Eyal Amir (UC Berkeley) Barbara Engelhardt (UC Berkeley) Factored Planning Eyal Amir (UC Berkeley) Barbara Engelhardt (UC Berkeley) Basic goal. – state in page 2 Factored Planning

Motivation Planning in structured domains Scale up planners to large domains Avoid backtracking of search for plans Techniques: Similar to structured exact logical and probabilistic reasoning (Pearl’88), (Dechter & Rish’94), (Amir & McIlraith ’00,’01), (McCartney etal. ’03) Factored Planning

Talk Outline Factored domains Factored planning algorithm Decomposition algorithm Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain move-left 2. close(1), close(2), … 3. move-right close(21), close(22), … Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) at2 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) at2 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) at1 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) at1 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) at1 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) done1 at1 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) done1 at1 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) done1 at2 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) done1 at2 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) done1 at2 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain Room 1 (20 windows) Room 2 (20 windows) done1 done2 at2 Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Example Planning Domain move-left 2. close(1), close(2), … 3. move-right close(21), close(22), … Fluents: closed(x), done1, done2, at1, at2 Actions: close(x), move-R, move-L Goal: done1,done2 (all windows closed) Initial state: at2 Factored Planning

Factored Planning Domain move-left 2. close(1), close(2), … 3. move-right close(21), close(22), … Fluents: closed(x) (1x20) done1, at1, at2 Actions: Close(x) (1x20) Move-R, move-L Fluents: closed(x) (21x40) done1,done2,at1,at2 Actions: Close(x) (21x40) Move-R, move-L at1,at2 done1 Factored Planning

Intuition Planning separately in different parts Combine separate plans to form complete plan Difficulty: want a sound + complete procedure that is always applicable Potential benefits: Fast planning & replanning Scaling to very large domains Factored Planning

Talk Outline Factored domains Factored planning algorithm Decomposition algorithm Factored Planning

Planning via Dynamic Program Room 1 (20 windows) Room 2 (20 windows) Send Messages (one way) Do some Processing In subdomain 1 Do some Processing In subdomain 2 + messages Factored Planning

Planning Algorithm (example) Room 1 (20 windows) Room 2 (20 windows) Find capabilities of subdomain 1 relevant to subdomain 2 Factored Planning

Planning Algorithm (example) Room 1 “if at1, then there is a way to make done1 true” Room 2 (20 windows) Find capabilities of subdomain 1 relevant to subdomain 2 Factored Planning

Planning Algorithm (example) Room 1 “if at1, then there is a way to make done1 true” Room 2 (20 windows) Find capabilities of subdomain 1 Create a new action In subdomain 2: relevant to subdomain 2 “make done1 true” Precond: at1 Effect: done1 Factored Planning

Planning Algorithm (example) Room 1 “if at1, then there is a way to make done1 true” Room 2 (20 windows) Find capabilities of subdomain 1 Find plan in subdomain 2 relevant to subdomain 2 “make done1 true” Precond: at1 Effect: done1 Factored Planning

Planning Algorithm (example) Room 2 Room 1 “if at1, then there is a way to make done1 true” Plan: move-left “make done1 true” move-right close(21), close(22), … Find capabilities of subdomain 1 Find plan in subdomain 2 relevant to subdomain 2 “make done1 true” Precond: at1 Effect: done1 Factored Planning

Planning Algorithm (example) Room 2 Room 1 “if at1, then there is a way to make done1 true” Plan: move-left “make done1 true” move-right close(21), close(22), … Find capabilities of subdomain 1 Expand plan to Include only atomic actions relevant to subdomain 2 Factored Planning

Planning Algorithm (example) Room 2 Room 1 “if at1, then there is a way to make done1 true” Plan: move-left A. close(1), B. close(2), … 3. move-right close(21), close(22), … Find capabilities of subdomain 1 Expand plan to Include only atomic actions relevant to subdomain 2 Factored Planning

Summary & Outlook So far: example of algorithm Next: algorithm + generalization Separator Fluents: closed(x) (0<x<21) done1, at1, at2 Actions: Close(x) (0<x<21) Move-R, move-L closed(x) (19<x<41) done1,done2,at1,at2 Close(x) (19<x<41) at1,at2 done1 Factored Planning

Planning Algorithm (2 partitions) INPUT: 2 Partitions of fluents and actions Initial state, Goal condition Iterate over values V for separator: A. Find achievable goals for part 1 from V B. Send found plans to part 2 Add new actions for plans of part 1 Find plan for goal in part 2 Replace new actions with atomic ones Factored Planning

General Messages Room 1 “if at1, then there is a way to make done1 true” Room 2 (20 windows) power Not true anymore What if we need more interactions between rooms? Example: robot must recharge batteries Factored Planning

General Messages Room 1 Room 2 “if at1, and when (20 windows) needed battery_ok, then we can make done1 true” Room 2 (20 windows) power What if we need more interactions between rooms? Example: robot must recharge batteries Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Factored Planning

Planning Algorithm INPUT: m Partitions of fluents and actions Initial state, Goal condition Find plan in final partition Replace new actions with atomic actions Factored Planning

Analysis of Algorithm Theorem: Planning algorithm is sound and complete. Theorem: Algorithm runs in time O(m • 2k1•k2) m = number of partitions k1 = # fluents in largest partition k2 = “plan width”: # back-and-forth interactions between partitions in a plan Factored Planning

Analysis of Algorithm Theorem: Planning algorithm is sound and complete. Theorem: Algorithm runs in time O(m • 2k1•k2) Two Rooms Example: m = 2 k1 = 24 k2 = 1 Factored planning: O(2 • 224) Traditional planning: O(244) Factored Planning

Experiment: Ring of Rooms Time (in milliseconds) Number of rooms Factored Planning

Talk Outline Factored domains Factored planning algorithm Decomposition algorithm Factored Planning

Decomposition Algorithm Convert into a graph problem Find a tree decomposition of low width Decompose the problem using tree Factored Planning

Decomposition Algorithm 1. Convert into a graph problem closed(1) close(1) close(21) closed(21) closed(2) close(2) close(22) closed(22) done1 move-R done2 move-L at1 at2 Factored Planning

Decomposition Algorithm 1. Convert into a graph problem closed(1) close(1) close(21) closed(21) closed(2) close(2) close(22) closed(22) done1 move-R done2 move-L at1 at2 Factored Planning

Decomposition Algorithm 1. Convert into a graph problem closed(1) close(1) close(21) closed(21) closed(2) close(2) close(22) closed(22) done1 move-R done2 move-L at1 at2 Factored Planning

Decomposition Algorithm 1. Convert into a graph problem closed(1) close(1) close(21) closed(21) closed(2) close(2) close(22) closed(22) done1 move-R done2 move-L at1 at2 Factored Planning

Decomposition Algorithm 2. Find a tree decomposition of low width closed(1) close(1) close(21) closed(21) closed(2) close(2) close(22) closed(22) done1 move-R done2 move-L at1 at2 Factored Planning

Decomposition Algorithm 2. Find a tree decomposition of low width closed(1) close(1) close(21) closed(21) closed(2) close(2) close(22) closed(22) done1 move-R done2 move-L at1 at2 Factored Planning

Decomposition Algorithm 3. Decompose planning problem accordingly closed(1) close(1) close(21) closed(21) closed(2) close(2) close(22) closed(22) done1 move-R done2 move-L at1 at2 Factored Planning

Decomposition Algorithm 3. Decompose planning problem accordingly done1 Fluents: closed(x) (0<x<21) done1, at1, at2 Actions: Close(x) (0<x<21) Move-R, move-L Fluents: closed(x) (19<x<41) done1,done2,at1,at2 Actions: Close(x) (19<x<41) Move-R, move-L at1 at2 Factored Planning

Decomposition Algorithm 3. Decompose planning problem accordingly Room 1 (20 windows) Room 2 (20 windows) Factored Planning

Decomposition Algorithm Convert into a graph problem Find a tree decomposition of low width Can be done using known algorithms (e.g., (Rose ’76), (Amir 2001)) Decompose the problem using tree Factored Planning

Conclusions Factored planning algorithm Decomposition algorithm relies on known graph algorithms Algorithm applicable to all domains Always sound and complete (unlike (Guestrin etal. ’01) - MDPs) Tractability of algorithm depends on quality of domain decomposition and decomposition properties of solution Factored Planning

Applications & Future Work Nondeterministic domains Stochastic domains First-order decompositions Automatic generation of subsumption architectures Factored Planning

THE END Factored Planning

Related Works Factored reasoning [Pearl’88], [Amir & McIlraith’00,’01], [MacCartney etal.’03] Structured planning: Hierarchical planning, structured planning [Lanskey & Getoor ’95], Agents [Lansky’91], … Stochastic planning: [Parr’99], [Guestrin etal. ’01] Factored Planning

Factored Planning