The Ludic FallacySPG

11th Feb 2011

• Ludic - Of or pertaining to games of chance

• Fallacy - An argument which seems to be correct but which contains at least one error.

Example

Example• Suppose you flip a coin, what is the chance it comes

up heads?

Example• Suppose you flip a coin, what is the chance it comes

up heads?

• 50/50

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?

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.

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?

Origins

Origins

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

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.

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.

"Gambling With the Wrong Dice"

"Gambling With the Wrong Dice"

• Case Study based on Las Vegas casino.

"Gambling With the Wrong Dice"

• Case Study based on Las Vegas casino.

• Extensive and sophisticated systems and models to account for potential cheating.

"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.

"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.

Blinded By Probability

Blinded By Probability

• Because we see numbers as solvable, we focus on solving them.

Blinded By Probability

• Because we see numbers as solvable, we focus on solving them.

• Lose sight of the broader picture.

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.

Back to Coins

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

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

• 0.5^99 = 1.8x10^-30

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?

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?

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?

Off-model Consequences

Off-model Consequences

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

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.

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.

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"

Coins Again

Coins Again• We talk about coins having a head and a tail side and

50/50 chance of either.

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 :

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

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.

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"

What Am I Driving At?

Probabilistic Planning

Probabilistic Planning

• PPDDL is a prime example of "doing it wrong"

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.

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.

Summary

Summary• Models are typically incomplete.

Summary• Models are typically incomplete.

• Models are frequently wrong.

Summary• Models are typically incomplete.

• Models are frequently wrong.

• Probabilistic models make even more assumptions!

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.

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.

So What Can We Do?

Introduce Noise

Introduce Noise

• Most basic approach is to add noise to probabilistic models.

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

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

Epsilon-separation of states

Epsilon-separation of states

• Similar concept to that used in temporal actions.

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.

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.

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.

State Charts

State Charts

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

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.

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?

Abstract / Anonymous Actions

Abstract / Anonymous Actions

• In Prolog _ represents the anonymous variable.

Abstract / Anonymous Actions

• In Prolog _ represents the anonymous variable.

• Nothing analogous to this in PDDL.

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?

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?

Brainstorm!