Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Principles of Ar.ficial Intelligence Vasant Honavar Ar3ficial Intelligence Research Laboratory College of Informaon Sciences and Technology Bioinformacs and Genomics Graduate Program The Huck Ins3tutes of the Life Sciences Pennsylvania State University [email protected] hHp://vhonavar.ist.psu.edu hHp://faculty.ist.psu.edu/vhonavar Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Goal-based agents • The agent seeks to achieve a specified goal • AHaining a goal may require a long sequence of ac3ons • Needs a model (representaon) of the world Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Goal-based agents: Problem solving as search • Goal-based agents • Design of simple goal-based agents – Discrete, fully observable states – Discrete ac3ons • Problem formulaon – Problem solving as search – State space search – Example problems • (Review of) Basic (Uninformed) Search Algorithms Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Problem Formulaon • Formulate the goals – Explicit specificaon – Implicit specificaon (goal predicate) • Formulate the ac3ons – Precondi3ons (before) – Post-condi3ons (aer) • Design a representaon that – Captures relevant aspects of the world – Abstracts away unimportant details Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Example: 8-puzzle • States? – Posi3on of each 3le on the board • Ini3al state? – Any state can be ini3al • Acons? – {Le#, Right, Up, Down} • Goal test? Check whether goal configuraon is reached Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Problem Formulaon Simplifying assump3ons • Discrete, fully observable states – ‘in class’, ‘at home’ • Discrete ac3ons – Mary executes ac3on ‘Go home’ in state ‘in class’ to reach the ‘at home’ state – In this setup, we can’t speak of Mary being on her way home • Passive environment – All state changes due to the agent’s ac3on – Mary can’t end up at home because her mom picked her up Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Representaon A representaon • Maps each (physical) state of the external environment into the corresponding abstract state via sensors • Maps each (physical) ac3on on an environmental state into an abstract ac3on on the corresponding abstract state • Maps effects of an abstract ac3on on an abstract state into a corresponding effect on the corresponding environmental state via effectors The mapping from • environmental states and abstract states is many to one • abstract state to an environmental state is one to many Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Representaon The mapping from environmental states and abstract states is many to one abstract state to an environmental state is one to many A representaon induces a par33on over environmental states 4 abstract states, acons may allow only lateral or ver7cal moves – not all environmental state transi7ons can be modeled by the agent Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Representaon • Effects of abstract ac3ons in the abstract state space may be fully determinis3c and predictable… but… • The corresponding effects of the physical ac3ons on the environmental state space are predictable only to the extent – allowed by the resolu3on of the representaon and the fidelity of sensors and effectors – That the environment is indeed determinis3c Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Representaon • Is a surrogate inside an agent’s ‘brain’ for en33es that exist in the external world • Is not just a data structure – why? • Derives its seman3cs through seman3c grounding (sensors, effectors) – Correspondence between descrip3ons and states of the world or ac3ons that change the state of the world • Embodies a set of ontological commitments – assump3ons about the en33es, proper3es, relaonships, and ac3ons that we care about • Choice of representaon maers! Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Problem Formulaon • Formulate the goals – Explicit specificaon – Implicit specificaon (goal predicate) • Formulate the ac3ons – Precondi3ons (before) – Post-condi3ons (aer) • Design a representaon that – Captures relevant aspects of the world – Abstracts away unimportant details Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Example: Missionaries and Cannibals • Ini3al state: 3 missionaries, 3 cannibals, and the boat on the leX bank of the river • Goal: all on the right bank • Constraints: – The boat which can carry at most 2 people at a 3me – If missionaries are outnumbered by cannibals, the cannibals will eat the missionaries • States: The posi3ons of missionaries, cannibals, and the boat on either side of the river • Acons: Movement of the boat with its occupants from one side of the river to the other • Soluon: A sequence of boat trips across the river complete with their passenger lists Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Example: Geng around in Romania Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Example: Geng around in Romania • On holiday in Romania; currently in Arad – Flight leaves tomorrow from Bucharest • Formulate goal – Be in Bucharest • Formulate problem – States: various ci3es – Ac3ons: drive between ci3es • Find soluon – Sequence of ci3es; e.g. Arad, Sibiu, Fagaras, Bucharest, … Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Problem formulaon in the observable, determinis3c case • A problem is defined by: – An ini3al state, e.g. Arad – Successor funcon S(X)= set of ac3on-state pairs • e.g. S(Arad)={<Arad → Zerind, Zerind>,…} – Goal test, can be • Explicit, e.g. x=‘at bucharest’ • Implicit, e.g. checkmate(x) • Ini3al state + successor func3on defines a state space • A soluon is a sequence of ac3ons from the ini3al to goal state Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Basic State Space Search Problem A state space search problem is specified by a 3-tuple (s, A, G) where • s is a start state – s ∈ S, the set of possible start states • O is the set of ac3ons (operators) – Par3al func3ons that map a state into another • G the set of goal states – G may be explicitly enumerated or implicitly specified using a goal predicate goal (g) = True iff g ∈ G Solu3on to a state space search problem is a sequence of ac3on applicaons leading from the start state s to a goal g ∈ G Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Problem formulaon – finding an op3mal solu3on • A problem is defined by: – An ini3al state, e.g. Arad – Successor funcon S(X)= set of ac3on-state pairs • e.g. S(Arad)={<Arad → Zerind, Zerind>,…} ini3al state and the successor func3on together define the state space – Goal test • Explicit, e.g. x=‘at bucharest’ • Implicit, e.g. checkmate(x) – Path cost (addi3ve) • e.g. sum of distances, number of ac3ons executed, … • c(x,a,y) is the step cost, assumed to be ≥ 0 Op3mal solu3on has the lowest path cost Principles of Artificial Intelligence, IST 597F, Fall 2014, (C) Vasant Honavar Pennsylvania State University College of Information Sciences and Technology Artificial Intelligence Research Laboratory Finding an op3mal solu3on • All operator applicaons may not be equally expensive • Suppose we have a cost func3on c: S x O à ℜ+ • c (s,o,r)