P LANNING WITH I NCOMPLETE U SER P REFERENCES AND D OMAIN M ODELS - PowerPoint PPT Presentation

P LANNING WITH I NCOMPLETE U SER P REFERENCES AND D OMAIN M ODELS Tuan Anh Nguyen Graduate Committee Members: Subbarao Kambhampati (Chair) Chitta Baral Minh B. Do Joohyung Lee David E. Smith

M OTIVATION Automated Planning In practice… Research:  Action models are not  Actions available upfront  Preconditions  Cost of modeling  Effects  Error-prone  Deterministic  Users usually don’t  Non-deterministic exactly know what  Stochastic  Initial situation they want  Goal conditions  Always want to see more than one plan  What a user wants about plans  Find a (best) plan! 2 Planning with incomplete user preferences and domain models

Preferences in Planning – Traditional View  Classical Model: “Closed world” assumption about user preferences.  All preferences assumed to be fully specified/available Full Knowledge of Preferences Two possibilities  If no preferences specified — then user is assumed to be indifferent. Any single feasible plan considered acceptable.  If preferences/objectives are specified, find a plan that is optimal w.r.t. specified objectives. Either way, solution is a single plan 3 3

Preferences in Planning — Real World Full Knowledge Real World: Preferences not fully known of Preferences is  lacking Unknown preferences  For all we know, user may care about every thing --- the flight carrier, the arrival and departure times, the type of flight, the airport, time of travel and cost of travel… Partially known  We know that users cares only about travel time and cost. But we don’t know how she combines them… 4 4

Domain Models in Planning – Traditional View  Classical Model: “Closed world” assumption about action descriptions. Full Knowledge  Fully specified preconditions and effects of domain models  Known exact probabilities of outcomes pick-up :parameters (?b – ball ?r – room) :precondition (and (at ?b ?r) (at-robot ?r) (free-gripper)) :effect (and (carry ?b) (not (at ?b ?r)) (not (free-gripper))) 5 5

Domain Models in Planning – (More) Practical View  Completely modeling the domain dynamics  Time consuming  Error-prone  Sometimes impossible  What does it mean by planning with incompletely specified domain models?  Plan could fail! Prefer plans that are more likely to succeed…  How to define such a solution concept? 6 6

Problems and Challenges  Incompleteness representation  Solution concepts  Planning techniques 7 7

D ISSERTATION OVERVIEW “Model - lite” Planning Preference Domain incompleteness incompleteness  Representation  Representation  Solution concept  Solution concept  Solving techniques  Solving techniques 8

D ISSERTATION OVERVIEW “Model - lite” Planning Preference Domain incompleteness incompleteness  Representation: two levels  Representation of incompleteness  Actions with possible  User preferences exist, but preconditions / effects totally unknown  Optionally with weights  Partially specified for being the real ones  Complete set of plan  Solution concept: “robust” attributes plans  Parameterized value function, unknown  Solving techniques: trade-off values synthesizing robust plans  Solution concept: plan sets  Solving techniques: 9 synthesizing high quality plan sets

D ISSERTATION O VERVIEW “Model - lite” Planning Preference incompleteness  Distance measures w.r.t.  Representation: two levels base-level features of plans of incompleteness (actions, states, causal links)  User preferences exist, but  CSP-based and local-search totally unknown based planners  Partially specified  Full set of plan attributes  IPF/ICP measure  Parameterized value  Sampling, ICP and Hybrid function, unknown approaches trade-off values  Solution concept: plan sets with quality  Solving techniques: 10 synthesizing quality plan sets

D ISSERTATION OVERVIEW “Model - lite” Planning Preference Domain incompleteness incompleteness Publication Publication  Representation: two levels  Representation of incompleteness  Domain independent approaches  Assessing and Generating  Actions with possible for finding diverse plans . IJCAI Robust Plans with Partial  User preferences exist, but preconditions / effects (2007) Domain Models . ICAPS-WS totally unknown  Optionally with weights (2010)  Planning with partial preference  Partially specified for being the real ones models. IJCAI (2009)  Synthesizing Robust Plans under  Full set of plan Incomplete Domain Models.  Solution concept: “robust”  Generating diverse plans to attributes AAAI-WS(2011), NIPS (2013) plans handle unknown and partially  Parameterized value known user preferences. AIJ 190  A Heuristic Approach to function, unknown  Solving techniques: (2012) Planning with Incomplete trade-off values synthesizing robust plans STRIPS Action Models. ICAPS (with Biplav Srivastava, Subbarao  Solution concept: plan sets (2014) Kambhampati, Minh Do, Alfonso (with Subbarao Kambhampati,  Solving techniques: Gerevini and Ivan Serina) 11 Minh Do) synthesizing high quality plan sets

P LANNING WITH I NCOMPLETE D OMAIN M ODELS 12

R EVIEW : STRIPS  Predicate set R : clear(x – object), on- table(x – object), on(x – object, y – object), holding(x – object), hand-empty  Operators O :  Name (signature): pick-up(x – object)  Preconditions: hand-empty, clear(x)  Effects: ~hand-empty, holding(x), ~clear(x)  A single complete model! 13

P LANNING P ROBLEM WITH STRIPS  Set of typed objects {𝑝 1 , … , 𝑝 𝑙 }  Together with predicate set 𝑄 , we have a set of grounded propositions 𝐺  Together with operators 𝑃 , we have a set of grounded actions 𝐵  Initial state: 𝐽 ∈ 𝐺  Goals: 𝐻 ⊆ 𝐺 14

P LANNING P ROBLEM WITH STRIPS (2)  Find : a plan 𝜌 achieves 𝐻 starting from 𝐽 : 𝛿 𝜌, 𝐽 ⊇ 𝐻.  Transition function: 𝑏 , 𝑡 = 𝑡 ∪ 𝐵𝑒𝑒 𝑏 ∖ 𝐸𝑓𝑚(𝑏) for applying 𝑏 ∈ 𝐵  𝛿 in 𝑡 ⊆ 𝐺 s.t. 𝑄𝑠𝑓 𝑏 ⊆ 𝑡 .  Applying 𝜌 = 〈𝑏 1 , … , 𝑏 𝑜 〉 at state 𝑡 : 𝛿 𝜌, 𝑡 = 𝛿( 𝑏 𝑜 , 𝛿( 𝑏 2 , … , 𝑏 𝑜−1 , 𝑡)) 15

I NCOMPLETE D OMAIN M ODELS  Predicate set 𝑺 : clear(x – object), on-table(x – object), on(x – object, y – object), holding(x – object), hand- empty, light(x – object), dirty(x – object)  Operators 𝑷  Name (signature): pick-up(x – object) Incompleteness  Preconditions: hand-empty, clear(x) in deterministic  Possible preconditions: light(x) domains  Effects: ~hand-empty, holding(x), ~clear(x)  Possible effects: dirty(x) Stochastic domains = 〈𝑺, 𝑷〉  Incomplete domain 𝑬  At “schema” level with typed variables (no objects)  With K “annotations”, we have 2 𝐿 possible complete models, one of which is the true model . 16

P LANNING P ROBLEM WITH I NCOMPLETE DOMAIN  Set of typed objects {𝑝 1 , … , 𝑝 𝑙 }  Together with predicate set 𝑄 , we have a set of grounded propositions 𝐺  Together with operators 𝑃 , we have a set of grounded actions 𝐵  Initial state: 𝐽 ∈ 𝐺  Goals: 𝐻 ⊆ 𝐺  Find : a plan 𝜌 “achieves” 𝐻 starting from 𝐽  An ill-defined solution concept! 17  Need a definition for “goal achievement”

T RANSITION F UNCTION , applying 𝝆 in s results in a set of possible  Under 𝑬 states: 𝜹 𝑬 𝒋 (𝝆, 𝒕) 𝜹 𝝆, 𝒕 = ≫ 𝑬 𝒋 ∈≪𝑬  The probability of ending up in 𝒕 ′ ∈ 𝜹(𝝆, 𝒕) is equal to 𝑸𝒔(𝑬 𝒋 ) ≫, 𝒕 ′ =𝜹 𝑬𝒋 (𝝆,𝒕) 𝑬 𝒋 ∈≪𝑬 where 𝑸𝒔 (𝑬 𝒋 ) is the probability of 𝑬 𝒋 being the true 18 model.

T RANSITION F UNCTION 𝜹 𝑬 ( 𝒃 , 𝒕) :  STRIPS Execution (SE): 𝐸 (〈𝑏〉, 𝑡) = 𝑡 ∖ 𝐸𝑓𝑚 𝐸 𝑏 ∪ 𝐵𝑒𝑒 𝐸 𝑏 , 𝑗𝑔 𝑄𝑠𝑓 𝐸 𝑏 ⊆ 𝑡 𝑝𝑢ℎ𝑓𝑠𝑥𝑗𝑡𝑓 𝛿 𝑇𝐹 𝑡 ⊥ = {⊥} , 𝑄𝑠𝑓 𝐸 𝑏 ⊈ 𝑡 ⊥ , 𝐻 ⊈ 𝑡 ⊥ ⊥ ∉ 𝐺  Generous Execution (GE): 𝐸 (〈𝑏〉, 𝑡) = 𝑡 ∖ 𝐸𝑓𝑚 𝐸 𝑏 ∪ 𝐵𝑒𝑒 𝐸 𝑏 , 𝑗𝑔 𝑄𝑠𝑓 𝐸 𝑏 ⊆ 𝑡 𝛿 𝐻𝐹 𝑡, 𝑝𝑢ℎ𝑓𝑠𝑥𝑗𝑡𝑓 20

 Initial state 𝐽 = {𝑞 2 }  Proposition set 𝐺 = {𝑞 1 , 𝑞 2 , 𝑞 3 } 21  Goal 𝐻 = {𝑞 3 }

A M EASURE FOR P LAN R OBUSTNESS  Naturally, we prefer plan that succeeds in as many complete models as possible 𝑆 𝜌 = |Π| 2 𝐿 𝑺 𝑻𝑭 𝝆 ≤ 𝑺 𝑯𝑭 (𝝆) R GE 𝜌 = 6/8 R GE 𝜌 = 4/8 22

A BIT MORE GENERAL …  Predicate set 𝑺 : clear(x – object), on-table(x – object), on(x – object, y – object), holding(x – object), hand-empty, light(x – object), dirty(x – object)  Operators 𝑷  Name (signature): pick-up(x – object)  Preconditions: hand-empty, clear(x)  Possible preconditions: light(x) with a weight of 0.8  Effects: ~hand-empty, holding(x), ~clear(x)  Possible effects: dirty(x) with an unspecified weight  Treat weights as probabilities with random variables  Robustness measure: 𝑺 𝝆 ≝ 𝐐𝐬 (𝑬 𝒋 ) 23 〉〉:𝜹 𝑬𝒋 𝝆,𝑱 ⊨𝑯 𝑬 𝒋 ∈ 〈〈𝑬