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← 08-07 Partially Observable Vacuum Cleaner Example

Unit 8 7 Partially Observable Vacuum Cleaner Example

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Showing Revision 1 created 11/28/2012 by Amara Bot.

  1. [Narrator] We've been considering sensor-less planning in a deterministic world.
  2. Now I want to turn our attention to partially observable planning
  3. but still in a deterministic world.
  4. Suppose we have what's called local sensing,
  5. that is our vacuum can see what location
  6. it is in and it can see
  7. what's going on in the current location, that is
  8. whether there's dirt in the current location or not,
  9. but it can't see anything about
  10. whether there's dirt in any other location.
  11. So here's a partial diagram of the--
  12. part of the belief state from that world,
  13. and I want it to show
  14. how the belief state unfolds
  15. as 2 things happen.
  16. First, as we take action,
  17. so we start in this state,
  18. and we take the action of going right,
  19. and in this case we still go
  20. from 2 world states in our belief state
  21. to 2 new ones,
  22. but then, after we do an action,
  23. we do an observation, and we have the act
  24. precept cycle, and now,
  25. once we get the observation,
  26. we can split that world,
  27. we can split our belief state to say,
  28. "If we observe that we're in
  29. location B and it's dirty, then we know
  30. we're in this belief state here,
  31. which happens to have exactly 1 world state in it,
  32. and if we observe that we're clean
  33. then we know that we're in this state,
  34. which also has exactly 1 in it.
  35. Now what is the act-observe cycle do
  36. to the sizes of the belief states?
  37. Well in a deterministic world,
  38. each of the individual world states within
  39. a belief state maps into exactly 1 other one.
  40. That's what we mean by deterministic,
  41. and so that means the size of the belief state
  42. will either stay the same or it might decrease
  43. if 2 of the actions sort of accidentally
  44. end up bringing you to the same place.
  45. On the other hand, the observation
  46. works in kind of the opposite way.
  47. When we observe the world, what we're doing
  48. is we're taking the current belief state and
  49. partitioning it up into pieces.
  50. Observations alone can't introduce
  51. a new state--a new world state into the belief state.
  52. All they can do is say,
  53. "Some of them go here and some of them go here."
  54. Now maybe that for some observation
  55. all the belief states go into 1 bin,
  56. and so we make an observation
  57. that we don't learn anything new, but at least
  58. the observation can't make us more confused
  59. than we were before the observation.