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peer-to-peer and agent-based computing Basic Theory of Agency

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2 Plan of next two lectures Motivation States and actions Runs State transformer functions Agents and systems Purely reactive agents Perception Agents with state Utilities Achievement and maintenance tasks Agent synthesis

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3 An Abstract Agent Architecture We need a way to tie down the concept of an agent We present an abstract architecture to formalise the concepts of: –environmental state –actions and state transformations –agent decision making

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4 Why not look at Java code? Answer: –A program is not the best way to communicate with humans about computations Code is verbose (i.e., lots of it!) and may contain a lot of unnecessary housekeeping: –Open sockets, parse XML, set variables/flags, loops,… Abstractions help us understand essential features

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Let us assume that The environment is part of a finite set E of discrete, instantaneous states: E = {e 1, e 2, …} Agents have a repertoire of actions available to them, which transform the state of the environment: Ac = { 1, 2, …} 5 States and actions (1)

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6 States and actions (2) Sample environments: –Readings from a thermostat E = {-10,-9,…,0,1,…,39,40} Sample actions: –Turning on/off heating (or leaving it alone) Ac = {on, off, nil}

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A run r of an agent in an environment is a sequence of interleaved states and actions: r : e 0 e 1 e 2 e 3 … e n Let: – R be the set of all possible finite runs (over E and Ac) – R Ac be the subset of finite runs that end with an action – R E be the subset of finite runs that end with a state 7 Runs (1) 0 n -1 1 2 3

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8 A sample run, using previous environment & actions: r : 10 20 30 25 … -1 Sets: –R = {(10,off),(30,off,20),(-1,nil,10,on,12),…} –R Ac ={(10,off),(10,off,5,on),…} –R E = {(30,off,20),(35,off,10,nil,-2),…} Runs (2) on nil off nil nil

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A state transformer function represents the behaviour of the environment: : R Ac (E ) –Environments: history-dependent & non-deterministic –If (r )=, then there are no possible successor states to r ; i.e. the system has ended its run. Formally, an environment consists of –A set of environment states E –The initial state e 0 –A transformer function Env = E,e 0, 9 State transformer functions (1)

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10 Given R Ac ={(10,off),(10,off,5,on),…} and E = {-10,-9,…,0,1,…,39,40} We can define the following state transformer function ((10,off)) = {-10,…,10} ((10,off,5,on)) = {6,…,40} … A sample environment Env = {-10,…,0,…,40},0, State transformer functions (2)

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An agent is a function mapping runs to actions: Ag : R E Ac –An agent decides which action to perform based on the history it has witnessed so far… Let AG = {Ag 1, Ag 2,…, Ag n } be the set of all agents in a multi-agent system. 11 Agents (1)

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12 Given R E = {(30,off,20),(35,off,10,off,-2),…} we can define the following agent function: –Ag ((30,off,20)) = off –Ag ((35,off,10,nil,-2)) = on –… N.B.: there are compact ways to describe functions: –Ag ((…,on,x)) = off, if x 20 –Ag ((…,on,x)) = nil, if x < 20 –Ag ((…,off,x)) = on, if x < 20 –Ag ((…,nil,x)) = on, if x < 20 –Ag ((…,nil,x)) = nil, if x 20 –… Agents (2)

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A system comprises a pair agent/environment: Ag, Env –Any system has a set of possible runs associated with it The set of runs of an agent in an environment is: R (Ag, Env) –Although the set of runs can be infinite, each run is finite –I.e., we do not consider (for the time being) infinite runs… 13 Systems (1)

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14 A sample system: Ag, {-10,…,0,…,40},0, where –Ag (r ) = Ac (agent defd as a function) – (r ) = ({-10,…,0,…,40}) (state transformer function) A sample set of runs of an agent in an environment: R (Ag, {-10,…,40},0, ) = {(0,on,20,nil,15),…} Systems (2)

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A sequence (e 0, 0, e 1, 1, e 2, …) represents a run of an agent Ag in an environment Env = E, e 0, if 15 Systems (3) 1. e 0 is the initial state of Env 2. 0 =Ag (e 0 ) ; and 3. for i > 0, e i ((e 0, 0,…, i -1 )) where i = Ag ((e 0, 0, …, e i ))

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Two agents Ag 1 and Ag 2 are behaviourally equivalent with respect to environment Env if, and only if, R (Ag 1, Env) = R (Ag 2, Env) Two agents Ag 1 and Ag 2 are behaviourally equivalent if, and only if, they are behaviourally equivalent with respect to all environments Env. 16 Behavioural equivalence of agents

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Some agents decide what to do without reference to their history: –Their decision-making is based entirely on the present –I.e., there is no reference whatsoever to the past! Such agents are called purely reactive: Ag : E Ac A thermostat is a purely reactive agent: Ag (e ) = off if e 20 Ag (e ) = on if e < 20 17 Purely Reactive Agents

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18 We can now introduce a perception system: –see : agents ability to observe the environment –action : agents decision making function Perception (1)

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The output of the see function is a percept: see : E Per which maps environmental states to percepts action is now a function action : Per * Ac which maps sequences of percepts to actions Agents are considered from now on as the pair Ag = see, action 19 Perception (2)

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20 Sample see functions: –Robot with an infrared sensor –Sofware agent performing commands such as ls or finger or retrieving a Web page –The output is stored in some data structure Sample action functions: –Move towards direction of source of heat –Delete all files with extension.jpg obtained via ls –Submit a Web form using the retrieved page Perception (3)

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21 Suggested Reading An Introduction to Multi-Agent Systems, M. Wooldridge, John Wiley & Sons, 2002. Chapter 2.

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