Hardness aware restart policies
This presentation is the property of its rightful owner.
Sponsored Links
1 / 14

Hardness-Aware Restart Policies PowerPoint PPT Presentation


  • 63 Views
  • Uploaded on
  • Presentation posted in: General

Hardness-Aware Restart Policies. Yongshao Ruan, Eric Horvitz, & Henry Kautz. IJCAI 2003 Workshop on Stochastic Search. Randomized Restart Strategies for Backtrack Search. Simple idea: randomize branching heuristic, restart with new seed if solution is not found in a reasonable amount of time

Download Presentation

Hardness-Aware Restart Policies

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Hardness aware restart policies

Hardness-Aware Restart Policies

Yongshao Ruan, Eric Horvitz, & Henry Kautz

IJCAI 2003 Workshop on Stochastic Search


Randomized restart strategies for backtrack search

Randomized Restart Strategies for Backtrack Search

  • Simple idea: randomize branching heuristic, restart with new seed if solution is not found in a reasonable amount of time

  • Effective on a wide range of structured problems (Luby 1993, Gomes et al 1997)

  • Issue: when to restart?


Complete knowledge of rtd

Complete Knowledge of RTD

P(t)

D

T*

t


No knowledge of rtd

No Knowledge of RTD

  • Can we do better?

    • Information about progress of the current run (looking good?)

    • Partial knowledge of RTD


Answers

Observation horizon

Short

Long

Median run time

Answers

  • (UAI 2001) – Can predict a particular run’s time to solution (very roughly) based on features of the solver’s trace during an initial window

  • (AAAI 2002) – Can improve time to solution by immediately pruning runs that are predicted to be long

    • Scenario: You know RTD of a problem ensemble. Each run is from a different randomly-selected problem. Goal is solve some problem as soon as possible (i.e., you can skip ones that look hard).

    • In general: optimal policy is to set cutoff conditionally on value of observed features.


Answers continued

Answers (continued)

  • (CP 2002) – Given partial knowledge about an ensemble RTD, the optimal strategy uses the information gained from each failed run to update its beliefs about the shape of the RTD.

    • Scenario: There is a set of k different problem ensembles, and you know the ensemble RTD of each. Nature chooses one of the ensembles at random, but does not tell you which one. Each run is from a different randomly-chosen problem from that ensemble. Your goal is to solve some problem as soon as possible.

    • In general: cutoffs change for each run.


Answers final

Answers (final!)

  • (IJCAI 2003 Workshop) – The unknown RTD of a particular problem instance can be approximated by the RTD of a sub-ensemble

    • Scenario: You are allowed to sample a problem distribution and consider various ways of clustering instances that have similar instance RTD’s. Then you are given a new random instance and must solve it as quickly as possible (i.e., you cannot skip over problems!)

    • Most realistic?


Partitioning ensemble rtd by instance median run times

Partitioning ensemble RTD by instance median run-times

Instance median > ensemble median

Ensemble RTD

Instance median < ensemble median


Mse versus number of clusters

MSE versus number of clusters


Computing the restart strategy

Computing the restart strategy

  • Assume that the (unknown) RTD of the given instance is well-approximated by the RTD of one of the clusters

  • Strategy depends upon your state of belief about which cluster that is

  • Formalize as an POMDP:

    • State = state of belief

    • Actions = use a particular cutoff K

    • Effect = { solved, not solved }


Solving

Solving

  • Bellman equation:

  • Solve by dynamic programming (ouch!)

Optimal expected time to solution from belief state s

Probability that running with cutoff t in state s fails (resulting in state s’)


Simple example

Simple Example

  • Suppose RTD of each instance is a scaled Pareto controlled by a parameter b  Uniform[11, 200]

  • Median run time = 2b, so medians are uniformly distributedin [22, 200]

  • Cluster into two sub-distributions

    • Median  110

    • Median > 110

  • Dynamic programming solution:

    201 ,222 ,234 ,239 ,242 ,244 …


Empirical results

Empirical Results


Summary

Summary

  • Last piece in basic mathematics for optimal restarts with partial information

  • See paper for details of incorporating observations

  • RTD alone gives log speedup over Luby universal (still can be significant)

  • Unlimited potential for speedup with more accurate run-time predictors!


  • Login