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Learning objectives
At the end of the class you should be able to:
characterize simplifying assumptions made in building AIsystems
determine what simplifying assumptions particular AIsystems are making
suggest what assumptions to lift to build a moreintelligent system than an existing one
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 1 1 / 25
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Dimensions
Research proceeds by making simplifying assumptions,and gradually reducing them.
Each simplifying assumption gives a dimension ofcomplexityI multiple values in a dimension: from simple to complexI simplifying assumptions can be relaxed in various
combinations
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Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchical
Planning horizon non-planning, finite stage,indefinite stage, infinite stage
Representation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 3 3 / 25
Page 4
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stage
Representation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 4 3 / 25
Page 5
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relations
Computational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 5 3 / 25
Page 6
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationality
Learning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 6 3 / 25
Page 7
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learned
Sensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 7 3 / 25
Page 8
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observable
Effect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 8 3 / 25
Page 9
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochastic
Preference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 9 3 / 25
Page 10
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferences
Number of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 10 3 / 25
Page 11
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agents
Interaction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 11 3 / 25
Page 12
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 12 3 / 25
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Modularity
Model at one level of abstraction: flat
Model with interacting modules that can be understoodseparately: modular
Model with modules that are (recursively) decomposedinto modules: hierarchical
Example: Planning a trip from here to a see the MonaLisa in Paris.
Flat representations are adequate for simple systems.
Complex biological systems, computer systems,organizations are all hierarchical
A flat description is either continuous or discrete.Hierarchical reasoning is often a hybrid of continuous anddiscrete.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 13 4 / 25
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Modularity
Model at one level of abstraction: flat
Model with interacting modules that can be understoodseparately: modular
Model with modules that are (recursively) decomposedinto modules: hierarchical
Example: Planning a trip from here to a see the MonaLisa in Paris.
Flat representations are adequate for simple systems.
Complex biological systems, computer systems,organizations are all hierarchical
A flat description is either continuous or discrete.Hierarchical reasoning is often a hybrid of continuous anddiscrete.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 14 4 / 25
Page 15
Modularity
Model at one level of abstraction: flat
Model with interacting modules that can be understoodseparately: modular
Model with modules that are (recursively) decomposedinto modules: hierarchical
Example: Planning a trip from here to a see the MonaLisa in Paris.
Flat representations are adequate for simple systems.
Complex biological systems, computer systems,organizations are all hierarchical
A flat description is either continuous or discrete.Hierarchical reasoning is often a hybrid of continuous anddiscrete.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 15 4 / 25
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Planning horizon
...how far the agent looks into the future when deciding whatto do.
Static: world does not change
Finite stage: agent reasons about a fixed finite number oftime steps
Indefinite stage: agent reasons about a finite, but notpredetermined, number of time steps
Infinite stage: the agent plans for going on forever(process oriented)
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 16 5 / 25
Page 17
Planning horizon
...how far the agent looks into the future when deciding whatto do.
Static: world does not change
Finite stage: agent reasons about a fixed finite number oftime steps
Indefinite stage: agent reasons about a finite, but notpredetermined, number of time steps
Infinite stage: the agent plans for going on forever(process oriented)
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 17 5 / 25
Page 18
Planning horizon
...how far the agent looks into the future when deciding whatto do.
Static: world does not change
Finite stage: agent reasons about a fixed finite number oftime steps
Indefinite stage: agent reasons about a finite, but notpredetermined, number of time steps
Infinite stage: the agent plans for going on forever(process oriented)
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 18 5 / 25
Page 19
Planning horizon
...how far the agent looks into the future when deciding whatto do.
Static: world does not change
Finite stage: agent reasons about a fixed finite number oftime steps
Indefinite stage: agent reasons about a finite, but notpredetermined, number of time steps
Infinite stage: the agent plans for going on forever(process oriented)
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 19 5 / 25
Page 20
Representation
Much of modern AI is about finding compact representationsand exploiting the compactness for computational gains.A agent can reason in terms of:
Explicit states — a state is one way the world could be
Features or propositions.I States can be described using features.I 30 binary features can represent 230 = 1, 073, 741, 824
states.
Individuals and relationsI There is a feature for each relationship on each tuple of
individuals.I Often an agent can reason without knowing the
individuals or when there are infinitely many individuals.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 20 6 / 25
Page 21
Representation
Much of modern AI is about finding compact representationsand exploiting the compactness for computational gains.A agent can reason in terms of:
Explicit states — a state is one way the world could be
Features or propositions.I States can be described using features.I 30 binary features can represent 230 = 1, 073, 741, 824
states.
Individuals and relationsI There is a feature for each relationship on each tuple of
individuals.I Often an agent can reason without knowing the
individuals or when there are infinitely many individuals.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 21 6 / 25
Page 22
Representation
Much of modern AI is about finding compact representationsand exploiting the compactness for computational gains.A agent can reason in terms of:
Explicit states — a state is one way the world could be
Features or propositions.I States can be described using features.I 30 binary features can represent 230 = 1, 073, 741, 824
states.
Individuals and relationsI There is a feature for each relationship on each tuple of
individuals.I Often an agent can reason without knowing the
individuals or when there are infinitely many individuals.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 22 6 / 25
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Computational limits
Perfect rationality: the agent can determine the bestcourse of action, without taking into account its limitedcomputational resources.
Bounded rationality: the agent must make good decisionsbased on its perceptual, computational and memorylimitations.
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Computational limits
Perfect rationality: the agent can determine the bestcourse of action, without taking into account its limitedcomputational resources.
Bounded rationality: the agent must make good decisionsbased on its perceptual, computational and memorylimitations.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 24 7 / 25
Page 25
Learning from experience
Whether the model is fully specified a priori:
Knowledge is given.
Knowledge is learned from data or past experience.
. . . always some mix of prior (innate, programmed) knowledgeand learning (nature vs nurture).
Learning is impossible without prior knowledge (bias).
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Learning from experience
Whether the model is fully specified a priori:
Knowledge is given.
Knowledge is learned from data or past experience.
. . . always some mix of prior (innate, programmed) knowledgeand learning (nature vs nurture).
Learning is impossible without prior knowledge (bias).
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 26 8 / 25
Page 27
Learning from experience
Whether the model is fully specified a priori:
Knowledge is given.
Knowledge is learned from data or past experience.
. . . always some mix of prior (innate, programmed) knowledgeand learning (nature vs nurture).
Learning is impossible without prior knowledge (bias).
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 27 8 / 25
Page 28
Learning from experience
Whether the model is fully specified a priori:
Knowledge is given.
Knowledge is learned from data or past experience.
. . . always some mix of prior (innate, programmed) knowledgeand learning (nature vs nurture).
Learning is impossible without prior knowledge (bias).
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 28 8 / 25
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Uncertainty
There are two dimensions for uncertainty. In each dimensionan agent can have
No uncertainty: the agent knows what is true
Disjunctive uncertainty: there is a set of states that arepossible
Probabilistic uncertainty: a probability distribution overthe worlds.
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Why probability?
Agents need to act even if they are uncertain.
Predictions are needed to decide what to do:I definitive predictions: you will be run over tomorrowI disjunctions: be careful or you will be run overI point probabilities: probability you will be run over
tomorrow is 0.002 if you are careful and 0.05 if you arenot careful
Acting is gambling: agents who don’t use probabilitieswill lose to those who do.
Probabilities can be learned from data and priorknowledge.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 30 10 / 25
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Why probability?
Agents need to act even if they are uncertain.
Predictions are needed to decide what to do:I definitive predictions: you will be run over tomorrowI disjunctions: be careful or you will be run overI point probabilities: probability you will be run over
tomorrow is 0.002 if you are careful and 0.05 if you arenot careful
Acting is gambling: agents who don’t use probabilitieswill lose to those who do.
Probabilities can be learned from data and priorknowledge.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 31 10 / 25
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Sensing uncertainty
Whether an agent can determine the state from its stimuli:
Fully-observable: the agent can observe the state of theworld.
Partially-observable: there can be a number states thatare possible given the agent’s stimuli.
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Sensing uncertainty
Whether an agent can determine the state from its stimuli:
Fully-observable: the agent can observe the state of theworld.
Partially-observable: there can be a number states thatare possible given the agent’s stimuli.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 33 11 / 25
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Effect uncertainty
If an agent knew the initial state and its action, could itpredict the resulting state?
The dynamics can be:
Deterministic: the resulting state is determined from theaction and the state
Stochastic: there is uncertainty about the resulting state.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 34 12 / 25
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Effect uncertainty
If an agent knew the initial state and its action, could itpredict the resulting state?The dynamics can be:
Deterministic: the resulting state is determined from theaction and the state
Stochastic: there is uncertainty about the resulting state.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 35 12 / 25
Page 36
Effect uncertainty
If an agent knew the initial state and its action, could itpredict the resulting state?The dynamics can be:
Deterministic: the resulting state is determined from theaction and the state
Stochastic: there is uncertainty about the resulting state.
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 36 12 / 25
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Preference
What does the agent try to achieve?
achievement goal is a goal to achieve. This can be acomplex logical formula.
complex preferences may involve tradeoffs betweenvarious desiderata, perhaps at different times.I ordinal only the order mattersI cardinal absolute values also matter
Examples: coffee delivery robot, medical doctor
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 37 13 / 25
Page 38
Preference
What does the agent try to achieve?
achievement goal is a goal to achieve. This can be acomplex logical formula.
complex preferences may involve tradeoffs betweenvarious desiderata, perhaps at different times.
I ordinal only the order mattersI cardinal absolute values also matter
Examples: coffee delivery robot, medical doctor
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 38 13 / 25
Page 39
Preference
What does the agent try to achieve?
achievement goal is a goal to achieve. This can be acomplex logical formula.
complex preferences may involve tradeoffs betweenvarious desiderata, perhaps at different times.I ordinal only the order matters
I cardinal absolute values also matter
Examples: coffee delivery robot, medical doctor
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 39 13 / 25
Page 40
Preference
What does the agent try to achieve?
achievement goal is a goal to achieve. This can be acomplex logical formula.
complex preferences may involve tradeoffs betweenvarious desiderata, perhaps at different times.I ordinal only the order mattersI cardinal absolute values also matter
Examples: coffee delivery robot, medical doctor
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 40 13 / 25
Page 41
Preference
What does the agent try to achieve?
achievement goal is a goal to achieve. This can be acomplex logical formula.
complex preferences may involve tradeoffs betweenvarious desiderata, perhaps at different times.I ordinal only the order mattersI cardinal absolute values also matter
Examples: coffee delivery robot, medical doctor
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 41 13 / 25
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Number of agents
Are there multiple reasoning agents that need to be taken intoaccount?
Single agent reasoning: any other agents are part of theenvironment.
Multiple agent reasoning: an agent reasons strategicallyabout the reasoning of other agents.
Agents can have their own goals: cooperative, competitive, orgoals can be independent of each other
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Interaction
When does the agent reason to determine what to do?
reason offline: before acting
reason online: while interacting with environment
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Page 44
Dimensions of complexity
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 44 16 / 25
Page 45
State-space search
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 45 17 / 25
Page 46
Deterministic planning
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 46 18 / 25
Page 47
Decision networks
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 47 19 / 25
Page 48
Markov decision processes (MDPs)
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 48 20 / 25
Page 49
Decision-theoretic planning
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 49 21 / 25
Page 50
Reinforcement learning
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 50 22 / 25
Page 51
Classical game theory
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 51 23 / 25
Page 52
Humans
Dimension ValuesModularity flat, modular, hierarchicalPlanning horizon non-planning, finite stage,
indefinite stage, infinite stageRepresentation states, features, relationsComputational limits perfect rationality, bounded rationalityLearning knowledge is given, knowledge is learnedSensing uncertainty fully observable, partially observableEffect uncertainty deterministic, stochasticPreference goals, complex preferencesNumber of agents single agent, multiple agentsInteraction offline, online
c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 52 24 / 25
Page 53
The dimensions interact in complex ways
Partial observability makes multi-agent and indefinitehorizon reasoning more complex
Modularity interacts with uncertainty and succinctness:some levels may be fully observable, some may bepartially observable
Three values of dimensions promise to make reasoningsimpler for the agent:I Hierarchical reasoningI Individuals and relationsI Bounded rationality
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