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Generalized Planning via Abstraction: Arbitrary Numbers of Objects Le on Illanes Sheila A. McIlraith Department of Computer Science University of Toronto Toronto, Ontario, Canada AAAI 2019 Motivating Example: Retail Delivery Le on

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Generalized Planning via Abstraction: Arbitrary Numbers of Objects Le´

n Illanes

Sheila A. McIlraith

Department of Computer Science University of Toronto Toronto, Ontario, Canada

AAAI 2019

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Motivating Example: Retail Delivery

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Motivating Example: Retail Delivery

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Retail Delivery Solution

Solution 1: A plan for a delivery problem instance

1 deliver package1 2 deliver package2 3 deliver package3

. . .

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Retail Delivery Solution

Solution 2: A generalized solution for the problem

1 while there is some undelivered package do 2

deliver it

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Generalized Planning

Workflow overview

Generalized Problem Classical Problem Generalized Planner Generalized Policy Policy Executor Plan Instantiator Classical State Classical Plan Action

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Generalized Planning

Workflow overview

Generalized Problem Classical Problem Generalized Planner Generalized Policy Policy Executor Plan Instantiator Classical State Classical Plan Action

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Representation: Quantified Problems

∃

“There is at least one package for NY in Paris” ∃[x : NY-pkg(x)] in-Paris(x)

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Automated Generalization

From classical problem to quantified problem Use recent reformulation techniques:12

Model indistinguishable objects with counting

Abstract away the counters

1Riddle et al. 2015. 2Fuentetaja and de la Rosa 2016.

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Nondeterministic Actions

∃

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Nondeterministic Actions

∃ ∃

?

∃ ∃

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Nondeterministic Actions

Problem dynamics are actually deterministic Results in unfair nondeterminism

Some of the outcomes are actually impossible

Strong cyclic solvers typically assume fairness We need to deal with the unfairness345

3Bonet et al. 2017. 4Illanes and McIlraith 2017. 5Bonet and Geffner 2018.

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Generalized Planning

Workflow overview

Generalized Problem Classical Problem Generalized Planner Generalized Policy Policy Executor Plan Instantiator Classical State Classical Plan Action

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The Loom Algorithm

Based on PRP6

state-of-the-art planner for fair fully-observable nondeterministic (FOND) problems

Incorporates verification step for termination7

6Muise, McIlraith, and Beck 2012. 7Srivastava et al. 2011.

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Background: Idealized Version of PRP

Start with empty policy Goal-closed? Yes No Find a new weak plan for some state not handled by the policy Done Incorporate it into the policy

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Idealized Version of Loom

Start with empty policy Goal-closed? Yes No Find a new weak plan for some state not handled by the policy Terminating? No Yes Done Incorporate it into the policy

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Evaluation

Given a generalized problem, produce a generalized solution Execute it over a many problem instances Compare to a classical planning approach

Produce a plan for every instance Using Lama-First

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Generalized solutions with Loom

Small overhead in most cases

Domain Time to generalized solution (s) Recycling 0.03 Logistics 0.53 Hamburger 0.03 Construction 0.17 Roundabout 297.89

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Executing generalized solutions

Significant improvements in most cases

Loom Lama-First Domain Execution time (s) Planning time (s) Relative (normalized average) (normalized average) Recycling 5.39 11.99 45% Logistics 0.04 0.03 133% Hamburger 0.05 0.26 19% Construction 0.10 1.47 7% Roundabout 0.004 0.006 67%

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Problems solved over time

Construction domain

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Summary

GP is synthesis of domain-specific planners Arbitrary numbers of objects can be abstracted into unfair nondeterminism

This can be done automatically

Solve with modified FOND planning

In turn leveraging classical planning techniques

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Related Work

Bonet, Blai and Hector Geffner (2018). “Features, Projections, and Representation Change for Generalized Planning”. IJCAI. Bonet, Blai et al. (2017). “Generalized Planning: Non-Deterministic Abstractions and Trajectory Constraints”. IJCAI. Fuentetaja, Raquel and Tom´ as de la Rosa (2016). “Compiling irrelevant

bjects to counters. Special case of creation planning”. AI Comm. 29.3.

Illanes, Le´

n and Sheila A. McIlraith (2017). “Numeric Planning via

Abstraction and Policy Guided Search”. IJCAI. Muise, Christian J., Sheila A. McIlraith, and J. Christopher Beck (2012). “Improved Non-Deterministic Planning by Exploiting State Relevance”. ICAPS. Riddle, Patricia J et al. (2015). “Automated transformation of PDDL representations”. SoCS. Srivastava, Siddharth et al. (2011). “Qualitative Numeric Planning”. AAAI.

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SLIDE 23

Generalized Planning via Abstraction: Arbitrary Numbers of Objects Le´

n Illanes

Sheila A. McIlraith

Department of Computer Science University of Toronto Toronto, Ontario, Canada