artificial intelligence, lecture 1.2, page 1 · characterize simplifying assumptions made in...

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

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

c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 2 2 / 25

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 23 7 / 25

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

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 25 8 / 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).

c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 26 8 / 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).

c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 27 8 / 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).

c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 28 8 / 25

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.

c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 29 9 / 25

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

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

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 32 11 / 25

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

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

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

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

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

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

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

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

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

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

c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 42 14 / 25

Interaction

When does the agent reason to determine what to do?

reason offline: before acting

reason online: while interacting with environment

c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 43 15 / 25

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

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

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

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

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

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

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

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

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

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

c©D. Poole and A. Mackworth 2017 Artificial Intelligence, Lecture 1.2, Page 53 25 / 25