1. Robust Asynchronous Optimization Using Volunteer Computing Grids
Travis Desell, Boleslaw Szymanski, Carlos Varela,
Nathan Cole, Heidi Newberg, Malik Magdon-Ismail
Rensselaer Polytechnic Institute
Department of Computer Science
BOINC Workshop 2009
October 22
Barcelona, Spain

2. Overview Motivation What is Optimization?
Astro-Informatics at
Making Optimization Asynchronous
Partial Verification Strategies
Results
Future Work
03/19/08 2

3. Motivation Distribution is essential for modern scientific computing
Scientific models are becoming increasingly complex
Rates of data acquisition are far exceeding increases in computing power
Scientists need easily accessible distributed optimization tools
Traditional optimization strategies not well suited to large scale computing
Lack scalability and fault tolerance
03/19/08 3

4. What is Optimization?
What parameters x’ give the maximum (or minimum) value of f(x)?
f is typically very complex with multiple minima
Values of x can be continuous or discreet
This talk focuses on continuous optimization
03/19/08 4

5. What is the structure and origin of the Milky Way galaxy?
Astro-Informatics
What is the structure and origin of the Milky Way galaxy?
Being inside the Milky Way provides 3D data:
SLOAN digital sky survey has collected over 10 TB data.
Can determine its structure – not possible for other galaxies.
Very expensive – evaluating a single model of the Milky Way with a single set of parameters can take hours or days on a typical high-end computer.
Models determine where different star streams are in the Milky Way, which helps us understand better its structure and how it was formed.
03/19/08 5

6. Milkyway@Home Progress
03/19/08 6

7. Traditional Optimization Strategies
Traditional continuous optimization strategies are evolutionary, imitating biology.
Individual members or entire populations improve monotonically, through recombination.
Individual-based Evolution:
Differential Evolution
Particle Swarm Optimization
Population-based Evolution:
Genetic Search
03/19/08 7

8. Issues With Traditional Optimization
Traditional global optimization techniques are dependent and iterative
Current population (or individual) is used to generate the next population (or individual)
Dependencies and iterations limit scalability and impact performance
With volatile hosts, what if an individual in the next generation is lost?
Redundancy is expensive
Scalability limited by population size
03/19/08 8

9. Asynchronous Optimization Strategy
Use an asynchronous methodology
No dependencies on unknown results
No iterations
Continuously updated population
N individuals are generated randomly for the initial population
Fulfill work requests by applying recombination operators to the population
Update population with reported results
03/19/08 9

10. Asynchronous Search Architecture
BOINC Clients
Workers (Fitness Evaluation)
Report results and update population
Validate and assimilate results
Request Work
WU Request
Send Work
Send WUs
Population
Unevaluated Individuals
Fitness (1)
Individual (1)
Unevaluated Individual (1)
Fitness (2)
Individual (2)
Unevaluated Individual (2)
Generate work when queue is low . . .
WUs ready to send less than 500
Fitness (n)
Individual (n)
Unevaluated Individual (n)
Assimilator
Work Units
03/19/08 10

11. Genetic Search Generate initial random population
Iteratively generate new populations:
N best individuals survive through ‘selection’
M individuals mutated
O individuals generated through ‘recombination’
03/19/08 11

12. Genetic Search Example
optimize sum of squares: f(pi) = pi[0]2 + pi[1]2 + pi[2]2
iteration
sort 25
0, 4, -3 14
2, 3, -1 5
0, 1, -2 13
-2, 0, 3 26
-3, 1, -4
f(pi) pi 1
f(pi) pi 5
0, 1, -2
recombination (average 3 pairs)
mutation (1 random)
selection (1 best) 9
2, -2, -1
6.75
-2.5, .5, -.5
12.5
0, 2.5, -2.5
10.5
-.5, 2, -2.5 9
2, -2, -1
f(pi) pi 5
0, 1, -2
6.75
-2.5, .5, -.5
12.5
0, 2.5, -2.5
10.5
-.5, 2, -2.5 2
f(pi) pi 5
0, 1, -2
recombination (average 3 pairs)
mutation (1 random)
selection (1 best) 10
0, 1, 3
1.1875
-.25, -.75, -.75
3.625
.75, 0, -1.75
4.6875
-1.25, 0.25, -1.75
03/19/08 12

13. Alternate Recombination
Double Shot - two parents generate three children
Average of the parents
Outside the less fit parent, equidistant to parent and average
Outside the more fit parent, equidistant to parent and average
03/19/08 13

14. Alternate Recombination (2)
Randomized Simplex
N parents generate one or more children
Points randomly along the line created by the worst parent, and the centroid (average) of the remaining parents
03/19/08 14

15. Steady State and Asynchronous GS
Steady State is less parallel than Classical GS:
Generate initial random population
Randomly choose mutation or recombination to generate new individual
If new individual improves population, insert it and remove worst member
We modify this approach for Asynchronous GS:
Randomly choose mutation or recombination to generate new individuals for work requests
When fitness reported, insert members if they improve the population
03/19/08 15

16. Asynchronous vs Iterative Genetic Search
03/19/08 16

17. Particle Swarm Optimization
Particles ‘fly’ around the search space.
Move according to their previous velocity and are pulled towards the global best found position and their locally best found position.
Analogies:
cognitive intelligence (local best knowledge)
social intelligence (global best knowledge)
03/19/08 17

18. Particle Swarm Optimization
PSO:
vi(t+1) = w * vi(t) + c1 * r1 * (li - pi(t)) + c2 * r2 * (g - pi(t))
pi(t+1) = pi(t) + vi(t+1)
w, c1, c2 = constants
r1, r2 = random float between 0 and 1
vi(t) = velocity of particle i at iteration t
pi(t) = position of particle i at iteration t
li = best position found by particle i
g = global best position found by all particles
03/19/08 18

19. Particle Swarm Optimization (Example)
w * vi(t)
current: pi(t)
velocity: vi(t)
previous: pi(t-1)
global best
local best
c2 * (g - pi(t))
c1 * (li - pi(t))
possible new
positions
03/19/08 19

20. Differential Evolution (In Brief)
Many variations:
best/n/bin
rand/n/bin
best/n/exp
rand/n/exp
current/n/bin
current/n/exp
In general:
Perform binary or exponential recombination between the current individual and another individual modified by a scaled difference between n pairs of other individuals
03/19/08 20

21. Differential Evolution (Details)
DE (best/1/bin):
pi,j(t+1)
= gj(t) + c * (pr1,j(t) - pr2,j(t))
= pi,j(t)
if r3 == j or r4 < cr
otherwise
if f(p(t+1)) < f(p(t)) then p(t+1) = p(t)
pi,j(t) = jth parameter of ith member of population at iteration t
gj = jth parameter of global best member at iteration t
c = scaling factor
r1, r2 = random int between 0 and population size, r1 != r2
r3 = random int between 0 and number of parameters
r4 = random float between 0 and 1
cr = crossover rate
03/19/08 21

22. Asynchronous DE & PSO
Note that generating new positions does not necessarily require the fitness of the previous position
1. Generate new particle or individual positions to fill work queue
2. Update local and global best on results
DE:
If result improves individual, update individual’s position
PSO:
If result improves particles local best, update local best, particle’s position and velocity of the result
03/19/08 22

23. Optimization Method Comparison
Tracked best fitness across 5 separate searches for each combination of search parameters.
Used Sagittarius stripe 22:
100,789 observed stars
3 streams
20 optimization parameters
03/19/08 23

24. Optimization Method Comparison
Genetic Search (Simplex & Mutation)
Particle Swarm
DE best/p/bin
DE rand/p/bin
03/19/08 24

25. Latency Effects Is BOINC a good platform for optimization?
Fast turnaround required to keep populations evolving
Many slow clients -- are these resources wasted?
03/19/08 25

26. Operator Examination (1) - BlueGene
03/19/08 26

27. Operator Examination (2) - BOINC
03/19/08 27

28. Operator Examination (3) - BOINC
03/19/08 28

29. Operator Examination (4) - BOINC
03/19/08 29

30. Operator Examination (5) - BOINC
03/19/08 30

31. Operator Examination (6) - BOINC
03/19/08 31

32. Operator Examination (7) - BOINC
03/19/08 32

33. Partial Verification
Only results that will be inserted into the population need to be verified
BOINC verifies every work unit
Partial Verification:
Ignore false-negatives (results that won’t be inserted)
Verify results which potentially improve the search
03/19/08 33

34. Partial Verification Strategies (2)
Required combining assimilation and validation
Slow validation of good results slows convergence
Strategy:
Queue potentially good results
Randomly determine to send results for verification or optimization at an verification rate.
Prematurely terminate unvalidated results if better results are received -- particularly beneficial for DE & PSO.
03/19/08 34

35. Limiting Redundancy (Genetic Search)
Genetic Search (v = 0.3)
Genetic Search (v = 0.6)
Genetic Search (v = 0.9)
03/19/08 35

36. Limiting Redundancy (PSO)
Particle Swarm (v = 0.3)
Particle Swarm (v = 0.6)
Particle Swarm (v = 0.9)
03/19/08 36

37. Limiting Redundancy (DE best/n/bin)
DE best/n/bin (v = 0.3)
DE best/n/bin (v = 0.6)
DE best/n/bin (v = 0.9)
03/19/08 37

38. Limiting Redundancy (DE rand/p/bin)
DE rand/n/bin (v = 0.3)
DE rand/n/bin (v = 0.6)
DE rand/n/bin (v = 0.9)
03/19/08 38

39. Conclusions BOINC is good for optimization
BOINC’s redundancy is not optimal for optimization
Global optimization requires lots of tuning
Verifying results quickly can be especially important for optimization
03/19/08 39

40. Future Work
Discreet parameter optimization
Generic optimization framework for BOINC
Compare limited verification to BOINC’s verification
Adaptive verification strategies
Meta-Heuristics
Simulation with Benchmark Test Functions
03/19/08 40

41. Questions?
03/19/08 41

42. Thanks! http://wcl.cs.rpi.edu http://milkyway.cs.rpi.edu
Work partially supported by:
NSF AST No
NSF IIS No
NSF MRI No
NSF CAREER CNS Award No
03/19/08 42

43. Extra Slides
03/19/08 43

44. Search Parameters Population Size: 300 Mutation Rate: 0.3 Simplex:
1 Child
Parents
Points generated between -1.5 * (worst – centroid) to 1.5 * (worst - centroid)‏
03/19/08 44

45. Asynchronous GS-Simplex on BlueGene
03/19/08 45

46. Asynchronous GS-Simplex on BOINC‏
03/19/08 46

47. Simplex Operator Analysis
Even with a long time to report, results still can improve the population
Generation near reflection has highest insert rate
Generation near centroid provides the most population improvement for fast report times
Generation near reflection provide most population improvement for long report times
03/19/08 47

48. Simplex Operator Improvement (2)‏
03/19/08 48

49. Simplex Operator Improvement (3)‏
03/19/08 49