Recommended
Recommended
More Related Content
What's hot
What's hot (17)
Similar to Deterministic Oversubscription Action Planning with General Utility Functions - seminar slides 2016
Similar to Deterministic Oversubscription Action Planning with General Utility Functions - seminar slides 2016 (20)
Recently uploaded
Recently uploaded (20)
Deterministic Oversubscription Action Planning with General Utility Functions - seminar slides 2016
- 1. Overview From Private to General Case Empirical Evaluation Future Work The General Case of Deterministic Oversubscription Action Planning Daniel Muller Advisor: Prof. Carmel Domshlak Faculty of Industrial Engineering and Management Technion - Israel Institute of Technology mullerdm@gmail.com December 25, 2016
- 2. Overview From Private to General Case Empirical Evaluation Future Work Classical Planning Problem A problem of finding trajectories in large-scale yet concisely represented state-transition systems INIT Goal Objective Find a sequence of actions achieving goal state at minimal cost
- 3. Overview From Private to General Case Empirical Evaluation Future Work Over-subscription (OSP) Planning Problem A problem of finding trajectories in large-scale yet concisely represented state-transition systems INIT Budget = 5 u( )=1 u( )=2 u( )= -3 OSP Goal U=4 U = 2 U = 7 U = 8 u( )=0 u( )= -1 U = -1 Objective Find a sequence of actions to the most valuable state, within a limited cost budget
- 4. Overview From Private to General Case Empirical Evaluation Future Work Model-oriented problem solving Planner (Solver) Plan (Solution)LanguageProblem Problem Representation In the spirit of Mirkis & Domshlak (2014) the OSP model compactly represented as sextuple: state variables initial state state value function operators operator cost function Task budget OSP Task
- 5. Overview From Private to General Case Empirical Evaluation Future Work Language state variables initial state state value function operators operator cost function Task budget OSP Task Planner (Solver) Plan (Solution)LanguageProblem State Representation: V = {v1, . . . , vn} is a finite set state variables Each complete assignment to V representing a state S = dom(v1)×· · ·×dom(vn) dom(va) = {on(a, b), on(a, c), on(a, d), ontable(a), holding(a)}
- 6. Overview From Private to General Case Empirical Evaluation Future Work Language state variables initial state state value function operators operator cost function Task budget OSP Task Planner (Solver) Plan (Solution)LanguageProblem Initial State Representation: s0 ∈ S va = ontable(a), vb = ontable(b), ve = ontable(e), vf = on(f, b), vd = on(d, f), vc = on(c, e), vca = clear(a), vcd = clear(d), vcc = clear(c), varm = armEmpty
- 7. Overview From Private to General Case Empirical Evaluation Future Work Language state variables initial state state value function operators operator cost function Task budget OSP Task Planner (Solver) Plan (Solution)LanguageProblem Actions Representation: O is a finite set of operators represented by preconditions and effects, which are partial assignments to V pre(o) = {vc = on(a, b), vca = clear(a)} eff(o) = {va = holding(a), vcb = clear(b), vca = not clear(a)}
- 8. Overview From Private to General Case Empirical Evaluation Future Work Language - OSP Extensions state variables initial state state value function operators operator cost function Task budget OSP Task Planner (Solver) Plan (Solution)LanguageProblem INIT Budget = 5 u( )=1 u( )=2 u( )= -3 OSP Goal U=4 U = 2 U = 7 U = 8 u( )=0 u( )= -1 U = -1
- 9. Overview From Private to General Case Empirical Evaluation Future Work Recent Advances in OSP With the advantage of 20 years of research Classical Planning OSP Mirkis and Domshlak, ECAI-14, Best Paper Award approximation techniques based on state-space abstractions approximation technique based on logical landmarks for goal reachability heuristic BFBB
- 10. Overview From Private to General Case Empirical Evaluation Future Work Recent Advances in OSP INIT Budget = 5u( )=1 u( )=2 u( )= -3 OSP Goal U=4U = 2 U = 7 U = 8 u( )=0 u( )= -1 This work Mirkis & Domshlak work Mirkis and Domshlak, ECAI-14, Best Paper Award approximation techniques based on state-space abstractions approximation technique based on logical landmarks for goal reachability heuristic BFBB
- 11. Overview From Private to General Case Empirical Evaluation Future Work Non-Negative Rewards Framework OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1
- 12. Overview From Private to General Case Empirical Evaluation Future Work Non-Negative Rewards Framework Generate an auxiliary classical planning problem s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Auxiliary Classical Planning Problem OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1
- 13. Overview From Private to General Case Empirical Evaluation Future Work Non-Negative Rewards Framework Use off-the-shelf classical planning tool to provide a disjunctive formula of ’what must happen’ Transform to: Classical Planning off-the-shelf Tool s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Auxiliary Classical Planning ProblemOSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1
- 14. Overview From Private to General Case Empirical Evaluation Future Work Non-Negative Rewards Framework Compile the acquired formula into the original OSP task to reduce search space OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Auxiliary Classical Planning Problem Transform to: Classical Planning off-the-shelf Tool Compile the acquired formula into the original OSP task to reduce search space OSP task with Budget = b’ < b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1
- 15. Overview From Private to General Case Empirical Evaluation Future Work Non-Negative Rewards Framework Execute OSP solver on the reduced problem solve reduced task OSP task with Budget = b’ < b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Equivalent Classical Planning Problem Transform to: Classical Planning off-the- shelf Tool Compile the acquired formula into the original OSP task to reduce search space
- 16. Overview From Private to General Case Empirical Evaluation Future Work Non-Negative Rewards Framework Learning based, closed loop of incrementally improving best solution so far, and reducing the search space solve reduced task Best solution so far s6 If learned new valuable state Learned valuable states DB New valuable state OSP task with Budget = b’ < b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Transform to: Classical Planning off-the- shelf Tool Compile the acquired formula into the original OSP task to reduce search space Auxiliary Classical Planning Problem s4 s6 o2 o5 s0 U=1 s6 sj si
- 17. Overview From Private to General Case Empirical Evaluation Future Work Alleviate the Dependence on Value Non-Negativity Our work contribution Best solution so far s6 Learned valuable states DB New valuable state OSP task with Budget = b’ < b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Auxiliary Classical Planning Problem Classical Planning off-the- shelf Tool Formula adjustment to wider range of values Compile the acquired formula into the original OSP task to reduce search space s4 s6 o2 o5 s0 U=1 s6 sj si OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 solve reduced task s3 s4 s6 s7 o1 o2 o4 o5 s0 U=1 Search status snapshot o6 Value independent representation Transform to:
- 18. Overview From Private to General Case Empirical Evaluation Future Work Alleviate the Dependence on Value Non-Negativity Our work contribution Best solution so far s6 Learned valuable states DB New valuable state OSP task with Budget = b’ < b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Auxiliary Classical Planning Problem Transform to: Compile the acquired formula into the original OSP task to reduce search space s4 s6 o2 o5 s0 U=1 s6 sj si OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 solve reduced task s3 s4 s6 s7 o1 o2 o4 o5 s0 U=1 Search status snapshot o6 Value independent representation OSP task with Budget = b’ < b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 solve reduced task Formula adjustment to wider range of values Classical Planning off-the- shelf Tool
- 19. Overview From Private to General Case Empirical Evaluation Future Work Alleviate the Dependence on Value Non-Negativity Generate an auxiliary classical planning problem compatible with the classical planning off-the-shelf tool Transform to: Classical Planning off-the-shelf Tool s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Auxiliary Classical Planning ProblemOSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1
- 20. Overview From Private to General Case Empirical Evaluation Future Work Why Negative Values Effects Need Special Treetment? Classical planing & non negative OSP strive to collect the goals (or valuable facts) which are a partial assignment to state variables
- 21. Overview From Private to General Case Empirical Evaluation Future Work Why Negative Values Effects Need Special Treetment? Generate an auxiliary classical planning problem s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Auxiliary Classical Planning Problem OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1
- 22. Overview From Private to General Case Empirical Evaluation Future Work Why Negative Values Effects Need Special Treetment? General OSP take in account the entire state, avoiding collection of facts carrying negative values
- 23. Overview From Private to General Case Empirical Evaluation Future Work Dependency between facts Consider the following BlocksWorld example BA C BA C BA C Stack(c,b) Stack(c,a) Put down(c) G U=2 U=2 U=3BA C Current State C AClear( ) = 1 Clear( ) = 1 Clear( ) = 1 B
- 24. Overview From Private to General Case Empirical Evaluation Future Work Dependency between facts When the focus is on goal or valuable facts, we have 3 goal states BA C BA C BA C Stack(c,b) Stack(c,a) Put down(c) G U=2 U=2 U=3BA C Current State C AClear( ) = 1 Clear( ) = 1 Clear( ) = 1 B ANot Clear( ) = - 2 Not Clear( ) = - 2 Not Clear( ) = - 2 B C
- 25. Overview From Private to General Case Empirical Evaluation Future Work Dependency between facts When considering a wider set of facts, we stay with one goal state BA C BA C BA C Stack(c,b) Stack(c,a) Put down(c) G U=0 U=0 U=3BA C Current State C AClear( ) = 1 Clear( ) = 1 Clear( ) = 1 B ANot Clear( ) = - 2 Not Clear( ) = - 2 Not Clear( ) = - 2 B C
- 26. Overview From Private to General Case Empirical Evaluation Future Work Ignore Sub Goals Within Negative Context s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 odummy G odummy odummy Auxiliary Classical Planning Problem OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1
- 27. Overview From Private to General Case Empirical Evaluation Future Work Dependency between states When the focus is just on target state, we have a goal Stack(c,a) G BA C Current State C AClear( ) = 10 Clear( ) = 1 Clear( ) = 5 B BA C Current State U = 6
- 28. Overview From Private to General Case Empirical Evaluation Future Work Dependency between states When we consider also action origin state, it seems to be less attractive Stack(c,a) G BA C Current State C AClear( ) = 10 Clear( ) = 1 Clear( ) = 5 B BA C Current State U = 6U = 11
- 29. Overview From Private to General Case Empirical Evaluation Future Work Focus on Actions with Positive Net Values s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 G odummy odummy U(s11 - s8) = -1 U(s6 - s3) = 2 U(s10 – s6) = 1 o13 Auxiliary Classical Planning Problem OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1
- 30. Overview From Private to General Case Empirical Evaluation Future Work Utility Function Defenition for General OSP Definition For an OSP action o, the total outcome utility of o is uout o (o) = v∈V(eff(o)) uv (eff(o)[v])
- 31. Overview From Private to General Case Empirical Evaluation Future Work Utility Function Defenition for General OSP Definition For an OSP action o, the total outcome utility of o is uout o (o) = v∈V(eff(o)) uv (eff(o)[v]) Captures fact dependencies takes in account the entire effect list of an action, rather than just single facts
- 32. Overview From Private to General Case Empirical Evaluation Future Work Utility Function Defenition for General OSP Definition For an OSP action o, the net utility of o is unet o (o) = v∈V(eff(o)) [uv (eff(o)[v]) − uv (pre(o)[v])].
- 33. Overview From Private to General Case Empirical Evaluation Future Work Utility Function Defenition for General OSP Definition For an OSP action o, the net utility of o is unet o (o) = v∈V(eff(o)) [uv (eff(o)[v]) − uv (pre(o)[v])]. Captures state dependencies traces total benefit of an action with respect to its origin state in OSP, goal could be achieved just through an action with total positive net value
- 34. Overview From Private to General Case Empirical Evaluation Future Work Different Action Utilities Example B A CB A C B A C B A C B A C -8 -6 -4 -2 0 2 4 6 8 10 12 unstack(c,a) putdown(c) pickup(b) stack (b,c) outcome utility net utility state utility state facts utility clear(a) 2 clear(b) 0 clear(c) -5 not clear(a) 3 not clear(b) -4 not clear(c) 3 on table(a) 1 on table(b) -4 on table(c) 6 on (c,a) 5 on (b,c) -4 handempty 0 not handempty -2
- 35. Overview From Private to General Case Empirical Evaluation Future Work Different Perspective - Actions Become The Goal Lemma For each π with u(s π ) > 0, there exists a prefix π such that: 1 u(s π ) ≤ u(s π ), and 2 for the last operator olast along π , we have unet o (olast) > 0.
- 36. Overview From Private to General Case Empirical Evaluation Future Work Different Perspective - Actions Become The Goal Lemma For each π with u(s π ) > 0, there exists a prefix π such that: 1 u(s π ) ≤ u(s π ), and 2 for the last operator olast along π , we have unet o (olast) > 0. The objective with the net value of an action definition and the lemma in hand, actions become the goal
- 37. Overview From Private to General Case Empirical Evaluation Future Work Different Perspective - Actions Become The Goal Generate an auxiliary classical planning problem s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 G odummy odummy U(s11 - s8) = -1 U(s6 - s3) = 2 U(s10 – s6) = 1 o13 Auxiliary Classical Planning Problem OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1
- 38. Overview From Private to General Case Empirical Evaluation Future Work Different Perspective - Actions Become The Goal New operator example goal defined to be vg := 1 put-down(c): pre:{vc := holding (c), vcc := not clear (c)} eff:{vc := ontable(c), vcc := clear (c), vg := 1}
- 39. Overview From Private to General Case Empirical Evaluation Future Work Implications on Received Formula Tighter and more accurate formula of actions that must happen Transform to: Classical Planning off-the-shelf Tool OSP task with Budget = b s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 o13 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 U=1 U =2 U=3 U=1 s3 s4 s6 s7 o8 s9 o3 o6 o1 o2 o4 o5 s5 s11 s12 s10 o9 o10 o11 o12 o14 o7 s8 s0 G odummy odummy U(s11 - s8) = -1 U(s6 - s3) = 2 U(s10 – s6) = 1 o13 Equivalent Classical Planning Problem
- 40. Overview From Private to General Case Empirical Evaluation Future Work Implications on Search Space The formula when the focus is on facts with positive utility (a1 ∨ a2) ∧ (a3 ∨ a4 ∨ a5 ∨ a6) ∧ (a8 ∨ a9 ∨ a10) ∧ (a12 ∨ a14 ∨ a15) s1 s2 s5 s6 o8 s10 o4 o4 o1 o2 o6 o5 o12 s4 s14 s15 s11o10 o13s9 s0 s18o16 o10 o13 s16 s7 s12o9 s17 s3 s13o15s8o9 o3 o3 o14 o15 o14 OSP task with Budget = 4 o11
- 41. Overview From Private to General Case Empirical Evaluation Future Work Implications on Search Space Actions that we aimed to reduced thier cost (a1 ∨ a2) ∧ (a3 ∨ a4 ∨ a5 ∨ a6) ∧ (a8 ∨ a9 ∨ a10) ∧ (a12 ∨ a14 ∨ a15) s1 s2 s5 s6 o8 s10 o4 o4 o1 o2 o6 o5 o12 s4 s14 s15 s11o10 o13s9 s0 s18o16 o10 o13 s16 s7 s12o9 s17 s3 s13o15s8o9 o3 o3 o14 o15 o14 OSP task with Budget = 4 Reduced Budget = 0 o11
- 42. Overview From Private to General Case Empirical Evaluation Future Work Implications on Search Space Secondary effect: more actions with reduced cost (a1 ∨ a2) ∧ (a3 ∨ a4 ∨ a5 ∨ a6) ∧ (a8 ∨ a9 ∨ a10) ∧ (a12 ∨ a14 ∨ a15) s1 s2 s5 s6 o8 s10 o4 o4 o1 o2 o6 o5 o12 s4 s14 s15 s11o10 o13s9 s0 s18o16 o10 o13 s16 s7 s12o9 s17 s3 s13o15s8o9 o3 o3 o14 o15 o14 OSP task with Budget = 4 Reduced Budget = 0 o11
- 43. Overview From Private to General Case Empirical Evaluation Future Work Implications on Search Space Reduced search space (a1 ∨ a2) ∧ (a3 ∨ a4 ∨ a5 ∨ a6) ∧ (a8 ∨ a9 ∨ a10) ∧ (a12 ∨ a14 ∨ a15) s1 s2 s5 s6 o8 s10 o4 o4 o1 o2 o6 o5 o12 s4 s14 s15 s11o10 o13s9 s0 s18o16 o10 o13 s16 s7 s12o9 s17 s3 s13o15s8o9 o3 o3 o14 o15 o14 OSP task with Budget = 4 Reduced Budget = 0 o11
- 44. Overview From Private to General Case Empirical Evaluation Future Work Implications on Search Space Ignore false goals by taking in account net action value (a1 ∨ a2) ∧ (a3 ∨ a4 ∨ a5 ∨ a6) ∧ (a8 ∨ a9 ∨ a10) ∧ (a12 ∨ a14 ∨ a15) (a1 ∨ a2) ∧ (a5 ∨ a6) ∧ a8 ∧ a13 s1 s2 s5 s6 o8 s10 o4 o4 o1 o2 o6 o5 o12 s4 s14 s15 s11o10 o13s9 s0 s18o16 o10 o13 s16 s7 s12o9 s17 s3 s13o15s8o9 o3 o3 o14 o15 o14 OSP task with Budget = 4 Reduced Budget = 0 o11
- 45. Overview From Private to General Case Empirical Evaluation Future Work Implications on Search Space Tight and accuret formula of actions that must happen (a1 ∨ a2) ∧ (a3 ∨ a4 ∨ a5 ∨ a6) ∧ (a8 ∨ a9 ∨ a10 ∨ a11) ∧ (a14 ∨ a15) (a1 ∨ a2) ∧ (a5 ∨ a6) ∧ a8 ∧ a13 s1 s2 s5 s6 o8 s10 o4 o4 o1 o2 o6 o5 o12 s4 s14 s15 s11o10 o13s9 s0 s18o16 o10 o13 s16 s7 s12o9 s17 s3 s13o15s8o9 o3 o3 o14 o15 o14 OSP task with Budget = 4 Reduced Budget = 0
- 46. Overview From Private to General Case Empirical Evaluation Future Work Implications on Search Space Reduce discounted actions = reduce more search space (a1 ∨ a2) ∧ (a3 ∨ a4 ∨ a5 ∨ a6) ∧ (a8 ∨ a9 ∨ a10 ∨ a11) ∧ (a14 ∨ a15) (a1 ∨ a2) ∧ (a5 ∨ a6) ∧ a8 ∧ a13 s1 s2 s5 s6 o8 s10 o4 o4 o1 o2 o6 o5 o12 s4 s14 s15 s11o10 o13s9 s0 s18o16 o10 o13 s16 s7 s12o9 s17 s3 s13o15s8o9 o3 o3 o14 o15 o14 OSP task with Budget = 4 Reduced Budget = 0
- 47. Overview From Private to General Case Empirical Evaluation Future Work Action-Oriented vs. Fact-Oriented Goals Expanded Nodes - Setting u(dom(v)) ∈ {{0}, {1, 2}} Figure: Empirical results in terms of expanded nodes with different budget restrictions, where full budget is the minimal cost of achieving maximal utility in a task
- 48. Overview From Private to General Case Empirical Evaluation Future Work Action-Oriented vs. Fact-Oriented Goals Expanded Nodes - Setting u(dom(v)) ∈ {{0}, {1, 2}} Figure: Empirical results in terms of expanded nodes with different budget restrictions, where full budget is the minimal cost of achieving maximal utility in a task
- 49. Overview From Private to General Case Empirical Evaluation Future Work Action-Oriented vs. Fact-Oriented Goals Expanded Nodes - Setting u(dom(v)) ∈ {{0}, {0, 1, 2}} Figure: Empirical results in terms of expanded nodes with different budget restrictions, where full budget is the minimal cost of achieving maximal utility in a task
- 50. Overview From Private to General Case Empirical Evaluation Future Work Action-Oriented vs. Fact-Oriented Goals Expanded Nodes - Setting u(dom(v)) ∈ {{−1, 0}, {0, 1}} Figure: Empirical results in terms of expanded nodes with different budget restrictions, where full budget is the minimal cost of achieving maximal utility in a task
- 51. Overview From Private to General Case Empirical Evaluation Future Work Budget Reduction Method Mesure of Quality Domain Name: OP Fact blocks 1.79 7.25 depot 30.48 7.00 driverlog 9.88 16.00 grid 90.54 70.60 gripper 4.33 48.00 logistics00 1.07 10.20 logistics98 3.54 2.43 miconic 7.44 14.55 pipesworld-notankage 1571.97 1745.29 pipesworld-tankage 2465.88 3796.00 rovers 10.09 11.85 tpp 2.54 6.32 trucks 62.29 133.00 zenotravel 27.36 50.88 airport 188.67 1028.79 freecell 142.47 1385.30 mystery 246.70 261.59 satellite 9.12 12.00 OVERALL 187.50 344.90 DISCOUNTED ACTIONS PER BUDGET UNIT
- 52. Overview From Private to General Case Empirical Evaluation Future Work Empirical Evaluation - Conclusions Action Oriented Approach reduction in the number of discounted actions along with an increase in their diversity effective in both, general utility functions and non-negative utility functions approach effectiveness grows with the increase in subscribed utilities and budget restrictions all in all, lower budget, restricted set of preferred actions, reduced search space
- 53. Overview From Private to General Case Empirical Evaluation Future Work Future Work reduce search space with tighter formula of actions that must happen capture more dependencies focus on group of action reaching the same state focus on sequence of actions (partial order plans) recognition of mutually exclusive actions, by preconditions analysis L (blind) = O L(focus on facts) L(focus on actions) L(tighter) We are here Future objective
- 54. Overview From Private to General Case Empirical Evaluation Future Work References Mirkis, V. & Domshlak, C. (2014) Landmarks in Oversubscription Planning In Proceedings of the 23rd European Conference on Artificial Intelligence (ECAI), pp. 633–638.
- 55. Overview From Private to General Case Empirical Evaluation Future Work Thank You!
- 56. Extensions Handling Actions with Partial Precondition List The problem false recognition of actions as goals redundant cost reduced operators Solution operators split compilation problem structure analysis for inference of mutually exclusive facts optimization steps