PARALLEL MODEL OF EVOLUTIONARY GAME DYNAMICS

1
PARALLEL MODEL OF EVOLUTIONARY GAME DYNAMICS

• Amanda Peters
• MIT 18.337
• 5/13/2009

2
Outline

• Motivation
• Model
• GPU Implementation
• Blue Gene Implementation
• Hardware
• Results
• Future Work

3
Motivation

• Why does cooperation evolve?
• Examples
• Total War vs. Limited War
• Quorum Sensing Bacteria
• Pathogens
• Goal of the project
• Create computational model to test role of
  behavioral strategies and related variables

4
Model

• Focus on finding evolutionarily stable strategies
• Five strategies
• Mouse
• Hawk
• Bully
• Retaliator
• Prober-Retaliator
• Payoffs
• Win 60
• Seriously Injured -100
• Small Injuries Each -2
• Emerge from Short Game uninjured 20

5
Why parallelize it?

• Reduce computational time
• Enable trials of more strategies
• Enable analysis of different variables roles
• Introduce more actions to the action space

6
CUDA Implementation

• Embarrassingly parallel code
• Distribute rounds of the game to different
  threads
• Only payoff array in global memory
• Copy it back for post processing

7
Sample Code

• __global__ void gameGPU(int player1, int player2,
  float d_payoff1, float d_payoff2,float
  rand_si, int max_rounds)
• //Thread index __global__ void gameGPU(int
  player1, int player2, float d_payoff1, float
  d_payoff2,float rand_si, int max_rounds)
• //Thread index
• const int tidblockDim.x blockIdx.x
  threadIdx.x
•  
• //Total number of threads in grid
• const int THREAD_N blockDim.x
  gridDim.x
•  
• int max_moves500
• for (int round tid round lt max_rounds
  round THREAD_N)
• play_round(player1, player2,
  d_payoff1round, d_payoff2round,
  rand_siround,max_moves)

8
Blue Gene Implementation
9
System Overview
10
Design Fundamentals

• Low Power PPC440 Processing Core
• System-on-a-chip ASIC Technology
• Dense Packaging
• Ducted, Air Cooled, 25 kW Racks
• Standard proven components for reliability and
  cost

11
(No Transcript)
12
BG/P
Blue Gene/L
System
Rack
32 node cards
180/360 TF/s 32 TB (For the original 64 rack
system)
Node card
(32 chips 4x4x2) 16 compute, 0-2 IO cards
2.8/5.6 TF/s 512 GB
Compute card
2 chips, 1x2x1
90/180 GF/s 16 GB
Chip
2 processors
5.6/11.2 GF/s 1.0 GB
2.8/5.6 GF/s 4 MB
13
Blue Gene/P
System
Cabled 8x8x16
Rack
32 Node Cards
1 PF/s 144 TB
14 TF/s 2 TB
Compute Card
1 chip, 20 DRAMs

• Key Differences
• 4 cores per chip
• Speed bump
• 72 racks (8)

435 GF/s 64 GB
Chip
4 processors
13.6 GF/s 2.0 (or 4.0) GB DDR
13.6 GF/s 8 MB EDRAM
14
BG System Overview Integrated system

• Lightweight kernel on compute nodes
• Linux on I/O nodes handling syscalls
• Optimized MPI library for high speed messaging
• Control system on Service Node with private
  control network
• Compilers and job launch on Front End Nodes

15
Blue Gene/L interconnection networks

• 3 Dimensional Torus
• Interconnects all compute nodes (65,536)
• Virtual cut-through hardware routing
• 1.4Gb/s on all 12 node links (2.1 GB/s per node)
• Communications backbone for computations
• 0.7/1.4 TB/s bisection bandwidth, 67TB/s total
  bandwidth
• Global Collective Network
• One-to-all broadcast functionality
• Reduction operations functionality
• 2.8 Gb/s of bandwidth per link Latency of tree
  traversal 2.5 µs
• 23TB/s total binary tree bandwidth (64k machine)
• Interconnects all compute and I/O nodes (1024)
• Low Latency Global Barrier and Interrupt
• Round trip latency 1.3 µs
• Control Network
• Boot, monitoring and diagnostics
• Ethernet
• Incorporated into every node ASIC
• Active in the I/O nodes (164)

16
C/MPI Implementation of Code

• Static Partitioning of work units
• work_unit number_rounds/partition_size
• Each node will get a chunk of the data
• Loops that in serial iterate over the length of
  the game will now be split up to handle specific
  rounds
• Bookkeeping Node
• MPI Collectives to coalesce data

17
Pseudo Code

• Foreach species
• Foreach species
• gamePlay(var1)
• MPI_Reduce(var1)
• If (rank0) Calculate_averages()
• If (rank0) Print_game_results

18
Results
19
Game Dynamics

• Evolutionarily Stable Strategies
• Retaliator
• Prober-Retaliator
• Result
• Limited War is a stable and dominant strategy
  given individual selection

20
CUDA Implementation
97 time reduction
21
CUDA Implementation
22
Blue Gene Implementation
99 time reduction
23
Blue Gene Implementation
24
Future Directions

• Investigate more behavioral strategies
• Increase action space
• CUDA implementation data management
• Blue Gene implementation
• Examine superlinearity
• Test larger problem sizes
• Optimize single node performance