This is a short talk I gave to the Strathclyde Planning Group on deficiencies I can see in the way we thing and reason about planning in non-deterministic environments. PPDDL - the accepted standard - is overly simplistic and can get us into hot water because we focus on solving the PPDDL problem, rather than the Real World problem it models. The breakout session that followed was very useful for generating a lot of ideas about different threads we could use to attack the weaknesses of PPDDL and work being done around the edges, which I hope to summarise at some point.

1. The Ludic Fallacy
SPG
11th Feb 2011

2. • Ludic - Of or pertaining to games of chance
• Fallacy - An argument which seems to be
correct but which contains at least one error.

3. Example

4. Example
• Suppose you flip a coin, what is the chance it comes
up heads?

5. Example
• Suppose you flip a coin, what is the chance it comes
up heads?
• 50/50

6. Example
• Suppose you flip a coin, what is the chance it comes
up heads?
• 50/50
• Suppose you flip the coin 100 times and the first 99
were tails. What is the chance of the final flip giving
heads?

7. Example
• Suppose you flip a coin, what is the chance it comes
up heads?
• 50/50
• Suppose you flip the coin 100 times and the first 99
were tails. What is the chance of the final flip giving
heads?
• Independent variables, still 50/50.

8. Example
• Suppose you flip a coin, what is the chance it comes
up heads?
• 50/50
• Suppose you flip the coin 100 times and the first 99
were tails. What is the chance of the final flip giving
heads?
• Independent variables, still 50/50.
• ...or is it?

9. Origins

10. Origins
• Originally postulated by Nassim Nicholas
Taleb in "The Black Swan".

11. Origins
• Originally postulated by Nassim Nicholas
Taleb in "The Black Swan".
• Broadly, the ability to describe the outcomes
of events gives an impression of control. It
does not give ACTUAL control of the events.

12. Origins
• Originally postulated by Nassim Nicholas
Taleb in "The Black Swan".
• Broadly, the ability to describe the outcomes
of events gives an impression of control. It
does not give ACTUAL control of the events.
• A complex but inaccurate model is most
importantly inaccurate.

13. "Gambling With the
Wrong Dice"

14. "Gambling With the
Wrong Dice"
• Case Study based on Las Vegas casino.

15. "Gambling With the
Wrong Dice"
• Case Study based on Las Vegas casino.
• Extensive and sophisticated systems and models
to account for potential cheating.

16. "Gambling With the
Wrong Dice"
• Case Study based on Las Vegas casino.
• Extensive and sophisticated systems and models
to account for potential cheating.
• Aim was to manage risk.

17. "Gambling With the
Wrong Dice"
• Case Study based on Las Vegas casino.
• Extensive and sophisticated systems and models
to account for potential cheating.
• Aim was to manage risk.
• But the vast majority of losses came from non-
gambling activity : a disgruntled ex-employee,
onstage accidents, failure to file correct paperwork
and a kidnap ransom.

18. Blinded By Probability

19. Blinded By Probability
• Because we see numbers as solvable, we
focus on solving them.

20. Blinded By Probability
• Because we see numbers as solvable, we
focus on solving them.
• Lose sight of the broader picture.

21. Blinded By Probability
• Because we see numbers as solvable, we
focus on solving them.
• Lose sight of the broader picture.
• The "game" becomes our main focus rather
than the world it represents.

22. Back to Coins

23. Back to Coins
• We flip 99 times, all tails.

24. Back to Coins
• We flip 99 times, all tails.
• 0.5^99 = 1.8x10^-30

25. Back to Coins
• We flip 99 times, all tails.
• 0.5^99 = 1.8x10^-30
• Which is more likely, this highly improbable event is
happening, or the assumptions that we used to build
the model don't hold true?

26. Back to Coins
• We flip 99 times, all tails.
• 0.5^99 = 1.8x10^-30
• Which is more likely, this highly improbable event is
happening, or the assumptions that we used to build
the model don't hold true?
• Is the coin fair?

27. Back to Coins
• We flip 99 times, all tails.
• 0.5^99 = 1.8x10^-30
• Which is more likely, this highly improbable event is
happening, or the assumptions that we used to build
the model don't hold true?
• Is the coin fair?
• What actually is the probability of getting heads next?

28. Off-model
Consequences

29. Off-model
Consequences
• When we have a model, we risk getting blinkered
into thinking about the model instead of the world.

30. Off-model
Consequences
• When we have a model, we risk getting blinkered
into thinking about the model instead of the world.
• But models are abstract representations.

31. Off-model
Consequences
• When we have a model, we risk getting blinkered
into thinking about the model instead of the world.
• But models are abstract representations.
• No PDDL model describes the effect of a meteorite
hitting a robot, yet it is an (unlikely) possibility.

32. Off-model
Consequences
• When we have a model, we risk getting blinkered
into thinking about the model instead of the world.
• But models are abstract representations.
• No PDDL model describes the effect of a meteorite
hitting a robot, yet it is an (unlikely) possibility.
• Outcomes of actions, or events, cannot be fully
enumerated. There exist "off-model consequences"

33. Coins Again

34. Coins Again
• We talk about coins having a head and a tail side and
50/50 chance of either.

35. Coins Again
• We talk about coins having a head and a tail side and
50/50 chance of either.
• This isn't strictly true - there's a third possibility we don't
model :

36. Coins Again
• We talk about coins having a head and a tail side and
50/50 chance of either.
• This isn't strictly true - there's a third possibility we don't
model :
• Edge

37. Coins Again
• We talk about coins having a head and a tail side and
50/50 chance of either.
• This isn't strictly true - there's a third possibility we don't
model :
• Edge
• This is Taleb's "Black Swan", highly unlikely but
theoretically possible events that are ignored.

38. Coins Again
• We talk about coins having a head and a tail side and
50/50 chance of either.
• This isn't strictly true - there's a third possibility we don't
model :
• Edge
• This is Taleb's "Black Swan", highly unlikely but
theoretically possible events that are ignored.
• A true Black Swan must also be "high impact"

39. What Am I Driving At?

40. Probabilistic Planning

41. Probabilistic Planning
• PPDDL is a prime example of "doing it wrong"

42. Probabilistic Planning
• PPDDL is a prime example of "doing it wrong"
• Extends PDDL by applying probabilities to
sets of effects. P(X=i) I occurs, P(X=j) J
occurs etc.

43. Probabilistic Planning
• PPDDL is a prime example of "doing it wrong"
• Extends PDDL by applying probabilities to
sets of effects. P(X=i) I occurs, P(X=j) J
occurs etc.
• Is the world really so cut and dry? Or is this
simply shoehorning probabilities into PDDL in
the most obvious way possible.

44. Summary

45. Summary
• Models are typically incomplete.

46. Summary
• Models are typically incomplete.
• Models are frequently wrong.

47. Summary
• Models are typically incomplete.
• Models are frequently wrong.
• Probabilistic models make even more assumptions!

48. Summary
• Models are typically incomplete.
• Models are frequently wrong.
• Probabilistic models make even more assumptions!
• We allow ourselves to be deceived by numbers into
believing we can quantify the unquantifiable.

49. Summary
• Models are typically incomplete.
• Models are frequently wrong.
• Probabilistic models make even more assumptions!
• We allow ourselves to be deceived by numbers into
believing we can quantify the unquantifiable.
• As a result, we get bogged down solving a problem
that isn't necessarily reflective of the real world.

50. So What Can We Do?

51. Introduce Noise

52. Introduce Noise
• Most basic approach is to add noise to
probabilistic models.

53. Introduce Noise
• Most basic approach is to add noise to
probabilistic models.
• If the model has P(x) = 0.2, test generated
plans at say P(x) = 0.2+-0.05

54. Introduce Noise
• Most basic approach is to add noise to
probabilistic models.
• If the model has P(x) = 0.2, test generated
plans at say P(x) = 0.2+-0.05
• Allows for a rudimentary "what happens if
these values are not spot on" check

55. Epsilon-separation of
states

56. Epsilon-separation of
states
• Similar concept to that used in temporal actions.

57. Epsilon-separation of
states
• Similar concept to that used in temporal actions.
• In this case epsilon denotes a marginal probability
of transitioning between any pair of states.

58. Epsilon-separation of
states
• Similar concept to that used in temporal actions.
• In this case epsilon denotes a marginal probability
of transitioning between any pair of states.
• Still not ideal, but at least captures the possibility
of events changing the state in an undetermined
way.

59. Epsilon-separation of
states
• Similar concept to that used in temporal actions.
• In this case epsilon denotes a marginal probability
of transitioning between any pair of states.
• Still not ideal, but at least captures the possibility
of events changing the state in an undetermined
way.
• Somewhat analogous to Van Der Waals forces.

60. State Charts

61. State Charts
• In the FSM family, State Charts frequently
used to represent interruptible processes e.g.
Embedded Systems

62. State Charts
• In the FSM family, State Charts frequently
used to represent interruptible processes e.g.
Embedded Systems
• One process interrupts the other, acts and the
the first can resume from its previous state.

63. State Charts
• In the FSM family, State Charts frequently
used to represent interruptible processes e.g.
Embedded Systems
• One process interrupts the other, acts and the
the first can resume from its previous state.
• Can we use this model to capture the
consequences of unmodelled events?

64. Abstract / Anonymous
Actions

65. Abstract / Anonymous
Actions
• In Prolog _ represents the anonymous variable.

66. Abstract / Anonymous
Actions
• In Prolog _ represents the anonymous variable.
• Nothing analogous to this in PDDL.

67. Abstract / Anonymous
Actions
• In Prolog _ represents the anonymous variable.
• Nothing analogous to this in PDDL.
• Would introducing this give us flexibility to
patch plans when off-model events occur?

68. Abstract / Anonymous
Actions
• In Prolog _ represents the anonymous variable.
• Nothing analogous to this in PDDL.
• Would introducing this give us flexibility to
patch plans when off-model events occur?
• Could this be used for actions (perhaps based
on DTG clusterings) be useful for this?

69. Brainstorm!