Basic Principles to Explore the Parameter Space of Social Simulation Models Takao TERANO Tokyo Institute of Technology http://www.trn.dis.titech.ac.jp
[email protected]
Abstract This tutorial discusses the problem regarding the parameter exploration of Agent-Based Simulation for social systems. Even simple models might have 10**10 parameter spaces. Because there are no Newton’s Laws, or the first principles in ABM for social systems, to convince ABM/ABS, we are required (i) to rigorously validate the models and simulators, (ii) to examine background social and organizational system theories, and (iii) to overcome the vast of parameters of both agent behaviors and models, or Multiverse of ABSs. (This is not the universe.) Also, (iv) we need multiple good results to design and analyze social complex task domains. One solution of the issue is to follow the KISS principle. As another solution, we propose a new method, which employs Generate and Test techniques in the simulation process. This follows the principles of Inverse Simulation and Genetics-Based Validation.. From our recent results, we also show the two methods work well.
1
Outline • • • • •
Starting Up Empirical Tactics for Testing of ABM Inverse Simulation and Genetics-Based Validation Technical Tips How IS & GV Work – – – –
Social Interaction Competing Firms Investors Behaviors Artificial History
• Cooling Down
Introduction • The best way to predict future is to invent it. – Allan Kay • Multi-Agent Simulation invents a new world. → Prediction by ABS
2
However,… • There are no Newton’s Laws in ABS for social systems. (Thus, we can invent it as we would like to…)
• Even simple models might have 10**10 parameter spaces. (It would takes over 10,000 days to complete them if we could search 10 spaces per second.)
• Issue: – How to cope with the vast space of • Agent behaviors • Parameters
• One Solution: – KISS Principle
The KISS Principle Although agent-based modeling employs simulation, it does not aim to provide an accurate representation of a particular empirical application. Instead, the goal of agent-based modeling is to enrich our understanding of fundamental processes that may appear in a variety of applications. This requires adhering to the KISS principle, which stands for the army slogan ‘keep it simple, stupid.’
3
Another Solution • Explore it via Generate and Test • We need multiple results • Validate and Convince them
Inverse Simulation Genetics-based Validation
Empirical Tactics for Testing of ABM • Simpler ones: – Run 100 times with different parameter seeds – Extend 10-100 times of the simulation steps – Change the parameters with the binary search • *2 and *1/2 rules
– Use appropriate graph representations – Observe and focus on “special cases”
• More Complex ones: – – – –
Clustering Parameters Cross Validation Competing Firms …
4
Inverse Simulation Forward Simulation
Inverse Simulation Method
Design the Model
Design a Model with Many Params.
Set Various Parameters
Set a Global Objective Fnc.
Execute Simulation
Execute Simulation to Optimize it
Evaluate Results
Evaluate Initial Parameters
They consider the approach Very Difficult!! GA techniques work well!!
Inverse Simulation • Avoid manual parameter tuning • Evolve ‘good’ societies based on fitness functions associated with Macrolevel Metrics • Analyze the Micro-level characteristics of the agents in the Evolved Society Pre-determined Features
Acquired Features
n-interval
Micro-Level Phenomena
Micro-Level Behavior
Evaluation Selection Crossover Mutation
n-interval Genes of Society Simulation of Artificial Societies
Fitness=Macro-Level Metrics
5
Genetics-Based Validation Individuals: Simulation Results When Inverse Simulation Terminates: - Every Important Parameter Converges - Non-Essential Parameters Show Genetic Drifts (They do Have Various Values) -Statistical Analysis can Validate these Phenomena Objective Func. Value
Non-Essential Dimension
Initial Simulation
Final Simulation
Essential Dimension
Genetics-Based Validation • For Binary Coded Genes: – Clustering of populations based on Geno/Pheno- Types – Flipping of Genes
• For Multi-valued or Real Coded Genes – Multivariate Statistics • Regression Analysis • Factor Analysis • Principal Components Analysis
6
Assumptions for IS and GV • Micro-Level Rich Functionality of the Agent Simulator with Enough Number of Parameters • Macro-Level Clear Specification of the Desired Results like min f(…) • Fast Execution of the Simulation • Good GA-Based Techniques
How to Use Tabu-Lists Population(t) TABU
Tabu List (Long Term)
Renew
Candidates(t+1) mutate
Renew
GA/ BOA pass
TABU
Tabu List (Short Term)
7
TABU-GA for MOP
Selection via Multi-class Tabu-List
Tabu listCandidatesSelection
Apply Genetic Operations
f1
f2 Population (t)
Crossover Mutation
Population (t+1) Pareto Ranking Selection
Pareto
Artificial Society TRURL World
Fitness trend
Net Forum
Fitness
Messages
Communication Network
8
Knowledge Transfer Kd={N,W,E,C} • Knowledge Exchange
N:name of the knowledge attribute W:importance weight of the attribute E:evaluation value of the attribute
Agent a K3
Agent b
K5 K7
K4
K6
C:credibility weight of the attributes
W3 W5 W7
W4 W6
Decision/Attitude of Agent i：
E3
E5
E7
E4
E6
C3
C5
C7
C4
C6
ΣWｊEｊ Kdi)
（j in
Metabolic Rules • M: metabolic = energy – decreases δ at each step and when Agent sends a message – increases δ when Agent receives a message that has higher credibility than the agent has.
• Agent retires when M becomes 0
Agent becomes motivated when messages are received Agent Retired
New Comer
Society
9
Agent Parameters Agent i = ({Kd},D,M,Cp,Cc,Ps,Pr,Pa,Pc,δ,μ,ｎ) {Kd}:a set of knowledge attributes (with parameters α,β,γ) D:decision level the agent makes M:motivation value or energy level of behaviors Cp:physical coordinates Cc:mental coordinates Ps:probability of message sending Pr:probability of message reading Pa:probability of replying attitudes for pros-and-cons Pc:probability of replying attitudes for comment adding δ:metabolic rate μ:mutation rate of knowledge attribute values ｎ:the number of knowledge attributes the agent has
Agent Architecture Pre-determined parameters define the agents’ congenital characteristics
Social genes
Probability of message sending / message reading / relying attitudes for pros-and-cons / relying attitudes for comment adding, physical coordinates,…
Pre-determined Features
Agent 1
agent1
Pre-determined features
Agent 2
Acquired features
Acquired parameters change with communication Knowledge attributes, weights of the attributes ...
agent2
10
Society with Conforming Attitudes • In EMS world Fitness = • Optimize:
n
m
∑∑w e , ij ij
i =1 j =1
← To get influenced agents
• (1) S.T.
– One agent with the strongest decisions – Other Agents with free parameters ← To get one influential agent
• (2) S.T.
– One agent with free parameters – Other agents with conforming attitudes
Convergence of Conforming Society via Tabu-GA TabuGA 70
60
Fitness
50
40
Max Ave Min
30
20
10
0
1
6
11
16
21
26
31
36
41
46
Generations
11
Characteristics of the Two Different Leaders in the Conforming Society 10.0 9.0
Solution Solution11 Solution 2 Sol
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0
Pa ra Pr m ob .( γ .C ) om m en tA Pr tti ob tu .C de om m en tA dd iti on Pr ob .R ea din g
Pa ra m .( α )
Ce rta in ty
tio n
ar am .( α )
Ra te
tP
le dg e
et ab ol ic M
ei gh W
Ev alu a
Nu m
of
Kn
ow
Pr ob .S
en
din g
At tr.
0.0
Observation of the Two Different Leaders in the Conforming Society • Solution 1: Specialist – Specialist Agent with Narrower Knowledge – Tend to Give Comments to the Similar Opinions
• Solution 2: Generalist – Leader Agent with Wider Knowledge – Tend to Give Comments with its Own
12
Simulation of Competing Firms Virtual Environment For Advanced Modeling
→ Agent-Based Social Simulator → Business Firms → GA-Based Multiobjective Opt.
Task Domain: Approach:
ABM+BSCs+MOO+GBV
Result:
Our Framework Works Well
Strategic DM of Competing Firms
In the Management Science Literature: Competing companies will thrive their organizations by choosing their customers, narrowing their focus, and dominating their markets [Treacy, Wiersema 1997] Issue: How to choose them, How to measure them? Translate the strategy of a company into action to get the profit [Kaplan, Norton 1996] Issue: BSCs (Performance measurement System) 〈=〉 ABM: (Actions → Measures)
13
Design of a Firm Agent Parts Vender
Decision of a Company 1. Invest. To Each Dept. within Financial Const. 2. Sale Price
Company A
#Supply
Invest.
Order
＃Order
Product.
Sales
(2) Quality Cost
(6) Relation. Cost (7) Blanding Cost
(4) Function Cost
R&D # Customers: 1,000 Product: 1 Kind Quality: High/Low # Competitors: 40
Share # Sales Benefit
Market
Investment (1)Sales Price
After Service
Logistics
(5) Service Cost
(3) Time Cost
Items (1)-(7) represent decision items (Genes)
Benchmarks of Value Proposition by K&N 製品／サービスの属性 Operational Excellence Oriented Business Strategy
顧客関係 価格 品質 時間 機能 サービス 関係 Attributes of Products & Services Customer Relationship Price Quality Time Function × ×
Image Bland
Ex.: Competitive Price; Quality for Customers; Short Lead-time to Buy （Emphasis on Efficiency, e.g., Low Price & Low Cost for Production） Customer Intimacy Oriented Business Strategy 価格 品質 時間 Attributes of Products & Services
×
×
機能 Customer サービス Relationship関係
×
×
Service
Relation
Image Bland
Ex.: Customer Relationship; Solutions (Emphasis on Individual Relationship) Product Leadership Oriented Business Strategy 価格 時間 Attributes of品質 Products & Services
×
×
Time
機能 Customer サービス Relationship関係
Function
×
×
Image Bland
Ex: Functionality and Performance of the Products and Services (Emphasis on New Products and R&D) : Differentiation ×
: General Items
14
Strategy Map of Kaplan & Norton
Robert S Kaplan and David P.Norton, The Strategy Focused Organization2001
Financial P.
Shareholders’ Value Profit Strategy New Products & Services
Productivity Strategy
Value Proposition
Cost Reduction
Resource Utilization
Customer P.
Operational Excellence Oriented Business Strategy
Customer Intimacy Oriented Business Strategy Product Leadership Oriented Business Strategy 価格 時間 Attributes of品質 Products & Services
×
×
Time
Internal 。 Prspctv
New Product/ Service
Learning & Thriving Prspctv。
機能 Customer サービス Relationship関係 ×
Function
Customer Intimacy
Strategic Competence
Operational Excellence
×
Image Bland
Good Partnership
Strategic Technology
Organizational Culture
Marketing Survey Data Clustering Consumer Behaviors High Purchase Interests BS TV：２１（３１％）
BS TV：３１（４６％）
Radio CDR：８（１０％）
Radio CDR：１２（１５％）
Elec. Shaver：１（２％）
Low
Elec. Shaver：3（6％）
Cluster B
Cluster A
Cluster C
Cluster D
BS TV：１２（１８％）
Quality Evaluation
High
BS TV：３（５％）
Radio CDR：３８（４９％）
Radio CDR：２０（２６％）
Elec. Shaver：9（18％）
Elec. Shaver：37（74％）
Low
15
Objectives of the Experiments ①Sensitivity Analysis of a BS TV Market ②Statistical Analysis of a BS TV Market ③Analysis among Multiple Objectives Alles 遺伝子座
Fitness 適応度
Individual 1 個体１ Individual 2 個体２ Individual 3 個体３ Individual 4 個体４ Individual 5 個体５ Individual 6 個体６
9 6 1 7 2 8
0 7 2 2 2 3
Individual M 個体Ｍ
3
3
8 3 0 0 6 2
5 2 0 3 5 5 ： ： 0 5
3 9 7 5 4 5
1 3 4 3 3 7
8
2
5 2 4 2 3 3
58566104 57878912 60458803 62240039 62609950 67592345 74596458 66743643 8 63409749
Validation 解の妥当性 of the Results
Convergence Graphs
ＢＳ市場 シェア最大化
BSテレビ市場 経常利益最大化
25000 1,600,000,000
1,400,000,000
20000 1,200,000,000
15000 販売個数
経常利益
1,000,000,000
800,000,000
10000 600,000,000
400,000,000
5000 200,000,000
289
297
281
273
265
97
257
94
249
241
233
225
217
209
201
193
185
177
169
161
153
145
137
129
121
97
113
89
105
81
73
65
57
49
41
9
33
25
17
97
94
91
100
88
85
82
79
76
73
70
67
64
61
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
7
13
4
1
10
Convergence of Max._benefit
1
0
0
Convergence of Max_market-share
世代数
世代数
BSテレビ市場 キャッシュフロー最大化
ＢＳテレビ市場 借入金の最小化
120,000,000
35000000
100,000,000
30000000
25000000
借入金
20000000 60,000,000
15000000 40,000,000
10000000 20,000,000
5000000
Convergence of Max_cash-flow
91
88
85
82
79
76
73
70
67
64
61
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
7
4
1
10
100
97
0 100
世代数
94
91
88
85
82
79
76
73
70
67
64
61
58
55
52
49
46
43
40
37
34
31
28
25
22
19
16
13
7
4
1
0 10
キャッシュフロー
80,000,000
世代数
Convergence of Min_borrowing
16
Multi Objective Optimization Results
Fitness1andFitness3 Fitness1and Fitness3
fitness1 1000000000
500000000
0
-500000000
-1000000000
1300000000
800000000
300000000
0
-200000000
-700000000
4000
2000
6000
4000 8000
6000
10000
Generation1 Generation5 Generation100
12000
12000
fitnes
10000
8000 fitnes
1500000000
fitness1
Generation1 Generation5 Generation100
14000
14000
16000
16000 18000
18000 20000
20000
Pareto Diagram for Benefit Max and Share Max (4 Objective Fnc. Case)
Pareto Diagram for Benefit Max and Share Max (2 Objective Fnc. Case)
Results of Genetics-Based Validation Maximize Cash Flow 記述統計量 度数 # GENE1 GEGE2 GENE3 GENE4 GENE5 GENE6 GENE7
Statistics
1 10 10 8 10 10 10
1.00 8.20 7.60 3.00 9.20 7.20 5.80
tabu２ Std. Dev.分散Var. 標準偏差 0.00 0.00 2.05 4.20 3.71 13.80 3.08 9.50 0.84 0.70 3.90 15.20 4.09 16.70
Data 最小値Min. 最大値 Max.
Ave. 平均値 5.40 8.40 6.20 1.80 9.00 8.20 2.00
tabu３ Std. Dev.分散 Var. 標準偏差 1.67 2.80 3.05 9.30 4.76 22.70 1.10 1.20 1.73 3.00 3.49 12.20 1.00 1.00
Data 最小値Min. 最大値 Max. 平均値 Ave. 5 5 5 5 5 5 5
1 5 1 1 8 2 1
Maximize Market Share 記述統計量 Statistics 度数 # GENE1 GEGE2 GENE3 GENE4 GENE5 GENE6 GENE7
5 5 5 5 5 5 5
4 3 1 1 6 2 1
8 10 10 3 10 10 3
Minimize Borrowing 記述統計量 度数 GENE1 GEGE2 GENE3 GENE4 GENE5 GENE6 GENE7
Statistics
# Data最小値Min. 最大値 Max. 平均値 Ave. 5 5 5 5 5 5 5
1 1 1 1 1 1 1
1 6 3 5 10 5 4
1.00 2.80 2.00 2.20 4.20 1.80 2.00
tabu４ Std. Dev.分散 Var. 標準偏差 0.00 0.00 2.17 4.70 1.00 1.00 1.64 2.70 3.70 13.70 1.79 3.20 1.22 1.50
17
Results of Changing the Strategies of the Other Firms Max_Benefit
ValueCurve(Fitness1)
Max_Cash_Flow ValueCurve(Fitness3)
12
12
10
10
8
8 Change 3 companies
le v e
Original 6
6
Change all companies 4
4
2
2
0
0 Price
Quality
Time
Function
Service
Customer relationship
Image
Price
Gene(Investment strategy)
Quality
Time
Function
Service
Customer relationship
Image
Gene(Investment strategy)
Background and Objectives • Efficiency of Market Hypothesis – Central Hypo. In Traditional Finance Theory
• Behavioral Finance – Has Doubt about the Central Hypo. • Systematic Biases about decision making activities • Limit of Arbitrage Trading
• Objectives: - Bridging Human Cognitive Models in Micro and Real Market Data in Macro via Agent-Based Modeling - Analyze the Effects of Passive Investment Strategy, when non-rational agents exist
18
Active vs Passive Investment • Active Investment is an attempt to apply human intelligence to find “Good Deals”. – To get better profits than average – Sometime, they fail, because of the “efficiency of the markets”
• Passive Investment makes no attempt to distinguish attractive from unattractive securities, – To keep average, using index information in the markets
• Passive is beneficial in an individual firm, then what would happen in a macro level
BASIC ABS ARCHITECTURE Benefit/Loss Input
Market Price output
feedback
Artificial Market
Rational Investor
Irrational Investor 1
Irrational Investor 2
19
DESIGN OF AGENT MODEL MODEL COMPONENTS • • • •
Number of Investor Agents：1000 Assets： Stocks(1k Units), Riskless one [Arthur] Changes of Benefits：Brownian Motion ［Sｈｌｅｉｆｅｒ］ Investor Types： Rational, Prospect, O-Conf., Trend – Each Investor Makes Trade Based on both Benefit/Loss Info and Market Prices
• The Agents Make Decisions on the Amount of Trades of the Two Assets Based on the Prediction Methods • The Market Price is Determined at the Point Demand and Supply Coincide with
DECISION MAKING OF INVESTORS • Common Part: – Use the Model Proposed in [Black 1992] Decide the Asset Allocation with Risk&Return Based on both Equilibrium Returns (Common) and Short Term Prediction (Dependent on each Agent)
• Investor Dependent Part (Short Term Prediction) – Rational Investor： Dividend Discount Model （Benefit/Discount Ratio) – Prospect Theory Investor： Estimate the Loss Twice Larger than Benefit from a Reference Point – Over-Confidence Investor： Estimate the Stock Risk Smaller – Trend Chasing Investor： Extrapolate the Past Days’ Trend
20
List of Simulation Parameters
Base Model ＋ Loss Over Estimation Investors • Passive Investors keep the middle
21
Introducing GA-Based Selection • Similar Results are Obtained! – When E.R. < Plus Const → Co-existence of Fundamentalists & Passive Investors
– When E.R. < Zero → Passive Investors
– When E. R. < Minus Const → Passive Investors
Introducing Random Mutation • After changing the strategies, give 1% random mutation • Co-existence of Fundamentalists and Passive Investors • Fundamentalists can get fund for investment from others
22
Keeping the Fundamental Value in AM Simulation: 100 step trading, evaluate the difference from the fundamental values Initial: random values Objective function：((E[ｘt])２＋Var[ｘt]） （where xt ＝（Pｔ−P０ｔ）/P０ｔ)，Pt ：Trading value, P０ｔ：Fundamental value) Population size: 100 Generation: 100 Ｎｏ． Parameters
Objective
１ １０１
・・・ ００１
・・
１００ ００１
・・・ １０１
・・
New Pop
GA
１１１
・・・ ０００
１１０
・・・ １１０
Changes of the Investor Types 1000
800
Fundamentalist Latest Trend(5days) Trend(10days) Trend(1day) Trend(20days) Average(5days) Average(10days) Average(20days)
700 600 500 400 300 200 100
900
800
Time Step
700
600
500
400
300
200
100
0 0
Number of Investors
900
１００シミュレーションの平均
Fundamentalists are increasing
23
Changes of Degree of Overconfidence Degree of Overconfident
1.20 1.00 0.80
Overconfident
0.60
Degree of Overconfident +1σ −1σ
0.40 0.20
Time Step
900
800
700
600
500
400
300
200
100
0
0.00
１００シミュレーションの平均
Roles of Big Investors？
Historical Simulation • we have analyzed a particular family line that had produced many successful candidates who had passed the civil service examination over a period of about 500 years, using technology based on the genealogical records Zokufu in China. We implemented an inverse simulation using a multiagent model with the family line network as an adjacency matrix, the personal prole data as an attribution matrix and the real prole data as an objective function. From this, we established that both grandfather and mother have a profound impact within a family on the transmission of cultural capital to children, and found the part of the system of the norm which is maintained by the family. This was supported by statistical analysis. • Presented on Tuesday Session!!
24
Concluding Remarks • Conclusion: – We must cope with the Explosion of Parameters of ABS – Inverse Simulation and Genetics-Based Validation Work Well for some ABS Systems
• Future Issues： – How to Convince ABS approach to others Artificial Anasazi
EpiSim
References [1] Robert Axelrod: The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration. Princeton University Press, 1997. [2] Robert Axtell: Why Agents? On the Varied Motivation for Agent Computing in the Social Sciences. Brookings Institution CSED Technical Report No. 17, November, 2000. [3] Carlos A. Coello Coello, David A. Van Veldhuizen, and Gary B. Lamont (eds.): Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, New York, 2002. [4] David E. Goldberg, The Design of Innovation, Lessons from and for Competent Genetic Algorithms. Kluwer Academic Publishers, Boston, 2002. [5] Yuji, Katsumata, Setsuya Kurahashi, Takao Terano: We Need Multiple Solutions for Electric Equipments Configuration in a Power Plant - Applying Bayesian Optimization Algorithm with Tabu Search –. Proc. 2002 IEEE World Cngresss on Computational Intelligence, pp. 1402-1407, 2002 [6] Setsuya Kurahashi, Takao Terano: A Genetic Algorithm with Tabu Search for Multimodal and Multiobjective Function Optimization. Proc. the Genetic and Evolutionary Computation Conference (GECCO-2000), pp. 291-298, 2000. [7] M. Richiardi, R. Leombruni, N. Saam, and M. Sonnessa: A Common Protocol for Agent-Based Social Simulation. Journal of Artificial Societies and Social Simulation, vol. 9, no. 1, 2006 http://jasss.soc.surrey.ac.uk/ 9/1/15.html. [8] Takao Terano, Setsuya Kurahashi, Ushio Minami: TRURL: Artificial World for Social Interaction Studies. Proc. 6th Int. Conf. on Artificial Life (ALIFE VI), pp. 326-335, 1998. [9] Hiroshi Takahashi, Takao Terano: Agent-Based Approach to Investors' Behavior and Asset Price Fluctuation in Financial Markets. Journal of Artificial Societies and Social Simulation, Vol. 6, No.3, Jun 30 2003 [10] Takao Terano, Kenichi Naitoh : Agent-Based Modeling for Competing Firms: From Balanced-Scorecards to Multi-Objective Strategies. Proceedings of the 37th Annual Hawaii International Conference on System Sciences 2004 (HICCS 2004), pp.1-8, January 5-8, 2004. [11] Takao Terano: Exploring the Vast Parameter Space of Multi-Agent Based Simulation. In L. Antunes and K. Takadama (Eds.): MABS 2006, LNAI 4442, pp. 1–14, 2007. [12] Setsuya, Kurahashi, Takao Terano: Historical Simulations: A Study of Civil Service Examinations, Family Line and Cultural Capital in China. ESSA 2007.
25
