Intention-based Decision Making for Strategic Scenarios Dynamics via Computational Logic

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IntroductionEvolution Prospection

Intention-based decision making

Intention-based Decision Making for StrategicScenarios Dynamics via Computational Logic

The Anh Han 1 ([email protected])Luıs Moniz Pereira 2 ([email protected])

1 AI lab, Computer Science Department, Vrije Universiteit Brussel2 CENTRIA, Departamento de Informatica, Universidade Nova de Lisboa

Portuguese Conference on Artificial Intelligence (EPIA’2013)Angra do Heroısmo, September 2013

T.A.Han, L.M.Pereira Intention-based Decision Making for Strategic Scenarios

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Intention-based decision makingIntention-based decision making

Outline

1 IntroductionIntention-based decision making framework

2 Evolution Prospection (EP)Concepts and constructs

3 Intention-based decision making in strategic scenariosIntention RecognitionEvolution Prospection with Intention Recognition


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Intention-based decision makingIntention-based decision making

Introduction

In strategic situations, achievement of a goal by an agentusually does not depend uniquely on its own actions, but alsoon the decisions of others.

Knowledge about intentions of others can enable to plan inadvance, either for a successful cooperation or for dealing withhostile behaviors.

We provide a logic-based framework for decision making thattakes into account intentions of other agents (via intentionrecognition) in strategic scenarios.


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Intention-based decision makingConcepts and constructs

Evolution Prospection (EP)

Enable an agent to look ahead prospectively into itshypothetical futures, to determine the best one to follow.

We implement several preference constructs.

Implement EP in NEG-ABDUAL, a XSB-Prolog abductionsystem.


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Constructs of EP

Active goals

Abducibles

Local preferences

Evolution-level preferences


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Active Goal

Definition

At each cycle, the agent has a set of active goals to be satisfied

on observe(AG )← Body

”on observing Body trigger goal AG”

Example

1 on observed(choose)← game turn.

2 choose ← move(a1). choose ← move(a2).choose ← move(a3)


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A Priori Preference

Definition (A priori preferences)

Preferences over abducibles

a / b ← Body

”Prefer abducible a to abducible b”

Example

1 move(X )/move(Y )← cost(X , C1), cost(Y , C2), C1 < C2).


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A Posteriori Preference

Definition (A posteriori preferences)

Preferences over abductive solutions

Ai � Aj ← holds given(Li , Ai), holds given(Lj , Aj)

”Ai is preferred to Aj if Li and Lj are true consequences of Ai andAj , respectively”


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Maximin and Minimax

Definition (Maximin)

Ai � Aj ← min utility(Ai , Ui ), min utility(Ai , Uj), Ui > Uj

”Ai is preferred to Aj a posteriori if a consequence of Ai withminimal utility has greater utility than that of Aj . ”

Example

1. abds([b1/0, b2/0]).

expect(b1). expect(b2).

2. on_observe(b_choose).

b_choose <- b1. b_choose <- b2.

3. c(b1,a1) <- b1. c(b1,a2) <- b1. c(b1,a3) <- b1.

4. c(b2,a1) <- b2. c(b2,a2) <- b2. c(b2,a3) <- b2.

5. Ai << Aj <- min_utility(Ai, V1),

min_utility(Aj, V2), V1 > V2.


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Example (cont.): Utility specification

Example

beginProlog. % beginning of just Prolog code

6. consequences([c(b1,a1), c(b1,a2), c(b1,a3),

c(b2,a1), c(b2,a2), c(b2,a3)]).

7. util(c(b1,a1),3). util(c(b1,a2),-1). util(c(b1,a3),6).

util(c(b2,a1),3). util(c(b2,a2), 5). util(c(b2,a3),1).

endProlog. % end of just Prolog code


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Generalized A Posteriori Preference



Ai � Aj ← expected utility(Ai , Ei ),

expected utility(Ai , Ej), Ei > Ej(1)

”Ai is preferred to Aj a posterior if the expected utility of relevantconsequences of Ai is greater than that of Aj”

Example

8. pr(a1, 0.1). pr(a2, 0.4). pr(a3, 0.5).

9. prc(c(_,X), P) :- pr(X, P).


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Evolution Result A Posteriori Preference



Ei ≪ Ej ←expected utility evol(Ei , Ui ),

expected utility evol(Ej , Uj), Ui > Uj(2)

”Ei is preferred to Ej if the expected utility of relevantconsequences of pursuing Ei is greater than the expected utility ofthe ones when pursuing Ej”


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Example: Playing game with limited resource

Example

1. abds([invest_now/0, refuse_now/0,

invest_later/0, refuse_later/0]).

2. expect(invest_now). expect(refuse_now).

3. on_observe(choose) <- decide_invest_now.

choose <- invest_now. choose <- refuse_now.

4. gain1(100) <- invest_now. gain1(0) <- refuse_now.

lose_resource <- invest_now. save_resource <- refuse_now.

5. Ai << Aj <- holds_given(gain1(Gi), Ai),

holds_given(gain1(Gj), Aj), Gi > Gj.


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Example: Playing game with limited resource (cont)

Example

6. on_observe(decide) <- invest_opportunity.

decide <- invest_later. decide <- refuse_later.

7. expect(invest_later) <- save_resource.

expect(refuse_later).

8. gain2(1000,0.6) <- invest_later. gain2(0,1) <- refuse_later.

9. Ei <<< Ej <- expected_utility_evol(Ui, Ei),

expected_utility_evol(Uj, Ej), Ui > Uj.

begingProlog.

10. consequences([gain1(_), gain2(_,_)]).

11. util(gain1(U), U). util(gain2(U,_), U).

12. prc(gain1(_), 1). prc(gain2(_, P), P).

endProlog.


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Intention RecognitionEvolution Prospection with Intention Recognition

Intention Recognition

Infer intention of other agent based on observed actions.

Probabilistic approach via Bayesian Network.


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Bayesian Network for Intention Recognition

Causes/Reasons

C-2

C-N

I-1

I-M

A-1

C-1

A-P

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Intentions

Actions

Subject to Changes

P(A1|I1,IM)

CPD table for each node X P(X|parents(X))

IR: Compute P(I-i|obs) i = 1,...,M

P(C1)


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Integration

In multi-agent setting, becoming aware of others’ intentionsmight help to make better choices

plan in advance to take advantage;act to take remedial actions, etc.

Technically, knowledge about intentions of others can figure inany EP constructs

Active goalsPreference rulesIntegrity constraints


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Example: BN for intention recognition in repeated games.

Example (Intention recognition in repeated games)

BN for intention recognition in repeated interaction settings.

oTrust (Tr): co-player’s trust in recognizer.

Intention (I): C or D; causally affected by oTrust.

pastObs (O): how frequently the recognized player cooperatedin the recent M (memory size) steps.

pastObs: is the only observed node.

oTrust (Tr) Intention (I) pastObs (O)


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Example: Implementing intention-based strategies inrepeated games via EP

Implementing the rule (Han et al., Adaptive Behavior 2011): preferto cooperate if the co-player intends to cooperate, and prefer todefect otherwise

Example

1. abds([move/1]).2. on observed(decide)← new interaction.3. decide ← move(c). decide ← move(d).← move(c), move(d).

4. expect(move(X )).5. move(c) / move(d)← has intention(co player , c).

move(d) / move(c)← has intention(co player , d).


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Example (cont.)

Implementing the rule (Han et al., Artificial Life 2012) which isbased on the recognized strategy of the co-player (e.g. TFT,WSLS)

Example

1. abds([move/1]).2. on observed(decide)← new interaction.3. decide ← move(c). decide ← move(d). ← move(c), move(d).4. expect(move(X )) ← has intention(co player , I , Pr), Pr > 0.7.5. move(d) / move(c)← has intention(co player , allc).

move(d) / move(c)← has intention(co player , alld).move(c) / move(d)← has intention(co player , tft)move(c) / move(d)← has intention(co player , wsls),

game state(s), (s = ‘R’; s = ‘P’).move(c) / move(d)← has intention(co player , wsls),

game state(s), (s = ‘T’; s = ‘S’).


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Conclusions

An intention-based decision making system on top ofEvolution Prospection and Intention Recognition systems.

Several extended intention-based constructs which are usefulfor knowledge representation and reasoning in strategicscenarios.


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Future works

Apply for other more complex games, such as games withimperfect information, multiplayer games and evolutionarygames.

We plan to systematically compare our decision makingframework with the existing ones.


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Thank you!

QUESTIONS


Intention-based Decision Making for Strategic Scenarios Dynamics via Computational Logic

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