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Experiments with STAGE

Experiments with STAGE. Wei Wei. Introduction. STAGE- Developed by Boyan Use value function approximation to automatically analyze sample trajectories. Speed up many local search methods. Diagram of STAGE. Produces new training data. Run p to Optimize Obj. Hillclimb to Optimize V.

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Experiments with STAGE

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  1. Experiments with STAGE Wei Wei

  2. Introduction • STAGE- Developed by Boyan • Use value function approximation to automatically analyze sample trajectories. • Speed up many local search methods

  3. Diagram of STAGE Produces new training data Run p to Optimize Obj Hillclimb to Optimize V Produces good start states

  4. Apply it to SAT • The base algorithm is WalkSAT (modified) • Got results better than pure WalkSAT

  5. Overview • We need to deal with four aspects of the problem: WalkSAT, STAGE, features, and to make the algorithm Markovian. • Hard to tune; not every combination works. stage WalkSAT features Marko-vianize

  6. Features • %clauses unsatisfied (-) • %clauses satisfied by 1 variable (+) • %clauses satisfied by 2 variables (-) • %critical variables (-) • %variables set to naïve setting (~)

  7. Markovianize • S/W1 : patience based, not Markovian • S/W2 : best-so-far • S/W3 : epsilon cutoff

  8. Parameter tuning • Noise 0.25 seems good • Patience 10,000 • Cutoff 1,000,000 • Epsilon .0001

  9. Function approximator V-bar-pi • Quadratic regression • Linear regression • Linear functions perform 25% better, and faster. • Linear functions are coarse approximators.

  10. results

  11. Results – Hemming Distance traveled by the V step

  12. results

  13. Feature 1 and 2 only

  14. Added feature: %variables set to true

  15. Discussion(1) • Linear regression is very bad approximation is this case, yet it gives better results than quadratic regression. Why? • Hit bottom very often • Lead to long more WalkSAT moves

  16. Discussion(2) • Features – coefficients vary a lot among instances. But relatively stable within one instance. • The signs are relatively stable

  17. Discussion(3) • Time vs evaluation • When # of evaluation is fixed, STAGE performs 3 times better, but time spent is doubled • When time is fixed, the result is 40% better than WalkSAT

  18. Discussion(4) • Can it hit the finish line? • It does vaguely(?) learn some concepts, which hopefully can direct WalkSAT to a good place. • Par-? Is a good set of problems to solve?

  19. One feature No improvement over WalkSAT.

  20. Random restart • 176 Random flips – Worse than S/W3, still better than WalkSAT • 1000 Random flips – Worse than one-run WalkSAT • Complete new start points – similar to the case above. • Parameters: cutoff – 10,000. Restart – 100.

  21. Hanoi • Parameters not yet carefully tuned • It would be interesting to see whether Hanoi4 can be solved by carefully tuned S/W3. I ran WalkSAT for 50,000,000 flips, but failed to solve it.

  22. Hanoi problems

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