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+# AI - lesson 03
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+#### Francesco Arrigoni
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+###### 14 October 2015
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+## Goal Oriented agents
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+Historically called __problem-solving agents__
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+
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+Steps involved:
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+1. __Formulate a problem__
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+ Usually performed by the designer
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+2. __Search for a solution__
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+ Usually performed by the agent itself
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+3. __Execute the actions__ that compose the solution.
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+ Performed by the agent
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+
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+This is different from usual systems in which step 2 (formulate the algorithm) is performed by a human.
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+
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+The types of algorithms created by the agents are usually simple, without IF statements.
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+
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+### Formulating the problem:
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+The __environment__ we have to interact with is:
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+- static
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+- deterministic
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+- fully observable
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+- known
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+- discrete
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+
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+The problem can be formulated defining the following five elements:
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+(example problem is the reduced version of 15 puzzle: 8 puzzle)
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+1. The __initial state__: a description of the initial situation of the problem
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+2. __Actions__ (s) = {actions that are applicable is s} Return the legal moves from the state s.
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+
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+ The state s<sub>0</sub> is
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+ 7|2|3
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+ ---|---|---
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+ 1|4|8
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+6|5|
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+
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+Actions(s<sub>0</sub>)={$\leftarrow,\uparrow$}
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+3. __Result__ (s,a) = s' have the chosen move as argument and returns the new state.
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+$a \in Action(s)$
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+The __result__ function is also called transition function (model)
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+
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+We are considering a deterministic model, so that the result of a given action is *fixed*
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+
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+I can state that __initial state__, __actions__ and __result__ are elements of a *graph* named __state space__
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+
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+In our __state space__ graph:
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+- *vertices* correspond to *states*
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+- *arcs* correspond to *actions*.
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+
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+The graph is *implicitly defined*, it's not represented with an incidence matrix.
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+For example the state space of chess game is estimated to be $10^{120}$.
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+It is almost impossible to represent, but we can build algorithm that can win a game exploring only a very small portion of the graph.
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+
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+The agents viewed at lesson are in a sense less powerful than Operating Research algoritms, but they don't require knowing the totality of the graph, and this is an advantage.
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+
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+A __path__ on a graph is a *sequence of states* that are connected on the graph.
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+
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+4. __Goal test__: returns true or false, it is a test to check if the case is final or not.
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+ - __explicit__ goal test: list of all the final states ex: 8 puzzle
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+ - __implicit__ goal test: condition that characterizes final states ex: chess
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+
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+Every path in the state space should be associate to a *cost* (number), that is the sum of the costs of the action composing the path.
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+5. __Path cost__: is the sum of the costs of the action composing the path.
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