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layout: post title: "Advanced AI Week1 notes" date: 2019-12-29 19:11:01 +0800

categories: [Advanced AI]

Goal of Artificial General Intelligence (AGI): \ Build general-purpose Super-Intelligences

HOW??? \ --> Build system by trail & error (Artificial Approach) \ --> Mimic human behavior (Natural Approach) (Not covered in this course)

So we need THEORIES to guide us.

For Artificial Approach:

• AI system includes:
  • Logic/language based
  • Economics inspired
  • Cybernetics
  • Machine Learning
  • Information processing

\ Intelligence does not have a formal definition yet.

Decision Theory = Probability + Utility Theory\ Uncertain world, environmental probability distribution is known.

Universal Induction = Ockham + Bayes + Turing\ Sequence prediction for unknown prior distribution.

AI = Decision Theory + Universal Induction

\ UAI covers all Reinforcement Learning(RL) problem types
--> Statistical Machine Learning:
Mostly independent and identically distributed(i.i.d.) data classification, regression, clustering
--> RL Problems & Algorithms:
Stochastic, unknown, non-i.i.d. environments
--> Artificial Intelligence:
Traditionally deterministic, known world/planning problem

\ Informal Definition of Intelligence:
Intelligence measures an agent's ability to achieve goals in a wide range of environments.

Induting a model of the environment --> Make predictions --> Make a decision --> Do the next action

Induction:

Occam's razor: Take simplest hypothesis consistent with data.

Then how to quantify "simplicity"?
Description Length!

--> Shortest description of object is best explanation.

Shortest description = Shortest prgram for a string on a Turing Machines T --> Best extrapolation = Prediction

$$KT(x) = \min{p}{\ell(p) : T(p) = x}$$

Kolmogorov-complexity(x):
$$K(x) = K_U(x) \leq K_T(x) + c_T$$

However, K(x) is uncomputable and p can not be easily found.

So we need to have prior for each possible p. That is why we introduce Bayes' rule here.

Bayes' rule:
$$P(H_i | D) = \cfrac{P(D|H_i) \cdot P(Hi)}{\sum{i}P(D|H_i) \cdot P(H_i)}$$

$P(H_i)$ is prior probability.
$P(H_i|D)$ is posterior probability.

$P(D | H_i)$ is easy to describe.
But we do not know how to choose $P(H_i)$.

Epicurus: If more than one theory is consistent with the observations, keep all theories.
So we refine Occam's razor with Kolmogorov complexity: $$P(Hi) := 2^{-K{T/U}(H_i)}$$

But if we use T, we do not know how to choose T.
If we use U, it is incomputable.

Solomonoff combined Occam, Epicurus, Bayes and Turing. --> Theory of sequential prediction

$M(x)$ = P(UTM outputs x when input is random)
$M(y|x) = M(xy)/M(x)$

The Minimum Description Length Principle
$y$ of highest $M(y|x)$ = $y$ of smallest $K_T(xy)$.

$x$ similar to $y$ --> $K(x|y) := \min \{\ell(p) : U(p,y) = x\}$