Additional notes 1996

Additional notes 1996

Here are some brief notes about other things I said is lectures that did not get into the notes. (This is partly to help me remember next year what I want to say or should have said.)

Lecture 1

  • There were about 30 students present.
  • I showed overhead slides of the www pages for the course.
  • I drew a little diagram to illustrate the idea of optimization in stages.

    Lecture 2

  • I asked students to sign a list if they wished supervision. There were 15 who signed.
  • I chatted a bit about my experience filming the game theory programme with the BBC on Friday.
  • This is a packed lecture, with about 5 minutes too much material in this lecture for comfort. But I managed to get through it pretty well this year.

    Lecture 3

  • We made arrangements for supervisions.
  • The conditions D, N or P are sufficient to guarantee that the limit lim_{s\rightarrow\infty} F_s(\pi,x) exists because of montone convergence; I should have added that we allow \infty as a possible value of the limit.

  • A student (E.J.Thomas) sent me email asking

    Does the min on the RHS of the statement of today's theorem need exist? The problem is resolved if we are assuming the set of possible controls is finite (for each x), but are we? It seems that the theorem would work equally if 'min' were replaced by 'inf' throughout.

    This is correct. We should write inf rather than min. I wonder why I wrote min rather than inf in the notes? The proof certainly seems OK even when the action space is infinite.

  • I included a digression on prisoners' dilemma, cigarette advertising and repeated games, with discounting.

    Lecture 4

  • In talking about the example in section 4.1, I also noted that the equation F(x)=max[1-1/x,F(x+1)] has many solutions, e.g. F(x)=10. Only F(x)=1 is actually the solution corresponding to the optimal value function.
  • I mentioned that we should write inf rather than min in Theorem 3.1.
  • I included a digression about the `find the oldest' problem.
  • A student asked afterwards what we mean by discounting in the drug trials of section 4.5. The answer is that we might imagine discounting for mathematical convenience (to keep the total reward over the infinite horizon finite). Or discounting might arise from a "catastrophe event", e.g. beta could be the probability that an even better drug does not arise between trials, where the invention of this better drug would cause the trial to end.
  • There is an error at the end of the equation at the middle of page 19. There ... /B(1-beta) should be ... B/(1-beta).

    Lecture 5

  • I included a digression about the Palasti conjecture problem.
  • I handed out summary sheet 1.

    Lecture 6

  • I included a digression about a self-organizing system.
  • A student asked me afterwards about the issue that Theorem 4.1 holds only if terminal costs are 0. This, and a problem on page 24, need some further explanation.

    Lecture 7

  • I handed out Examples Sheet 2.
  • I included a digression on Robert Aumann's repeated game with partial information.
  • I handed out a new version of notes for Lecture 5. The changes are in section 5.5.

    Lecture 8

  • This year I used overheads to speed up the description of the material in sections 8.1 and 8.2. Students need not know the formulae in these sections, simply that these extensions are possible.
  • I included a humourous digression on black magic and photocopiers.

    Lecture 9

  • This year I used some overheads to discuss the example in 9.1.
  • I included a digression about the instability of the aloha protocol.
  • Again I did not have time to go through the proof of Theorem 9.3 . But I said this is starred. The discussion of the infinite horizon case is certainly not essential.

    Lecture 10

  • I did a digression about the problem of searching for a moving object.

    Lecture 11

  • This plan for lecture is pretty full. I didn't have time to work through the example in the final section. All in all, the content of Lectures 7-11 should be reduced next year, probably by deleting stuff about the infinite horizon limit.

    Lecture 12

  • I began the lecture by going thorugh section 11.4.
  • My digression today was a brief reporting of some of the cute anecdotes about risk that I had heard from Ralph Keeney at the New Orleans INFORMS conference 1995.

    Lecture 13

  • Nothing special. Just the lecture as in notes.

    Lecture 14

  • Nothing special. Just the lecture as in notes.

    Lecture 15

  • I gave students time to fill in the course questionnaire.
  • I did a digression about the Lady's Nylon Stocking Problem.

    Lecture 16

  • I included a digression about Richard Steinberg's optimization model for pulsed advertising expenditure.
  • An interesting request in the course feedback was for notes to be printed in A4 rather then A5.
  • Five students raised their hands when I asked who had accessed the course web site.

    Return to the Optimization and Control course page.

    Richard Weber ( r.r.weber@statslab.cam.ac.uk )

    Last modified: Mon Dec 2 15:55:47 1996