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Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures.

Lecture



Example: There are 2 production sites that employ 100 workers. The task is to place them in sections in the best way, i.e. find the ratio x: y. The economic situation in 1 segment: 400x - 0.02x 2 = S x ; in the second - 280y - 0.4y 2 = S y , where x is the number of workers in the first section, y is in the second, S x, y is the income from the sections.

Explanation: The negative term symbolizes the restriction on the scope of work, many individuals interfere with each other.

The coefficient of x and y indicates the possibility of earning a single individual and depends on the properties of the environment (area).

Consider the options:

Option A {80.20}

Plot one 2
Number of workers x = 80 y = 20
Earned amount S x = 21760 S y = 5440
Total Earned Amount S = 27200
average salary 276 276

Because The average wage at the sites is the same; workers will not move from one site to another. We will have a steady state. Nash game.

B - {51.49}

Plot one 2
Number of workers x = 51 y = 49
Earned amount S x = 17748 S y = 12740
Total Earned Amount S = 30488
average salary 348 260

This situation is more beneficial in the public sense (more money is received). But due to the fact that the average salary is not the same (when moving from the second section to the first, the individual will receive an additional 88 rubles for the same job), the situation will not be sustainable. Game Mora.

Zetlin: "Inequality in payment is equivalent to the benefit of public interest."

But if you need to simultaneously combine the maximum of the social income of the game of Mora and the stability of the game of Nesh, then you must follow the rules of the game with a common cash register: everyone plays the game of Mora, but then everything is assembled into a common cash register and is divided into all.



Variable Structure Machine

In an automatic machine with a linear structure, one of the main parameters is the lobe depth - q. In a non-stationary environment, q should be small; in stationary - on the contrary. It is required to build an automaton that would determine for itself the quantity q.
Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures.
fig.4.1
Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures.
fig.4.2
Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures.
fig.4.3
Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures.
fig.4.4
Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures.
fig.4.5

Figure 4.1 shows an automatic with linear tactics (2; 2). Solid arrows show transitions for promotions, dotted lines - for fines. Deterministic automatic. Matrices of its transitions are shown in Figure 4.2. In Figure 4.3, the untrained, non-deterministic automaton. In it, transitions from one state to another are random and equally probable. The process of transition from a non-deterministic automaton to a deterministic automaton is the learning process.

Let the machine pass from state 1 to state 4 by chance, and the medium encouraged it. In this case, it increases the likelihood of such a transition. Figure 4.4 shows the transition matrix in the initial state and after the first impact. Initially, the transition matrix has equal transition probabilities (0.25 each). But then at the disadvantageous transition the probability decreases, while other options for the transition increase the likelihood at his expense. That is, the machine reduces the likelihood of transition when the environment fined it and increases it in the opposite case. After some time, the automaton from nondeterministic will go to deterministic. The parameter q is determined by itself. The machine itself will tune. If the environment changes the conditions of the game, the machine will reconfigure. Figure 4.5 shows the setup process of the machine.



Self study

An example showing that a machine, initially untrained, starts playing better than a teacher. Tic-tac-toe game. For convenience, we assume that the teacher plays with zeroes and always makes the first move. Accordingly, the machine plays with crosses. Suppose that for the first time the machine has lost. Therefore, the probability of all transitions leading to loss decreases. On the 3x3 field, after 20-30 games, the machine will at least reduce all games to a draw. Read more


Nature of learning

Is it possible to give a character to learning, i.e. give the machine some individual traits, make a variety. For example, an automaton wants to marry and the main criteria for its decision are such parameters as the presence of an apartment and the ability to cook. x = f (y 1 ; y 2 ) , where x is the output solution, y 1 , y 2 are input signals (let y 1 be the presence of an apartment, y 2 the ability to cook). All variables take one of the three values ​​{0, 0.5, 1}, i.e. “no”, “like yes, and maybe not”, “yes”.
y 1 y 2 x
0 0 0 0 0 ... 0
0 0.5 0 0 0 ... one
0 one 0 0 0 ... one
0.5 0 0 0 0 ... one
0.5 0.5 0.5 0 0 ... one
0.5 one 0.5 0 0 ... one
one 0 0 0 0 ... one
one 0.5 0.5 0 0.5 ... one
one one one one one ... one
min (y 1 , y 2 ) extreme
pessimist 		moderate
pessimist 		... optimist

The most sustainable society: 40% impassive; 40% of moderate pessimists; 20% moderate optimists.

Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures.
fig.4.6


Homogeneous structures

The system is described by three components Q, R, I (goal, resources, information). These components are inherent in both the system and its elements.

Examples of various systems:

System description System example
IRQ hive
I * RQ market
IR * Q fire Department
IRQ * taxis
I * R * Q trolleybus and tram management
IR * Q * performance service system
I * RQ * telephone network
I * R * Q * conveyor
* - no match for elements

Systems are divided into centralized and decentralized (Figure 4.7).

Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures.
fig.4.7

Decentralized systems are usually naturally formed systems, for example, the human body, the international telephone network, the Internet, and the worldwide organization of philatelists.

Characteristics of a centralized system
The consistency of commands, failure in the element leads to a failure in the triangle below it (a wave covering the bush). With increasing system size:
Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures. decreases the speed of execution of commands
Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures. the volume of the control superstructure is larger than the volume of the performing one, and the disproportion grows exponentially,
Machine with a variable structure. Self-study. The nature of learning. Homogeneous structures. the unreliability of the upper elements leads to a large bush of incorrect implementations ...

Characteristics of a decentralized system
Inconsistency of commands, failure results are difficult to predict, actions of system elements are possibly contradictory, resistance to system failures in general, system operation speed does not affect its size, for large sizes it is cost-effective, speed can be reduced due to the time for establishing agreements, survivability is high even in case of failure parts of the system, it is difficult to impose common goals from the outside, quite unexpected effects

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Artificial Intelligence

Terms: Artificial Intelligence