computer science project and need an explanation and answer to help me learn. Letting R (Ag, Env) denote the set of all possible runs of agent Ag in environment Env, letting u( r)

computer science project and need an explanation and answer to help me learn.

Letting R (Ag, Env) denote the set of all possible runs of agent Ag in environment Env,
letting u( r) denote the utility of a run r, and letting P( r| Ag, Env) denote the probability
that run r occurs given agent Ag is placed in environment Env, write an equation that
defines the properties of the optimal agent given u and Env.
Consider the environment Env1 = (E, e0, τ) defined as follows:
E = {e0, e1, e2, e3, e4, e5, e6, e7, e8}
τ(e0 0?? ) = {e1, e2}
τ(e0 1?? ) = {e3, e4}
τ(e0 2?? ) = {e5, e6}
τ(e0 3?? ) = {e7, e8}
There are four agents possible with respect to this environment, say Ag1, Ag2, Ag3 and Ag4:
Ag1(e0) = α0
Ag2(e0) = α1
Ag3(e0) = α2
Ag4(e0) = α3
Assume the probabilities of the various runs are as follows:
P (e0 0?? e1|Ag1, Env1) = 0.3,
P (e0 0?? e2|Ag1, Env1) = 0.5,
P (e0 1?? e3|Ag2, Env1) = 0.2,
P (e0 1?? e4|Ag2, Env1) = 0.3,
P (e0 2?? e5|Ag3, Env1) = 0.6,
P (e0 2?? e6|Ag3, Env1) = 0.7,
P (e0 3?? e7|Ag4, Env1) = 0.5,
P (e0 3?? e8|Ag4, Env1) = 0.4,
Assume the utility function u1 is defined as follows:
u1(e0 0?? e1) = 8,
u1(e0 0?? e2) = 7,
u1(e0 1?? e3) = 8,
u1(e0 1?? e4) = 4,
u1(e0 2?? e5) = 10,
u1(e0 2?? e6) = 2,
u1(e0 3?? e7) = 5,
u1(e0 3?? e8) = 6,

Given these definitions:
i) Determine the expected utility of the agents with respect to Env1 and u1 [8 marks]
ii) State with explanation which agent is optimal with respect to Env1 and u1 [2 marks]

Briefly identify the main advantages and disadvantages of specifying tasks via utility functions over runs, as in part (a), above, and suggest the main alternative.
The issue of telling an agent what to do (without telling it how to do it) is a central problem in multi agent systems. A number of approaches to this problem have been proposed, chief among them being the following:
utility functions over states;
utility functions over runs;
predicates over runs;
achievement tasks;
maintenance tasks.
Explain what you understand by each of these approaches, making clear the relative advantages and disadvantages of each and how these approaches relate to one-another. Illustrate your answer with examples as appropriate.

Requirements: | .doc file