# Hierarchical Finite State Controllers for Generalized Planning

IJCAI, pp. 3235-3241, 2016.

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Abstract:

Finite State Controllers (FSCs) are an effective way to represent sequential plans compactly. By imposing appropriate conditions on transitions, FSCs can also represent generalized plans that solve a range of planning problems from a given domain. In this paper we introduce the concept of hierarchical FSCs for planning by allowing control...More

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Introduction

- Finite state controllers (FSCs) are a compact and effective representation commonly used in AI; prominent examples include robotics [Brooks, 1989] and video-games [Buckland, 2004].
- FSCs offer two main benefits: 1) solution compactness [Backstrom et al, 2014]; and 2) the ability to represent generalized plans that solve a range of similar planning problems.
- A classical planning problem is a tuple P = hF, A, I, Gi, where F is a set of fluents, A is a set of actions, the author iss an initial state and G is a goal condition, i.e. a set of literals.

Highlights

- Finite state controllers (FSCs) are a compact and effective representation commonly used in AI; prominent examples include robotics [Brooks, 1989] and video-games [Buckland, 2004]
- In the goal is to Tree/Depth-First Search, the goal is to visit all nodes of a binary tree
- In this paper we have presented a novel formalism for hierarchical Finite State Controllers in planning in which controllers can recursively call themselves or other controllers to represent generalized plans more compactly
- We have introduced a compilation into classical planning which makes it possible to use an off-the-shelf planner to generate hierarchical Finite State Controllers
- We have showed that hierarchical Finite State Controllers can be generated in an incremental fashion to address more challenging generalized planning problems
- An iterative deepening approach could be implemented to automatically derive these bounds. Another issue is the specification of representative subproblems to generate hierarchical Finite State Controllers in an incremental fashion

Results

- The authors evaluate the approach in a set of generalized planning benchmarks and programming tasks taken from Bonet et al [2010] and Segovia-Aguas et al [2016].
- The authors run the classical planner Fast Downward [Helmert, 2006] with the LAMA-2011 setting [Richter and Westphal, 2010] on a processor Intel Core i5 3.10GHz x 4 with a 4GB memory bound and time limit of 3600s.
- In List, the goal is to visit all the nodes of a linked list.
- In the goal is to Tree/DFS, the goal is to visit all nodes of a binary tree.
- In Visitall, the goal is to visit all the cells of a square grid

Conclusion

- In this paper the authors have presented a novel formalism for hierarchical FSCs in planning in which controllers can recursively call themselves or other controllers to represent generalized plans more compactly.
- Just as in previous work on the automatic generation of FSCs, the compilation takes as input a bound on the number of controller states.
- An iterative deepening approach could be implemented to automatically derive these bounds.
- Another issue is the specification of representative subproblems to generate hierarchical FSCs in an incremental fashion.
- Inspired by “Test Driven Development” [Beck et al, 2001], the authors believe that defining subproblems is a step towards automation

Summary

## Introduction:

Finite state controllers (FSCs) are a compact and effective representation commonly used in AI; prominent examples include robotics [Brooks, 1989] and video-games [Buckland, 2004].- FSCs offer two main benefits: 1) solution compactness [Backstrom et al, 2014]; and 2) the ability to represent generalized plans that solve a range of similar planning problems.
- A classical planning problem is a tuple P = hF, A, I, Gi, where F is a set of fluents, A is a set of actions, the author iss an initial state and G is a goal condition, i.e. a set of literals.
## Results:

The authors evaluate the approach in a set of generalized planning benchmarks and programming tasks taken from Bonet et al [2010] and Segovia-Aguas et al [2016].- The authors run the classical planner Fast Downward [Helmert, 2006] with the LAMA-2011 setting [Richter and Westphal, 2010] on a processor Intel Core i5 3.10GHz x 4 with a 4GB memory bound and time limit of 3600s.
- In List, the goal is to visit all the nodes of a linked list.
- In the goal is to Tree/DFS, the goal is to visit all nodes of a binary tree.
- In Visitall, the goal is to visit all the cells of a square grid
## Conclusion:

In this paper the authors have presented a novel formalism for hierarchical FSCs in planning in which controllers can recursively call themselves or other controllers to represent generalized plans more compactly.- Just as in previous work on the automatic generation of FSCs, the compilation takes as input a bound on the number of controller states.
- An iterative deepening approach could be implemented to automatically derive these bounds.
- Another issue is the specification of representative subproblems to generate hierarchical FSCs in an incremental fashion.
- Inspired by “Test Driven Development” [Beck et al, 2001], the authors believe that defining subproblems is a step towards automation

- Table1: Number of controllers used, solution kind (OC=One Controller, HC=Hierarchical Controller, RP=Recursivity with Parameters) and, for each controller: number of states, number of instances in P, planning time and plan length

Related work

- The main difference with previous work on the automatic generation of FSCs [Bonet et al, 2010; Hu and De Giacomo, 2013] is that they generate single FSCs relying on a partially observable planning model. In contrast, our compilation generate hierarchical FSCs that can branch on any fluent since we consider all fluents as observable. Our approach also makes it possible to generate recursive slutions and to incorporate prior knowledge as existing FSCs, and automatically complete the definition of the remaining hierarchical FSC.

Hierarchical FSCs are similar to planning programs [Jimenez and Jonsson, 2015; Segovia-Aguas et al, 2016]. Programs are a special case of FSCs, and in general, FSCs can represent a plan more compactly. Another related formalism is automaton plans [Backstrom et al, 2014], which also store sequential plans compactly using hierarchies of finite state automata. However, automaton plans are Mealy machines whose transitions depend on the symbols of an explicit input string. Hence automaton plans cannot store generalized plans, and their focus is instead on the compression of sequential plans.

Funding

- This work is partially supported by grant TIN2015-67959 and the Maria de Maeztu Units of Excellence Programme MDM2015-0502, MEC, Spain
- Sergio Jimenez is partially supported by the Juan de la Cierva program funded by the Spanish government

Reference

- [Backstrom et al., 2014] Christer Backstrom, Anders Jonsson, and Peter Jonsson. Automaton plans. Journal of Artificial Intelligence Research, 51:255–291, 2014.
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- [Beck et al., 2001] Kent Beck, Mike Beedle, Arie Van Bennekum, Alistair Cockburn, Ward Cunningham, Martin Fowler, James Grenning, Jim Highsmith, Andrew Hunt, Ron Jeffries, et al. The agile manifesto, 2001.
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- [Brooks, 1989] R. Brooks. A robot that walks; emergent behaviours from a carefully evolved network. Neural Computation, 1:253–262, 1989.
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- [Jimenez and Jonsson, 2015] Sergio Jimenez and Anders Jonsson. Computing Plans with Control Flow and Procedures Using a Classical Planner. In Proceedings of the Eighth Annual Symposium on Combinatorial Search, SOCS-15, pages 62–69, 2015.
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- [Segovia-Aguas et al., 2016] Javier Segovia-Aguas, Sergio Jimenez, and Anders Jonsson. Generalized planning with procedural domain control knowledge. In Proceedings of the International Conference on Automated Planning and Scheduling, 2016.
- [Srivastava et al., 2011] Siddharth Srivastava, Neil Immerman, Shlomo Zilberstein, and Tianjiao Zhang. Directed search for generalized plans using classical planners. In International Conference on Automated Planning and Scheduling, pages 226–233, 2011.
- [Toropila and Bartak, 2010] D. Toropila and R. Bartak. Using Finite-State Automata to Model and Solve Planning Problems. In Proceedings of the 11th Italian AI Symposium on Artificial Intelligence (AI*IA), pages 183–189, 2010.

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Best Paper of IJCAI, 2016

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