[PPT] - Novel Is Not Always Better: On the Relation between Novelty and PowerPoint Presentation

SLIDE 1

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Novel Is Not Always Better: On the Relation between Novelty and Dominance Pruning

Joschka Groß, ´ Alvaro Torralba, Maximilian Fickert

SLIDE 2

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Classical Planning

Definition. A planning task is a 4-tuple Π = (V, A, I, G) where:
V is a set of state variables, each v ∈ V with a finite domain Dv.
A is a set of actions; each a ∈ A is a triple (prea, eff a, ca), of

precondition and effect (partial assignments), and the action’s cost ca ∈ R+

0 .

Initial state I (complete assignment), goal G (partial assignment).

→ Solution (“Plan”): Action sequence mapping I into s s.t. s | = G.

Groß, Torralba, Fickert Novel Is Not Always Better 2/18

SLIDE 3

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Classical Planning

Definition. A planning task is a 4-tuple Π = (V, A, I, G) where:
V is a set of state variables, each v ∈ V with a finite domain Dv.
A is a set of actions; each a ∈ A is a triple (prea, eff a, ca), of

precondition and effect (partial assignments), and the action’s cost ca ∈ R+

0 .

Initial state I (complete assignment), goal G (partial assignment).

→ Solution (“Plan”): Action sequence mapping I into s s.t. s | = G. Running Example: A B 100

V = {t, p1, p2, f}

with Dt = {A, B} and Dpi = {t, A, B}, Df = {100, 99, 98, . . . , 0}.

A = {load(pi, x), unload(pi, x), drive(x, x′)}

Groß, Torralba, Fickert Novel Is Not Always Better 2/18

SLIDE 4

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

What this is about?

Novelty (Lipovetzky and Geffner, 2012) (Lipovetzky and Geffner, 2017) (Katz, Lipovetzky, Moshkovich and Tuisov 2017) (Fickert 2018) A (pruning) technique which has greatly improved the state of the art in satisficing planning Dominance (Torralba and Hoffmann, 2015), (Torralba, 2017), (Torralba, 2018): A safe pruning technique for cost-optimal planning

Groß, Torralba, Fickert Novel Is Not Always Better 3/18

SLIDE 5

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Novelty

The novelty of s N(s) is defined to be the size of the smallest fact set it produces for the first time.

Groß, Torralba, Fickert Novel Is Not Always Better 4/18

SLIDE 6

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Novelty

The novelty of s N(s) is defined to be the size of the smallest fact set it produces for the first time. IW(K): Breadth first search, pruning all s with N(s) > k

Polynomial time
No guidance towards the goal
Good for exploration/achieving single goal facts

Groß, Torralba, Fickert Novel Is Not Always Better 4/18

SLIDE 7

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Novelty

The novelty of s N(s) is defined to be the size of the smallest fact set it produces for the first time. IW(K): Breadth first search, pruning all s with N(s) > k

Polynomial time
No guidance towards the goal
Good for exploration/achieving single goal facts

Novelty Heuristics:

Combine the definition of novelty with heuristics
State of the art in satisficing planning

Groß, Torralba, Fickert Novel Is Not Always Better 4/18

SLIDE 8

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Novelty

The novelty of s N(s) is defined to be the size of the smallest fact set it produces for the first time. IW(K): Breadth first search, pruning all s with N(s) > k

Polynomial time
No guidance towards the goal
Good for exploration/achieving single goal facts

Novelty Heuristics:

Combine the definition of novelty with heuristics
State of the art in satisficing planning

But, why is novelty so good?

Groß, Torralba, Fickert Novel Is Not Always Better 4/18

SLIDE 9

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B A B T 100 99 98 97 x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 10

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B A B T 100 99 98 97 x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 11

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B A B T 100 99 98 97 x x x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 12

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B A B T 100 99 98 97 x x x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 13

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B A B T 100 99 98 97 x x x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 14

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B A B T 100 99 98 97 x x x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 15

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B A B T 100 99 98 97 x x x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 16

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A)

A B A B T 100 99 98 97 x x x x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 17

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A)

A B

98

load(p1)

A B A B T 100 99 98 97 x x x x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 18

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A)

A B

98

load(p1)

A B A B T 100 99 98 97 x x x x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 19

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A)

A B

98

load(p1)

A B

97

drive(A, B)

A B A B T 100 99 98 97 x x x x x x x x

Groß, Torralba, Fickert Novel Is Not Always Better 5/18

SLIDE 20

Prune s if there exists t s.t. g(t) ≤ g(s) and s t A B

100

Groß, Torralba, Fickert Novel Is Not Always Better 7/18

SLIDE 26

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Dominance Pruning

Prune s if there exists t s.t. g(t) ≤ g(s) and s t A B

100

A B

100

load(p1) Groß, Torralba, Fickert Novel Is Not Always Better 7/18

Prune s if there exists t s.t. g(t) ≤ g(s) and s t A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B) Groß, Torralba, Fickert Novel Is Not Always Better 7/18

SLIDE 31

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Dominance Pruning

Prune s if there exists t s.t. g(t) ≤ g(s) and s t A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A) Groß, Torralba, Fickert Novel Is Not Always Better 7/18

SLIDE 32

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Dominance Pruning

Prune s if there exists t s.t. g(t) ≤ g(s) and s t A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A) Groß, Torralba, Fickert Novel Is Not Always Better 7/18

SLIDE 33

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Dominance Pruning

Prune s if there exists t s.t. g(t) ≤ g(s) and s t A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A)

A B

99

drive(A, B) Groß, Torralba, Fickert Novel Is Not Always Better 7/18

SLIDE 34

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Dominance Pruning

Prune s if there exists t s.t. g(t) ≤ g(s) and s t A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A)

A B

99

drive(A, B)

→Dominance pruning preserves at least an optimal solution.

Groß, Torralba, Fickert Novel Is Not Always Better 7/18

SLIDE 35

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

So, What Novelty and Dominance Have In Common?

Groß, Torralba, Fickert Novel Is Not Always Better 8/18

SLIDE 36

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

So, What Novelty and Dominance Have In Common?

Both compare new states s against all previously seen states T

Groß, Torralba, Fickert Novel Is Not Always Better 8/18

SLIDE 37

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

So, What Novelty and Dominance Have In Common?

Both compare new states s against all previously seen states T Safe dominance pruning ∃t ∈ T ∀v ∈ V s[v] t[v]

Groß, Torralba, Fickert Novel Is Not Always Better 8/18

SLIDE 38

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

So, What Novelty and Dominance Have In Common?

Both compare new states s against all previously seen states T Safe dominance pruning ∃t ∈ T ∀v ∈ V s[v] t[v] Novelty IW(1) pruning ∀v ∈ V ∃t ∈ T s[v] = t[v]

Groß, Torralba, Fickert Novel Is Not Always Better 8/18

SLIDE 39

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

So, What Novelty and Dominance Have In Common?

Both compare new states s against all previously seen states T Safe dominance pruning ∃t ∈ T ∀v ∈ V s[v] t[v] Novelty IW(1) pruning ∀v ∈ V ∃t ∈ T s[v] = t[v] →Novelty can be interpreted as (unsafe) dominance ∃t ∈ T h∗(t) ≤ h∗(s)

Groß, Torralba, Fickert Novel Is Not Always Better 8/18

SLIDE 40

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

So, What Novelty and Dominance Have In Common?

Both compare new states s against all previously seen states T Safe dominance pruning ∃t ∈ T ∀v ∈ V s[v] t[v] Novelty IW(1) pruning ∀v ∈ V ∃t ∈ T s[v] = t[v] →Novelty can be interpreted as (unsafe) dominance ∃t ∈ T h∗(t) ≤ h∗(s) Let R = {1, ..., k} be a set of relations on P. Let Q be a set of subsets of V. ∀Q ∈ Q : ∃t ∈ T : ∀v ∈ Q : s[v] t[v]

Groß, Torralba, Fickert Novel Is Not Always Better 8/18

SLIDE 41

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Unsafe Dominance Pruning

Q R

=

IW(1) IW(2) Duplicate

{V1} . . . {Vn} {V1, V2} . . . {Vi, Vj} {V1, . . . , Vn}

Groß, Torralba, Fickert Novel Is Not Always Better 9/18

SLIDE 42

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Unsafe Dominance Pruning

Q R

=

IW(1)

IW(2) Duplicate Safe Dominance

{V1} . . . {Vn} {V1, V2} . . . {Vi, Vj} {V1, . . . , Vn}

Groß, Torralba, Fickert Novel Is Not Always Better 9/18

SLIDE 43

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Unsafe Dominance Pruning

Q R

=

IW(1)

IW(2) Duplicate Safe Dominance IW(1) IW(2)

{V1} . . . {Vn} {V1, V2} . . . {Vi, Vj} {V1, . . . , Vn}

Groß, Torralba, Fickert Novel Is Not Always Better 9/18

SLIDE 44

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

Groß, Torralba, Fickert Novel Is Not Always Better 10/18

SLIDE 45

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1) Groß, Torralba, Fickert Novel Is Not Always Better 10/18

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B) Groß, Torralba, Fickert Novel Is Not Always Better 10/18

SLIDE 50

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B) Groß, Torralba, Fickert Novel Is Not Always Better 10/18

SLIDE 51

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A) Groß, Torralba, Fickert Novel Is Not Always Better 10/18

SLIDE 52

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Example IW(1)

A B

100

A B

100

load(p1)

A B

99

drive(A, B)

A B

100

unload(p1)

A B

99

drive(A, B)

A B

98

drive(B, A) Groß, Torralba, Fickert Novel Is Not Always Better 10/18

SLIDE 53

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Our Hypothesis

Hypothesis: IW(k) is not more unsafe than IW(k)

Groß, Torralba, Fickert Novel Is Not Always Better 11/18

SLIDE 54

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Our Hypothesis

Hypothesis: IW(k) is not more unsafe than IW(k) In theory not much can be said:

IW(k) is guaranteed to solve any task with width k or less

and using we lose this guarantee AX BY CY CX DX GX

Groß, Torralba, Fickert Novel Is Not Always Better 11/18

SLIDE 55

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Our Hypothesis

Hypothesis: IW(k) is not more unsafe than IW(k) In theory not much can be said:

IW(k) is guaranteed to solve any task with width k or less

and using we lose this guarantee AX BY CY CX DX GX

However, there are also tasks that are solved when using

but not when using =

Groß, Torralba, Fickert Novel Is Not Always Better 11/18

SLIDE 56

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Effective Width Analysis

100 101 102 103 104 105 106 107 100 101 102 103 104 105 106 107 IW(2) IW(2) Solved by: None Both Only IW(2) Only IW(2) 100 101 102 103 104 105 106 107 100 101 102 103 104 105 106 107 IW(2) IW(2)

IPC Instances 1-goal instances

Groß, Torralba, Fickert Novel Is Not Always Better 12/18

SLIDE 57

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Effective Width Analysis

100 101 102 103 104 105 106 107 100 101 102 103 104 105 106 107 IW(2) IW(2) Solved by: None Both Only IW(2) Only IW(2) 100 101 102 103 104 105 106 107 100 101 102 103 104 105 106 107 IW(2) IW(2)

IPC Instances 1-goal instances →In practice, replacing = by increases pruning without making it more unsafe!

Groß, Torralba, Fickert Novel Is Not Always Better 12/18

SLIDE 58

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Novelty Heuristics

A state is novel if it has a fact that no other state with the same

r lower heuristic value has

Groß, Torralba, Fickert Novel Is Not Always Better 13/18

SLIDE 59

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Novelty Heuristics

A state is novel if it has a fact that no other state with the same

r lower heuristic value has

Q R

=

IW(1)

IW(2) Duplicate Safe Dominance IW(1) IW(2)

{V1} . . . {Vn} {V1, V2} . . . {Vi, Vj} {V1, . . . , Vn}

Groß, Torralba, Fickert Novel Is Not Always Better 13/18

SLIDE 60

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Novelty Heuristics

A state is novel if it has a fact that no other state with the same

r lower heuristic value has

Q R

= =,

IW(1)

IW(2) Duplicate Safe Dominance IW(1) IW(2)

Nov. Heur.

{V1} . . . {Vn} {V1, V2} . . . {Vi, Vj} {V1, h} . . . {Vn, h} {V1, . . . , Vn}

Groß, Torralba, Fickert Novel Is Not Always Better 13/18

SLIDE 61

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Quantify Novelty

How non-novel is a state?

Groß, Torralba, Fickert Novel Is Not Always Better 14/18

SLIDE 62

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Quantify Novelty

How non-novel is a state? Previous work: compare to states with strictly smaller h (instead of ≤)

Groß, Torralba, Fickert Novel Is Not Always Better 14/18

SLIDE 63

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Quantify Novelty

How non-novel is a state? Previous work: compare to states with strictly smaller h (instead of ≤) This work: for each fact, count the number of states that have been seen with the same or better h value →Estimate the probability that the state is really dominated

Groß, Torralba, Fickert Novel Is Not Always Better 14/18

SLIDE 64

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Overview of Results:

We analyze three variants:

1. Changing R: = vs.
2. Changing Q
3. Changing quantification of non-novel states

Groß, Torralba, Fickert Novel Is Not Always Better 15/18

SLIDE 65

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Overview of Results:

We analyze three variants:

1. Changing R: = vs.
2. Changing Q
3. Changing quantification of non-novel states

Changing R: = vs.

Decreases the number of novel states
Expansions similar to baseline
Performance decreases due to overhead

Groß, Torralba, Fickert Novel Is Not Always Better 15/18

SLIDE 66

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Changing Q

Q1 Q2 Qcg

1,2

Qpre

1,2

Qcg Qpre Total Q1 – 14 8 9 8 9 1564 Q2 17 – 6 6 8 6 1551 Qcg

1,2

20 15 – 7 10 10 1609 Qpre

1,2

17 16 8 – 9 7 1618 Qcg 20 20 15 13 – 6 1630 Qpre 17 17 13 15 8 – 1634 →Best configuration in practice: choose subsets of variables that appear together in action preconditions

Groß, Torralba, Fickert Novel Is Not Always Better 16/18

SLIDE 67

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Non-novel priority: N− vs. N−

100

101 102 103 104 105 106 107 108 100 101 102 103 104 105 106 107 108 108 108 hQB(FF, Q1, =, N −) hQB(FF, Q1, =, N −

)

0.5 1

% Novel expansions (Q1)

Our non-novel priority is superior to the previous one!
But, not good synergy with changing Q

Groß, Torralba, Fickert Novel Is Not Always Better 17/18

SLIDE 68

Classical Planning Novelty Dominance Relation Novelty Heuristics Conclusions

Conclusions

Dominance: Compare states by looking at their outgoing plans Novelty: Compare states by looking at their facts →Our new framework on unsafe dominance generalizes both Can we use this to devise better variants of novelty?

Q: Use dominance relations in novelty
R: Look at different subsets of variables
Non-novel priority

→Inspire new ideas to further improve novelty methods!

Groß, Torralba, Fickert Novel Is Not Always Better 18/18