1. Distributed Planning for Large Teams Prasanna Velagapudi Thesis Committee: Katia Sycara (co-chair) Paul Scerri (co-chair) J. Andrew Bagnell Edmund H. Durfee Distributed Planning for Large Teams

2. Outline Motivation Background Approach – SI-Dec-POMDP – DIMS Preliminary Work – DPP – D-TREMOR Proposed Work Conclusion Distributed Planning for Large Teams2

3. Motivation 100s to 1000s of robots, agents, people Complex, collaborative tasks Dynamic, uncertain environment Offline planning Distributed Planning for Large Teams3

4. Motivation Scaling planning to large teams is hard – Need to plan (with uncertainty) for each agent in team – Agents must consider the actions of a growing number of teammates – Full, joint problem has NEXP complexity [Bernstein 2002] Optimality is going to be infeasible Find and exploit structure in the problem Make good plans in reasonable amount of time 4Distributed Planning for Large Teams

5. Motivation Exploit three characteristics of these domains 1. Explicit Interactions Specific combinations of states and actions where effects depend on more than one agent 2. Sparsity of Interactions Many potential interactions could occur between agents Only a few will occur in any given solution 3. Distributed Computation Each agent has access to local computation A centralized algorithm has access to 1 unit of computation A distributed algorithm has access to N units of computation Distributed Planning for Large Teams5

6. Example: Interactions Distributed Planning for Large Teams6 Rescue robot Cleaner robot Debris Victim

7. Example: Sparsity Distributed Planning for Large Teams7

8. Related Work Distributed Planning for Large Teams8 Scalability Generality

9. Related Work Distributed Planning for Large Teams9 Scalability Generality Structured Dec-(PO)MDP planners – JESP [Nair 2003] – TD-Dec-POMDP [Witwicki 2010] – EDI-CR [Mostafa 2009] – SPIDER [Marecki 2009] Restrict generality slightly to get scalability High optimality

10. Related Work Distributed Planning for Large Teams10 Scalability Generality Heuristic Dec-(PO)MDP planners – TREMOR [Varakantham 2009] – OC-Dec-MDP [Beynier 2005] Sacrifice optimality for scalability High generality

11. Related Work Distributed Planning for Large Teams11 Scalability Generality Structured multiagent path planners – DPC [Bhattacharya 2010] – Optimal Decoupling [Van den Berg 2009] Sacrifice generality further to get scalability High optimality

12. Related Work Distributed Planning for Large Teams12 Scalability Generality Heuristic multiagent path planners – Dynamic Networks [Clark 2003] – Prioritized Planning [Van den Berg 2005] Sacrifice optimality to get scalability

13. Scalability Generality Related Work Distributed Planning for Large Teams13 Our approach: Fix high scalability and generality Explore what level of optimality is possible

14. Distributed, Iterative Planning Inspiration: – TREMOR [Varankantham 2009] – JESP [Nair 2003] Reduce the full joint problem into a set of smaller, independent sub-problems Solve independent sub- problems with local algorithm Modify sub-problems to push locally optimal solutions towards high-quality joint solution Distributed Planning for Large Teams14

15. Thesis Statement Agents in a large team with known sparse interactions can find computationally efficient high-quality solutions to planning problems through an iterative process of estimating the actions of teammates, locally planning based on these estimates, and refining their estimates by exchanging coordination messages. Distributed Planning for Large Teams15

16. Outline Motivation Background Approach – SI-Dec-POMDP – DIMS Preliminary Work – DPP – D-TREMOR Proposed Work Conclusion Distributed Planning for Large Teams16 Problem Formulation Proposed Algorithm

17. Problem Formulation POMDP Dec-POMDP Sparse-Interaction Dec-POMDP Distributed Planning for Large Teams17

18. Review: POMDP Distributed Planning for Large Teams18 : Set of States : Set of Actions : Set of Observations : Transition function : Reward function : Observation function

19. Review: Dec-POMDP Distributed Planning for Large Teams19 : Joint Transition : Joint Reward : Joint Observation

20. Dec-POMDP  SI-Dec-POMDP Distributed Planning for Large Teams20

21. Sparse Interaction Dec-POMDP Distributed Planning for Large Teams21 : : :

22. Proposed Approach: DIMS Distributed Iterative Model Shaping Reduce the full joint problem into a set of smaller, independent sub-problems (one for each agent) Solve independent sub-problems with existing state-of-the-art algorithms Modify sub-problems such that local optimum solution approaches high- quality joint solution Distributed Planning for Large Teams22 Task Allocation Local Planning Interaction Exchange Model Shaping

23. Proposed Approach: DIMS Distributed Iterative Model Shaping Distributed Planning for Large Teams23 Task Allocation Local Planning Interaction Exchange Model Shaping Assign tasks to agents Reduce search space considered by agent Define local sub-problem for each robot

24. Proposed Approach: DIMS Distributed Iterative Model Shaping Distributed Planning for Large Teams24 Task Allocation Local Planning Interaction Exchange Model Shaping Assign tasks to agents Reduce search space considered by agent Define local sub-problem for each robot Full SI-Dec-POMDP Local (Independent) POMDP

25. Proposed Approach: DIMS Distributed Iterative Model Shaping Distributed Planning for Large Teams25 Task Allocation Local Planning Interaction Exchange Model Shaping Solve local sub-problems using off-the- shelf centralized solver Result: Locally-optimal policy

26. Proposed Approach: DIMS Distributed Iterative Model Shaping Distributed Planning for Large Teams26 Task Allocation Local Planning Interaction Exchange Model Shaping Given local policy: estimate local probability and value of interactions Communicate local probability and value of relevant interactions to team members Sparsity  Relatively small # of messages

27. Proposed Approach: DIMS Distributed Iterative Model Shaping Distributed Planning for Large Teams27 Task Allocation Local Planning Interaction Exchange Model Shaping Modify local sub-problems to account for presence of interactions

28. Proposed Approach: DIMS Distributed Iterative Model Shaping Distributed Planning for Large Teams28 Task Allocation Local Planning Interaction Exchange Model Shaping Reallocate tasks or re-plan using modified local sub-problem

29. Any decentralized allocation mechanism (e.g. auctions) Stock graph, MDP, POMDP solver Lightweight local evaluation and low-bandwidth messaging Methods to alter local problem to incorporate non-local effects Proposed Approach: DIMS Distributed Iterative Model Shaping Distributed Planning for Large Teams29 Task Allocation Local Planning Interaction Exchange Model Shaping

30. Outline Motivation Background Approach – SI-Dec-POMDP – DIMS Preliminary Work – DPP – D-TREMOR Proposed Work Conclusion Distributed Planning for Large Teams30

31. Preliminary Results Distributed Prioritized Planning (DPP) Distributed Team REshaping of MOdels for Rapid execution (D-TREMOR) Distributed Planning for Large Teams31 P. Velagapudi, K. Sycara, and P. Scerri, “Decentralized prioritized planning in large multirobot teams,” IROS 2010. P. Velagapudi, P. Varakantham, K. Sycara, and P. Scerri, “Distributed Model Shaping for Scaling to Decentralized POMDPs with hundreds of agents,” AAMAS 2011 (in submission).

32. Preliminary Results Distributed Prioritized Planning (DPP) Distributed Team REshaping of MOdels for Rapid execution (D-TREMOR) Distributed Planning for Large Teams32 No uncertainty Many potential interactions Simple interactions Action/Observation uncertainty Fewer potential interactions Complex interactions

33. Multiagent Path Planning 33Distributed Planning for Large Teams Start Goal

34. Multiagent Path Planning  SI-Dec-POMDP Only one interaction: collision Many potential collisions Few collisions in any solution Distributed Planning for Large Teams34

35. (Given) A* Path messages Prioritized configuration-time obstacles DIMS: Distributed Prioritized Planning Distributed Planning for Large Teams35 Task Allocation Local Planning Interaction Exchange Model Shaping

36. Assign priorities to agents based on path length Longer path length estimate  higher priority Distributed Planning for Large Teams36 [van den Berg, et al 2005] Prioritized Planning [van den Berg, et al 2005]

37. Sequentially plan from highest to lowest priority – Takes n steps for n agents Use previous agents as dynamic obstacles Distributed Planning for Large Teams37

38. Distributed Prioritized Planning 38Distributed Planning for Large Teams

39. Large-Scale Path Solutions 39Distributed Planning for Large Teams

40. Large-Scale Path Solutions 40Distributed Planning for Large Teams

41. Experimental Results Scaling Dataset – # robots varied: {40, 60, 80, 120, 160, 240} – Density of map constant: 8 cells per robot Density Dataset – # robots constant: 240 – Density of map varied: {32, 24, 16, 12, 8} cells per robot Cellular automata to generate 15 random maps Maps solved with centralized prioritized planning Distributed Planning for Large Teams41

42. High quality solutions Distributed Planning for Large Teams42 DPP Varying Team SizeVarying Density (240 agents)

43. Few sequential iterations Varying Team Size Varying Density (240 agents) Distributed Planning for Large Teams43

44. Summary of DPP DPP achieves high-quality solutions – Same quality as centralized PP Prioritization + sparsity = rapid convergence – Able to handle large numbers of collision interactions – Far fewer sequential planning iterations Distributed Planning for Large Teams44

45. Preliminary Results Distributed Prioritized Planning (DPP) Distributed Team REshaping of MOdels for Rapid execution (D-TREMOR) Distributed Planning for Large Teams45 No uncertainty Many potential interactions Simple interactions Action/Observation uncertainty Fewer potential interactions Complex interactions

46. A Simple Rescue Domain 46Distributed Planning for Large Teams Rescue Agent Cleaner Agent Narrow Corridor Victim Unsafe Cell Clearable Debris Clearable Debris

47. A Simple (Large) Rescue Domain 47Distributed Planning for Large Teams

48. Distributed POMDP with Coordination Locales [Varakantham, et al 2009] Subset of SI-Dec-POMDP: only modifies, Coordination locales (CLs) are subtypes of interactions: Distributed Planning for Large Teams48 Explicit time Explicit time constraint Implicitly construct interaction functions CL =

49. Decentralized auction EVA POMDP solver Policy sub-sampling and Coordination Locale (CL) messages Policy sub-sampling and Coordination Locale (CL) messages Prioritized/randomized reward and transition shaping Prioritized/randomized reward and transition shaping DIMS: D-TREMOR (extending [Varakantham, et al 2009]) Distributed Planning for Large Teams49 Task Allocation Local Planning Interaction Exchange Model Shaping

50. D-TREMOR: Task Allocation Assign “tasks” using decentralized auction – Greedy, nearest allocation Create local, independent sub-problem: Distributed Planning for Large Teams50

51. D-TREMOR: Local Planning Solve using off-the-shelf algorithm (EVA) Result: locally-optimal policies Distributed Planning for Large Teams51

52. D-TREMOR: Interaction Exchange Finding Pr CLi Evaluate local policy Compute frequency of associated s i, a i Distributed Planning for Large Teams52 [Kearns 2002] : Entered corridor in 95 of 100 runs: Pr CLi = 0.95

53. D-TREMOR: Interaction Exchange Finding Val CLi Sample local policy value with/without interactions – Test interactions independently Compute change in value if interaction occurred Distributed Planning for Large Teams53 No collision Collision Val CLi = -7 [Kearns 2002] :

54. D-TREMOR: Interaction Exchange Send CL messages to teammates: Sparsity  Relatively small # of messages Distributed Planning for Large Teams54

55. D-TREMOR: Model Shaping Shape local model rewards/transitions based on remote interactions Distributed Planning for Large Teams55 Probability of interaction Interaction model functions Independent model functions

56. D-TREMOR: Local Planning (again) Re-solve shaped local models to get new policies Result: new locally-optimal policies  new interactions Distributed Planning for Large Teams56

57. D-TREMOR: Adv. Model Shaping In practice, we run into three common issues faced by concurrent optimization algorithms: – Slow convergence – Oscillation – Local optima We can alter our model-shaping to mitigate these by reasoning about the types of interactions we have Distributed Planning for Large Teams57

58. D-TREMOR: Adv. Model Shaping Slow convergence  Prioritization – Majority of interactions are collisions – Assign priorities to agents, only model-shape collision interactions for higher priority agents – From DPP: prioritization can quickly resolve collision interactions – Similar properties for any purely negative interaction Negative interaction: when every agent is guaranteed to have a lower-valued local policy if an interaction occurs Distributed Planning for Large Teams58

59. D-TREMOR: Adv. Model Shaping Oscillation  Probabilistic shaping – Often caused by time dynamics between agents Agent 1 shapes based on Agent 2’s old policy Agent 2 shapes based on Agent 1’s old policy – Each agent only applies model-shaping with probability δ [Zhang 2005] – Breaks out of cycles between agent policies Distributed Planning for Large Teams59

60. D-TREMOR: Adv. Model Shaping Local Optima  Optimistic initialization – Agents cannot detect mixed interactions (e.g. debris) Rescue agent policies can only improve if debris is cleared Cleaner agent policies can only worsen if they clear debris Distributed Planning for Large Teams60 Pr CL = low, Val CL = low If (Val CL = low): optimal policy  do nothing Pr CL = low, Val CL = low

61. D-TREMOR: Adv. Model Shaping Local Optima  Optimistic initialization – Agents cannot detect mixed interactions (e.g. debris) Rescue agent policies can only improve if debris is cleared Cleaner agent policies can only worsen if they clear debris – Let each agent solve an initial model that uses an optimistic assumption of interaction condition Distributed Planning for Large Teams61

62. Preliminary Results Scaling Dataset Density Dataset Distributed Planning for Large Teams62

63. Experimental Setup D-TREMOR policies – Max-joint-value – Last iteration Comparison policies – Independent – Optimistic – Do-nothing – Random Scaling: – 10 to 100 agents – Random maps Density – 100 agents – Concentric ring maps 3 problems/condition 20 planning iterations 7 time step horizon 1 CPU per agent Distributed Planning for Large Teams63 D-TREMOR produces reasonable policies for 100-agent planning problems in under 6 hrs. (with some caveats) D-TREMOR produces reasonable policies for 100-agent planning problems in under 6 hrs. (with some caveats)

64. Preliminary Results: Scaling Distributed Planning for Large Teams64 Naïve Policies D-TREMOR Policies

65. Preliminary Results: Density Distributed Planning for Large Teams65 Do-nothing does the best? Ignoring interactions = poor performance

66. Preliminary Results: Density Distributed Planning for Large Teams66 D-TREMOR rescues the most victims D-TREMOR does not resolve every collision

67. Preliminary Results: Time Distributed Planning for Large Teams67 Why is this increasing?

68. Preliminary Results: Time Distributed Planning for Large Teams68 Increase in time related to # of CLs, not # of agents

69. Summary of D-TREMOR D-TREMOR produces reasonable policies for 100-agent planning problems in under 6 hrs. – Partially-observable, uncertain world – Multiple types of interactions & agents Improves over independent planning Resolved interactions in large problems Still some convergence/efficiency issues Distributed Planning for Large Teams69

70. Outline Motivation Background Approach – SI-Dec-POMDP – DIMS Preliminary Work – DPP – D-TREMOR Proposed Work Conclusion Distributed Planning for Large Teams70

71. Proposed Work Distributed Planning for Large Teams71

72. A* (Graph) A* (Graph) Policy evaluation & Prioritized exchange Prioritized shaping Prioritized shaping Given Proposed Work Distributed Planning for Large Teams72 Task Allocation Local Planning Interaction Exchange Model Shaping EVA (POMDP) EVA (POMDP) Auction Policy sub-sampling & Full exchange Stochastic shaping Stochastic shaping Optimistic initialization Optimistic initialization

73. Proposed Work Consolidate and generalize DIMS: 1. Interaction classification 2. Model-shaping heuristics 3. Domain evaluation – Search & Rescue – Humanitarian Convoy 73Distributed Planning for Large Teams D-TREMOR DIMS Framework DIMS Framework DPP

74. Interaction Classification What are the different classes of possible interactions between agents in DIMS? 74Distributed Planning for Large Teams ? ? Collisions (Reward Only) Collisions (Neg. Reward + Transition) Collisions (Neg. Reward + Transition) Debris Clearing (Transition + Delay) Debris Clearing (Transition + Delay) Model-shaping Terms:RewardTransitionObs. Collisions (DPP) x Collisions (D-TREMOR) xx Debris Clearing x Policy Effects:NegativePositiveMixed Collisions (DPP) x Collisions (D-TREMOR) x Debris Clearing x

75. Interaction Classification 1. Determine the sets of interactions that occur in the domains of interest 2. Formalize the characteristics of useful classes of interactions from this relevant set – Start with identifying differences between interactions in preliminary work: Collisions: Reward-only, same-time Collisions: Reward + Transition, same-time Debris-Clearing: Transition-only, different-time 3. Classify potential interactions by common features 75Distributed Planning for Large Teams

76. Model-shaping Heuristics Given classes of relevant interactions, what do we need to do to find good solutions? 76Distributed Planning for Large Teams Prioritized shaping Prioritized shaping Model Shaping Stochastic shaping Stochastic shaping Optimistic initialization Optimistic initialization ? ? Collisions (Reward Only) Collisions (Neg. Reward + Transition) Collisions (Neg. Reward + Transition) Debris Clearing (Transition + Delay) Debris Clearing (Transition + Delay) ? ?

77. Model-shaping Heuristics Explore which if, any, of the existing heuristics apply to each class of interaction Apply targeted heuristics for newly-identified classes of interactions Attempt to bound the performance of the heuristics for particular classes of interaction – e.g. Proved that prioritization converges for negative interactions 77Distributed Planning for Large Teams

78. Search and RescueHumanitarian Convoy Using our approach, how well can we do in realistic planning scenarios? Domain Evaluation Distributed Planning for Large Teams78

79. Domain Evaluation 79Distributed Planning for Large Teams Domain Search and RescueHumanitarian Convoy Model Simple ModelUSARSimSimple ModelVBS2 GraphDPP  MDP  POMDPD-TREMOR  DIMS

80. Proposed Work: Timeline DateDescription Nov 2010 – Feb 2011Develop classification of interactions Feb 2011 – Mar 2011Design heuristics for common interactions Mar 2011 – Jul 2011Implementation of DIMS solver Jul 2011 – Oct 2011Rescue experiments Oct 2011 – Jan 2012Convoy experiments Feb 2012 – May 2012Thesis preparation May 2012Defend Thesis Distributed Planning for Large Teams80

81. Outline Motivation Background Approach – SI-Dec-POMDP – DIMS Preliminary Work – DPP – D-TREMOR Proposed Work Conclusion Distributed Planning for Large Teams81

82. Conclusions (1/3): Work-to-date DPP: Distributed path planning for large teams D-TREMOR: Decentralized planning for sparse Dec-POMDPs with many agents Demonstrated complete distributability, fast heuristic interaction detection, and local message exchange to achieve high scalability Empirical results in simulated search and rescue domain Distributed Planning for Large Teams82

83. Conclusions (2/3): Contributions 1. DIMS: a modular algorithm for solving planning problems in large teams with sparse interactions – Single framework, applied to path planning, MDP, POMDP 2. Empirical results of distributed planning using DIMS in teams of at least 100 agents across two domains 3. Study of characteristics of interaction in sparse planning problems – Provide classification of interactions – Determine features for distinguishing interaction behaviors Distributed Planning for Large Teams83

84. Conclusions (3/3): Take-home Message This thesis will demonstrate that it is possible to efficiently, distributedly find high-quality solutions to planning problems with known sparse interactions with and without uncertainty for teams of at least a hundred agents. Distributed Planning for Large Teams84

85. Distributed Planning for Large Teams85

86. The VECNA Bear (Yes, it exists!) Distributed Planning for Large Teams86

87. SI-Dec-POMDP vs. other models DPCL – Extends DPCL model – Adds observational interactions – Time integrated in state rather than explicit EDI/EDI-CR – Adds complex transitions and observations TD-Dec-MDP – Allows simultaneous interaction (within epoch) Factored MDP/POMDP – Adds interactions that span epochs Distributed Planning for Large Teams87

88. Assign tasks to agents Create local sub-problems Assign tasks to agents Create local sub-problems Use local solver to find optimal solution to sub-problem Compute and exchange probability and expected value of interactions Alter local sub-problem to incorporate non-local effects Proposed Approach: DIMS Distributed Iterative Model Shaping Distributed Planning for Large Teams88 Task Allocation Local Planning Interaction Exchange Model Shaping

89. Motivation Distributed Planning for Large Teams89

90. D-TREMOR Distributed Planning for Large Teams90

91. D-TREMOR Distributed Planning for Large Teams91

92. D-TREMOR: Reward functions Probability that a debris will not allow a robot to enter the cell: – P_Debris = 0.9; Probability of action failure – P_ActionFailure = 0.2; Probability that success is observed if the action succeeded. – P_ObsSuccessOnSuccess = 0.8; Probability that success is observed if the action failed – P_ObsSuccessOnFailure = 0.2; Probability that a robot will return to the same cell after collision – P_ReboundAfterCollision = 0.5; Reward of saving a victim – R_Victim = 10.0; Reward of cleaning debris – R_Cleaning = 0.25; Reward of moving – R_Move = -0.5; Reward of observing – R_Observe = -0.25; Reward for a collision – R_Collision = -5.0; Reward for landing in an unsafe cell – R_Unsafe = -1; Distributed Planning for Large Teams92