## ← 08-07 Partially Observable Vacuum Cleaner Example

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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.