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Interesting topic, but I do not think I understand it very well. I have a couple questions

You say that you prove the existence of the optimal score function, is that still a to do? You also say you formalize the definition of RSI systems, but this formulization is not used anywhere. What is the use? Does it aid you in proofs? Is there related work or is this completely novel? How do the programs you generate look like? In general, how do you define a program? What's the rank of the program? "The expected numbers of steps from a program to find the optimal program following the defined procedure is a reasonable choice to describe the program's ability of future improvement." Why is that a reasonable choice? Or rather, if you define score as the number of steps to reach optimality and future improvement potential, how is optimality defined? How do we know the steps that are needed? RSI seems very similar to evolutionary algorithm? Is there any research in that field that could apply here? Or how does they relate?

Minor Things:

There is a decent amount of grammatical errors, I cherry-picked some:

• Baseilne of RSI -> A Baseline of RSI
• Recursive self-improving systems has been dreamed since -> Recursive self-improving systems have been dreamed of since
• how dose a program -> how does a program
• thesis [8] -> should use a wikipedia citation system

Marking Scheme

I a scale of 1 to 5, where 1 means "strongly disagree" and 5 means "strongly agree" please rate and comment on the following:

   The topic is relevant for the course. 5
   The writing is clear and the English is good. 2
   The page is written at an appropriate level for CPSC 522 students (where the students have diverse backgrounds). 5
   The formalism (definitions, mathematics) was well chosen to make the page easier to understand. 3
   The abstract is a concise and clear summary. 3 
   There were appropriate (original) examples that helped make the topic clear. 2
   There was appropriate use of (pseudo-) code. 1
   It had a good coverage of representations, semantics, inference and learning (as appropriate for the topic). 3
   It is correct. ?
   It was neither too short nor too long for the topic. 5
   It was an appropriate unit for a page (it shouldn't be split into different topics or merged with another page). 5
   It links to appropriate other pages in the wiki. 3
   The references and links to external pages are well chosen. 3
   I would recommend this page to someone who wanted to find out about the topic. ?
   This page should be highlighted as an exemplary page for others to emulate. 3

If I was grading it out of 20, I would give it: 14