Work 3 • Other points on mutex-computation spectrum • HSPr mutexes are limited to pairs of atoms • Do not consider actions directly • Could ADDs help state enumeration problem

  14. Future Work 4Progression / Regression • Why not generate heuristics backwards? • For what domains would this be faster? • Advantages? • Anytime planning

  15. Future Work 5Incomplete Info / Temporal • What is state space? • How to regress?

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