Techniques for Analysis and Calibration of Multi-

Agent Simulations

Manuel FehlerFranziska Klügl

Frank Puppe

Universität WürzburgLehrstuhl für Künstliche Intelligenz

und Angewandte Informatik

Outline

• Motivation and Problem Statement• Society Calibration Problem• Standard Solutions

• White Box Calibration Techniques• Discussion

Motivation and Problem Statement

Multi-agent society simulationGeneral starting point

• We want to understand and/or design societies by simulating them using multi agent simulation

Multi-Agent Simulation• Allows explicit representation of agents and societies from

original system in micro model• To learn from a society simulation model it must be valid in

terms of:• model structure• input parameter configuration controlling the structure

Calibration of society MASim• Model calibration means tuning the parameters so that some

desired (global) society goal(s) or behavior(s) are achieved• Validity of the current parameter configuration for a society

behavior must be evaluated by a goal function• Value of goal function for one parameter configuration is

computed by running the simulation

Society Calibration Problem

Calibrating multi agent society models is especially hard because:• Multi-agent society models often use much more

extensive sets of input parameters than other more restricted forms of modeling

• Model parameters influencing the simulation on a local or agent level have to be set in a way that a certain global society goal or behavior is reached

multi-level calibration problem society calibration problem

Standard Black Box CalibrationOverview:• Society simulation model as black box• Simulation computes some function, not explicitly written down• Try to obtain approximate relationship between input parameters

and simulation output to determine „optimal“ input settingExamples:

• Simulated Annealing, Genetic AlgorithmsAdvantages:

• Generally applicable to any simulation modelDisadvantages:

• Calibration of larger society simulation models possibly too complex to tackle:

• Large parameter configuration search spaces• Complex parameter relationships on different society levels• Multi-agent simulations very computationally expensive

White Box Calibration Approach

Explicitly use model knowledge to enhance calibration process• Knowledge about structural model properties• Knowledge about inter-parameter dependencies

Goal of white box approach:• Reduce parameter configuration search space• Reduce complexity of parameter relationships

Faster convergence of black box search methods• Reduce computational cost of running multi-agent

society simulation Allow to test more parameter configuration

search space points in same amount of time

Simple bee hive example used for illustration

Simulation of major activities in a bee hivea) Foster bee brood:

• Keep the brood warm• Keep the brood fed up

b) Forage a patch environment around the hive for nectar• Find good nectar sources• Communicate to exchange information about source

positions

Nectar

New bees

Starting Points for White Box Calibration

Model decompositon techniquesModel abstraction techniques

Proposed techniques generally applicable to any multi-agent simulation fulfilling requirements for

a technique

Model Decomposition Techniques

General Idea:• Break MASim into smaller submodels, that can be

treated as individual models for calibration• Merge calibrated submodels afterwards

Dimensions of model decomposition:• Decomposition based on:

• functional model units• distributed problem solving in societies• behavioral agent models• temporal phases and situations

Model Decomposition Techniques 2

Decomposition based on functional model units• Identify mostly independent functional units and

calibrate them separatelyTechniques:

• Independent macro model parts as functional unit

Full simulation model

Independent macro model

part 1

Independent macro model

part 2

Model Decomposition Techniques 2

Functional decomposition• Identify mostly independent functional units and

calibrate them separatelyTechniques:

• Independent macro model parts as functional unit• Non-agent environment as functional unit

Some (sub)model

Agents acting in environmental

submodel

Non-agent environmental

submodel

DefinesConstraintsFor Agents

Example

Model Decomposition Techniques 2

Functional decomposition• Identify mostly independent functional units and

calibrate them separatelyTechniques:

• Independent macro model parts as functional unit• Non-agent environment as functional unit• Groups of agents as functional units

All agents in submodel

Agent Group 1 solving some

task

Agent Group 2 solving some

task 2 independent from task 1

Example

Model Decomposition Techniques 2

Functional decomposition• Identify mostly independent functional units and

calibrate them separatelyTechniques:

• Independent macro model parts as functional unit• Non-agent environment as functional unit• Groups of agents as functional units• Individual agents as functional unitsAll agents in

submodel

Agent Group 1 solving some

task

Agent Group 2 solving some

task 2 independent from task 1

Agent class 1 aiding group by

performing independent

subtask 1

Agent class 2 aiding group by

performing independent

subtask 2 Example

Model Decomposition Techniques 3

Decomposition based on distributed problem solving property• Decompose global problem solved by society into

subproblem hierarchy• Calibrate mostly independent subproblems

individually• Merge submodels and refine calibrationGlobal Goal

Maximum amount of

nectar

Subgoal 1All agents

collect from optimal patch

Subgoal 2Optimally

efficient nectar collection

flights

Subgoal 1.1Optimally

efficient scout flights

Subgoal 1.2Optimally

share patch information

among agents

Subgoal 1.3Make optimal

use of avaiable patch

information

Subgoal 1.3.1Stop search

flights if information is

avaiable

Subgoal 1.3.2Forget patches

of lesser quality to be

recruited

Simple Example from Biology

Model Decomposition Techniques 4

Decomposition based on behavioral agent models• Classify parameters based on

their relevance to different possible agent behaviors

• Identify individual goal functions for each behavior class

• Apply optimization with fewer parameters for each goal

Agent without a Task

Search for Task

Task Selection/Allocation

Task Accomplishment

Parameters that trigger willingness to accomplish

a task

Parameters that define searching routines/

success

Parameters that define selection of task/between

different tasksParameters that make agent abandon/switch

tasks

No task selected

Parameters that make agent become idle

Task accomplished

Simple Example

Model Decomposition Techniques 5

Decomposition based on situations and temporal phases

• Identify independent temporal phases or situations of mostly independent behavior during one simulation run not all behavior occurs at the same time

• Separate calibration of the simulation during those phases• Reduce inner simulation time for one simulation run• Reduce parameter space for one temporal phase• If one phase creates precondition for another phase

Submodel calibration ordered by phasesSome (sub)model

Submodel 1:Starting situation

Submodel 2:Typical

situation

Submodel 3:Some critical

situation

Simple Example

Model Abstraction Techniques

General Idea:• Enable faster computation and easier model analysis

by abstracting model aspectsTechniques:

• Abstraction by aggregation of functional groups

• Calibrate individual group agents replace individual agents on group by one agent representing whole group

• Calibrate group behavior constraints for individual group agents

Model Abstraction Techniques

General Idea:• Enable faster computation and easier model analysis

by abstracting model aspectsTechniques:

• Abstraction by aggregation of functional groups• Abstraction reducing heterogeneity

• Homogeneous environments or agent abilities may allow to learn initial parameter configurations for full model calibration

Model Abstraction Techniques

General Idea:• Enable faster computation and easier model analysis

by abstracting model aspectsTechniques:

• Abstraction by aggregation of functional groups• Abstraction reducing heterogeneity• Abstraction at model scale

• Calibrate model of reduced scale (environment, agent numbers)

• Scaling relationships must be known

Model Abstraction Techniques

General Idea:• Enable faster computation and easier model analysis

by abstracting model aspectsTechniques:

• Abstraction by aggregation of functional groups• Abstraction reducing heterogeneity• Abstraction at model scale• Reduction of mass agent systems for easier

analysis• Mass agent systems solve problems by solving

similar smaller subproblems very often• Calibration of individual agent for smaller

subproblem can solve mass system problem

Model Abstraction Techniques

General Idea:• Enable faster computation and easier model analysis

by abstracting model aspectsTechniques:

• Abstraction by aggregation of functional groups• Abstraction reducing heterogeneity• Abstraction at model scale• Reduction of mass agent systems for easier analysis• Implementation optimization techniques

• Abstraction of deterministic agent actions• Meta models for calibrated macro model parts

Sketch of White Box Calibration Method

Sketch of a White Box Calibration Method

1. Calibrate problem setting (e. g. calibrate non agent environment)

2. Temporal and situation based decomposition• May be repeated recursively

3. Goal and behavior based decomposition of submodels• After successful decomposition Goto 1

4. Model analysis• Reduce mass agent systems in submodels for easier

analysis• Generate constraints by calibration of abstracted models

5. Identify goal functions for each submodel and calibrate

6. Merge submodels and calibrate linking parameters• Use abstracted models of calibrated submodels

Sketch of a White Box Calibration Method

1. Calibrate problem setting (e. g. calibrate non agent environment)

2. Temporal and situation based decomposition• May be repeated recursively

3. Goal and behavior based decomposition of submodels• After successful decomposition Goto 1

4. Model analysis• Reduce mass agent systems in submodels for easier

analysis• Generate constraints by calibration of abstracted models

5. Identify goal functions for each submodel and calibrate

6. Merge submodels and calibrate linking parameters• Use abstracted models of calibrated submodels

Sketch of a White Box Calibration Method

1. Calibrate problem setting (e. g. calibrate non agent environment)

2. Temporal and situation based decomposition• May be repeated recursively

3. Goal and behavior based decomposition of submodels• After successful decomposition Goto 1

4. Model analysis• Reduce mass agent systems in submodels for easier

analysis• Generate constraints by calibration of abstracted models

5. Identify goal functions for each submodel and calibrate6. Merge submodels and calibrate linking parameters

• Use abstracted models of calibrated submodels

Sketch of a White Box Calibration Method

1. Calibrate problem setting (e. g. calibrate non agent environment)

2. Temporal and situation based decomposition• May be repeated recursively

3. Goal and behavior based decomposition of submodels• After successful decomposition Goto 1

4. Model analysis• Reduce mass agent systems in submodels for easier

analysis• Generate constraints by calibration of abstracted models

5. Identify goal functions for each submodel and calibrate

6. Merge submodels and calibrate linking parameters• Use abstracted models of calibrated submodels

Sketch of a White Box Calibration Method

1. Calibrate problem setting (e. g. calibrate non agent environment)

2. Temporal and situation based decomposition• May be repeated recursively

3. Goal and behavior based decomposition of submodels• After successful decomposition Goto 1

4. Model analysis• Reduce mass agent systems in submodels for easier

analysis• Generate constraints by calibration of abstracted models

5. Identify goal functions for each submodel and calibrate6. Merge submodels and calibrate linking parameters

• Use abstracted models of calibrated submodels

Sketch of a White Box Calibration Method

1. Calibrate problem setting (e. g. calibrate non agent environment)

2. Temporal and situation based decomposition• May be repeated recursively

3. Goal and behavior based decomposition of submodels• After successful decomposition Goto 1

4. Model analysis• Reduce mass agent systems in submodels for easier

analysis• Generate constraints by calibration of abstracted models

5. Identify goal functions for each submodel and calibrate6. Merge submodels and calibrate linking parameters

• Use abstracted models of calibrated submodels

Discussion

Summary• Calibration of multi agent societies is a very hard problem in

terms of• Complexity of inter parameter dependencies• Size of parameter configuration search space• Computational complexity of running a simulation model

• Black box calibration methods fail in calibration of complex multi-agent society simulation models

• White box calibration methods can exploit structural modularity inherent to society MASims to simplify the calibration problem

• White box techniques need to be applied with great care in order to produce valid and usable results

Further Work• Bottom up calibration vs. top down calibration• Calibration for design