From Qualitative to Quantitative Dominance Pruning for Optimal - PowerPoint PPT Presentation

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions From Qualitative to Quantitative Dominance Pruning for Optimal Planning ´ Alvaro Torralba Saarland University HSDIP Workshop June 20, 2017 ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 1/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Outline Qualitative Dominance 1 From Qualitative to Quantitative Dominance 2 Finding Dominance 3 Action Selection Pruning 4 5 Experiments Conclusions 6 ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 2/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Dominance s t A B A B Compare states: Which one is better? ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 3/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Dominance s t A B A B t dominates s : s � t Compare states: Which one is better? : A � T � B ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 3/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Dominance s t A B A B t dominates s : s � t Compare states: Which one is better? : A � T � B s t ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 3/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Dominance s t A B A B t dominates s : s � t Compare states: Which one is better? : A � T � B s t t does not dominate s : s �� t ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 3/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Qualitative Dominance Does t dominate s ? → Yes/No answer ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 4/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Qualitative Dominance Does t dominate s ? → Yes/No answer Dominance Relation If s � t , then h ∗ ( s ) ≥ h ∗ ( t ) : t is at least as good as s ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 4/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Qualitative Dominance Does t dominate s ? → Yes/No answer Dominance Relation If s � t , then h ∗ ( s ) ≥ h ∗ ( t ) : t is at least as good as s s 1 � s 3 s 5 � I Prune n s if there exists n t s.t. s 1 s 5 g ( n t ) ≤ g ( n s ) and s � t s 2 s 6 Open or closed list s 3 s 7 I s 4 ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 4/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Qualitative Dominance Does t dominate s ? → Yes/No answer Dominance Relation If s � t , then h ∗ ( s ) ≥ h ∗ ( t ) : t is at least as good as s s 1 � s 3 s 5 � I Prune n s if there exists n t s.t. s 1 s 5 g ( n t ) ≤ g ( n s ) and s � t s 2 s 6 Open or closed list Closed list s 3 s 7 I Parent → Never unload a package in any location other s 4 than its destination! ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 4/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Outline Qualitative Dominance 1 From Qualitative to Quantitative Dominance 2 Finding Dominance 3 Action Selection Pruning 4 5 Experiments Conclusions 6 ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 5/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Quantitative Dominance By how much t dominates s ? → function D : S × S → R ∪ {−∞} ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 6/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Quantitative Dominance By how much t dominates s ? → function D : S × S → R ∪ {−∞} Dominance Function: D ( s , t ) ≤ h ∗ ( s ) − h ∗ ( t ) ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 6/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Quantitative Dominance By how much t dominates s ? → function D : S × S → R ∪ {−∞} Dominance Function: D ( s , t ) ≤ h ∗ ( s ) − h ∗ ( t )  t is strictly closer to the goal than s (by at least C ) C     0 t is at least as close as s  D ( s , t ) = − C t is at most C units of cost farther than s     −∞ we know nothing  ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 6/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Quantitative Dominance By how much t dominates s ? → function D : S × S → R ∪ {−∞} Dominance Function: D ( s , t ) ≤ h ∗ ( s ) − h ∗ ( t )  t is strictly closer to the goal than s (by at least C ) C     0 t is at least as close as s  D ( s , t ) = − C t is at most C units of cost farther than s     −∞ we know nothing  → Qualitative dominance is a special case if we use only 0 or −∞ ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 6/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Leveraging Quantitative Dominance Prune n s if there exists n t s.t. Qualitative g ( n t ) ≤ g ( n s ) and s � t Quantitative s 1 � s 3 s 5 � I s 1 s 5 s 2 s 6 s 3 s 7 I s 4 ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 7/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Leveraging Quantitative Dominance Prune n s if there exists n t s.t. Qualitative g ( n t ) ≤ g ( n s ) and s � t Quantitative D ( s , t ) + g ( n s ) − g ( n t ) ≥ 0 if D ( s , t ) ≥ 0 s 1 � s 3 s 5 � I s 1 s 5 s 2 s 6 s 3 s 7 I s 4 D ( s 4 , s 6 ) = 1 ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 7/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Leveraging Quantitative Dominance Prune n s if there exists n t s.t. Qualitative g ( n t ) ≤ g ( n s ) and s � t Quantitative D ( s , t ) + g ( n s ) − g ( n t ) ≥ 0 if D ( s , t ) ≥ 0 D ( s , t ) + g ( n s ) − g ( n t ) > 0 if D ( s , t ) < 0 s 1 � s 3 s 5 � I s 1 s 5 s 2 s 6 s 3 s 7 I s 4 D ( s 7 , I ) = − 1 D ( s 4 , s 6 ) = 1 ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 7/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Outline Qualitative Dominance 1 From Qualitative to Quantitative Dominance 2 Finding Dominance 3 Action Selection Pruning 4 5 Experiments Conclusions 6 ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 8/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Compositional Approach Consider a partition of the problem: Θ 1 , . . . , Θ k {� 1 , . . . , � k } is a label-dominance simulation if, whenever s � i t : Goal-respecting: s ∈ S G i implies that t ∈ S G i → s ′ in Θ i , there exists t l ′ l → t ′ in Θ i s.t.: For all s − − s ′ � i t ′ , 1 c ( l ′ ) ≤ c ( l ) , and 2 l ′ dominates l elsewhere 3 ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 9/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Compositional Approach Consider a partition of the problem: Θ 1 , . . . , Θ k {� 1 , . . . , � k } is a label-dominance simulation if, whenever s � i t : Goal-respecting: s ∈ S G i implies that t ∈ S G i → s ′ in Θ i , there exists t l ′ l → t ′ in Θ i s.t.: For all s − − s ′ � i t ′ , 1 c ( l ′ ) ≤ c ( l ) , and 2 l ′ dominates l elsewhere 3 : A � T � B : Identity ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 9/19

Qualitative Quantitative Finding Dominance Action Selection Pruning Experiments Conclusions Compositional Approach Consider a partition of the problem: Θ 1 , . . . , Θ k {� 1 , . . . , � k } is a label-dominance simulation if, whenever s � i t : Goal-respecting: s ∈ S G i implies that t ∈ S G i → s ′ in Θ i , there exists t l ′ l → t ′ in Θ i s.t.: For all s − − s ′ � i t ′ , 1 c ( l ′ ) ≤ c ( l ) , and 2 l ′ dominates l elsewhere 3 : A � T � B : Identity → s � t iff ∀ i ∈ [ 1 , k ] s i � i t i ´ Alvaro Torralba From Qualitative to Quantitative Dominance Pruning for Optimal Planning 9/19