Learning by Analogical Reasoning in General Problem Solving

245 Pages·2012·11.27 MB·English

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Learning by Analogical Reasoning
in General Problem Solving
Manuela M. Veloso
August 1992
CMU-CS-92-174
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy
School of Computer Science
Carnegie Mellon University
DI
Pittsburgh, PA 15213
SELECTE 0
0CT 2 81992
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Copyright 1992 Manuela M. Veloso..............
AU rights reserved
This research was supported by the Avionics Laboratory, Wright Research and Development
Center, Aeronautical Systems Division (AFSC), U.S. Air Force, Wright-Patterson AFB, Ohio 45433-
6543 under Contract F33615-90-C-1465, ARPA Order No. 7597. The views and conclusions con-
tained in this document are those of the author and should not be interpreted as representing the
official policies, either expressed or implied, of the Defense Advanced Research Projects Agency or
of the U.S. Government.
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Approvod for public releasO2 n
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92 10 2z' 19 211--66792?-l al|/(||
Keywords: Machine learning, analogical reasoning, general problem solving, strategy
level learning, scale up, case-based reasoning, PRODIGY
egle iSchool of Computer Science
DOCTORAL THESIS
in the field of
Computer Science
Learning by Analogical Reasoning Accesion For
in GeneralP urpose Problem Solving NTIS CRA&l
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MANUELA VELOSO JUusntaifnincoatuinocne d EJ
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By
Distribution I
Submitted in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy Availability Codes
Avail and/or
Dist Special
ACCEPTED:
AMJ~O'-19R FSO
DATE
DEAN DATE
APPROVED:
PROVOST DATE
To my husband, Josi Manuel,
and my sons, Andri Manuel and Pedro Manuel
Abstract
This dissertation integrates derivational analogy into general problem solving as a
method of learning at the strategy level to solve problems more effectively. The
derivational analogy method has been fully implemented in the PRODIGY architecture
and proven empirically to be amenable to scaling up both in terms of domain and
problem complexity.
Reasoning by analogy involves a set of challenging problems, namely: how to
accumulate episodic problem solving experience, how to define and decide when two
problem solving situations are similar, how to organize large amounts of knowledge
so that it may be efficiently retrieved, and finally the ultimate problem of how to
successfully transfer chains of reasoning from past experience to new problem solving
situations when only a partial match exists among corresponding problems. More
specifically, the dissertation automates the generation, storage, dynamic indexation,
retrieval and replay for multiple cases (i.e. derivational traces of past problem solving
episodes). Learning occurs by accumulation and flexible reuse of cases. The problem
solving search effort is reduced incrementally as more episodic experience is compiled
into the case library.
Scaling up the system proved to be very demanding. The current system has thus
far been demonstrated in multiple domains, including a complex logistics transporta-
tion domain where it generated a library of 1000 cases, showed strong improvements
in problem-solving performance, and pushed the solvability envelope to increaringly
more complex classes of problems.
Acknowledgments
First, I am grateful to my advisor, Jaime Carbonell. Working with Jaime was a
continuous learning experience. Jaime shared with me many of his ideas and helped
me solve many problems I faced along this work. He gave me extremely insightful
advice. With his sharp and quick understanding of the issues, he helped me organize
and apply my entangled thoughts and ideas. Jaime always trusted me and made me
feel confident about my thesis work.
I would like to thank my other thesis committee members, Tom Mitchell, Paul
Rosenbloom, and Herb Simon, for all the helpful suggestions and comments on my
research. Herb Simon a&id Tom Mitchell followed my work very closely. Herb Simon
was always interested on the detailed progress of my work. He encouraged me to
reach a full implementation of the system, so I could scale it up to tasks of realistic
size. Thanks to Herb Simon, I have a much broader view of this research. With him I
learned to appreciate many of the early research efforts in Al specially in learning. In
our several meetings, Tom Mitchell helped me keeping focused on my thesis goals, at
the same time thathe opened my interests to other related issues in machine learning.
He raised challenging questions while listening carefully to my ideas and discussing
his own with me. Through several email conversations, Paul Rosenbloom provided
me very useful feedback on my work. He helped me clarify some of my claims of this
work.
Allen Newell was not in my thesis committee. Still he shaped my thinking. We
had several long meetings where we discussed my work. Allen Newell was always
there pointing out the interesting points, forcing me to clarify my ideas, making sure
I myself would understand well the concepts, the algorithms, the implementation.
From Allen Newell I learned every day more and more what research is. Through
him I understood how to work dynamically towards my research goals. He was a real
mentor and friend.
I am thankful to all the members of the PRODIGY research group. Craig Knoblock
contributed in several ways to the accomplishment of this thesis. From very early, he
made me feel extremely at ease to discuss with him my most daring and controversial
research ideas. Craig was ready to listen, to criticize, and to help me develop what
was worth pursuing. I knew I could share with Craig my setbacks and enthusiasms.
I am also very grateful to Alicia P~rez for her help in implementing and debugging
NoLIMIT, the first nonlinear planner of PRODIGY. Alicia also implemented the first
version of part of the memory model that I designed in this thesis. Alicia and I built a
very strong and fruitful working relationship. Daniel Borrajo helped me with a major
part of the design and implementation of NOLIMIT. He put a large effort towards
this project, and accomplished it in a very short time while Daniel visited CMU. I
thank Yolanda Gil and Robert Joseph for many discussions and much support along
the years of my thesis. Special thanks go to Steven Minton for having started the
PRODIGY research project. Dan Kuokka, Oren Etzioni, Xuemei Wang, Jim Blythe,
Scott Reilly, Joe Bates, Dan Kahn, Masahiko Iwamoto, and Michael Miller all left
a touch in this thesis through discussions, suggestions, or help with system issues. i
thank Alicia P6rez, Angela Hickman, and Jim Blythe for having read major parts of
this thesis. Each one provided me with comments that improved the quality of the
presentation.
I want to thank in a very special way one of my officemates, Puneet Kumar. I
enjoyed immensely his company and thank him very much for his friendship. I ben-
efitted tremendously from his ceaseless help with system changes and enhancements.
His help extended much beyond school in a very wide range of situations, includ-
ing rides to the airport, cooking, shopping, and occasionally looking after my sons.
Thanks, Puneet!
I thank Satya and the CODA research group for having supplied me with a portable
laptop that I could use disconnected from the network. I acknowledge Jay Kistler's
thesis work which allowed the transparent disconnected operation. Special thanks to
Puneet Kumar and Jay Kistler for smoothing my involvement in this experimental
project.
The School of Computer Science at CMU is a special place. I acknowledge Nico
Habermann for having consistently promoted a community spirit among the members
of this large research group. I thank Sharon Burks for her constant willingness to
make more pleasant and facilitate our students' lives. Thanks to the facilities group in
general and to Bob McDivett in particular. Also I am thankful for the help provided
by Jennifer Jones in a variety of last-minute copying and mailing tasks.
During my years as a graduate student in SCS, I made many friends who con-
tributed to create such a unique working environment. Besides the friends already
mentioned, though certain that the list is not exhaustive, I would like to name Alan
Christiansen, Andrew Hastings, Raul Vald6s-Prez, Aarti Gupta, Anurag Acharya,
Dean Pomerleau, Spiro Michaylov, Francesmary Modugno, Amy Zaremski, Kevin
Knight, Peter Shell, Peter Jansen, Jill Fain, Mark Perlin, and David Steere.
Finally, I would like to thank my family. Back in Lisbon, my parents and all my
family courageously supported and encouraged this work, in spite of the inevitable
long separation. I thank them all for this. I am grateful to my parents and parents-
in-law for making our returns home on vacation so wonderful, full of the little things
they know we miss so much. Thank you for all their letters, their telephone calls,
their visits, thank you for all their love that really carried me through these years.
I am very thankful also for all their help taking care of my sons, Andr6 and Pedro,
who love so much going to Portugal to be with their grandparents, aunts, uncles, and
cousins.
Last, but most important, I would like to thank Manel, Pedro, Andr6, and B.rbara
for their loving support. My thesis research had its ups and downs and so did my
enthusiasm and my belief that it could be finished. Not always did I manage to leave
my research problems at CMU, but took them home with me consuming my mind. I
have no words to thank Manel, Andr6 and Pedro, for having lived with me through
this thesis. They were always here to love me, encourage me, and make me feel that
it was all worth. I fear that my thesis work stole from them much of my attention,
and deprived me from enjoying their company. In particular I want to thank Pedro
and Andr6 for the many weekends that we spent together at CMU. They were always
cheerful and packed their books and toys happily for the CMU journeys without any
complaint. It would have been very hard to complete this thesis without Manel's
support. I thank him also in particular for his surprise on the day of my defense.
With all my heart, I dedicate this thesis to Manel, Andr6, and Pedro.
Contents
1
Introduction 1
1.1 Machine learning and problem solving ..... ................. 2
1.2 The thesis within PRODIGY ............ ....................... 4
1.2.1 Analogy versus EBL in PRODIGY ........ ................ 5
1.3 The thesis ......... ................................. 7
1.3.1 Scientific contributions ............................ 9
2 Overview 13
2.1 Automatic case generation ................ ................ 14
2.1.1 Defining a problem ....... ........................ 14
2.1.2 Problem solving run ....... ....................... 15
2.1.3 Justification structure ....... ...................... 17
2.2 Automatic case storage ........ .......................... 19
2.2.1 Foot-printing the initial state ...... .................. 20
2.2.2 Introducing into memory another one-goal case ............ 21
2.2.3 Storing in memory two additional two-goal problems ..... ... 22
2.3 Automatic case retrieval ........ ......................... 27
2.4 Automatic case replay ................................ ... 28
2.5 Summary of the example ................................ 31
2.6 A reader's guide to the thesis ....... ...................... 32
3 The Problem Solver 35
3.1 Motivation ......... ................................. 35
3.1.1 Linear problem solving ....... ...................... 36
3.1.2 Nonlinear problem solving ....... .................... 40
3.2 NOLIMIT - The search algorithm ....... .................... 42
3.3 Formal definition of the problem solving procedure ............ ... 44
3.3.1 Failing and backtracking ........................... 48
3.3.2 Control knowledge ....... ........................ 50
3.4 An example: solving a one-way-rocket problem ................. 50
3.5 Summary ......... ................................. 54
CONTENTS
4 Automatic Generation of Cases 57
4.1 Annotating the search path ....................... 57
4.1.1 Decision points .......................... 59
4.1.2 Justification structures at decision nodes ................. 60
4.1.3 The language ........ ........................... 61
4.2 Formal description of the annotation procedure ................. 63
4.2.1 Annotating the subgoaling structure ..... .............. 63
4.2.2 Annotating the failures ............................. 65
4.3 An example in the extended-STRIPS domain ................... 66
4.4 Summary ......... ................................. 71
5 Automatic Storage of Cases 73
5.1 Identifying the independent subparts of a case ............ . . . 74
5.1.1 Transforming a total order into a partial order ............ 74
5.1.2 Goal indices ........ ............................ 78
5.2 Identifying the relevant initial state ......................... 80
5.2.1 Disambiguating the notion of "relevant". ................ 81
5.2.2 Foot-printing the initial state ....... ............... 83
5.3 Organization of the case library ...... ..................... 85
5.3.1 Parameterizing the problem solving situation .............. 87
5.3.2 The goal statement indexing structures ................. 88
5.3.3 The initial state discrimination network ................. 91
5.4 The complete storage algorithm ........................... 93
5.5 Summary ......... ................................. 98
6 Automatic Retrieval of Cases 99
6.1 The ground for the retrieval procedure ....... ................. 99
6.1.1 What are similar problem solving situations? . . . . . . . . . .. . . 101
6.1.2 How can retrieval be efficient in a large case library? . . .. .. . 102
6.2 Defining a similarity metric ...... ....................... 104
6.2.1 A direct similarity metric ....... .................... 105
6.2.2 Global foot-printing similarity metric ................... 105
6.2.3 Interacting foot-printing similarity metric ............... 107
6.3 The retrieval procedure ................................. 107
6.3.1 Making the implementation efficient ................... 110
6.3.2 Illustrative example ............................... 110
6.4 Trading off retrieval and search costs ........................ 117
6.5 Summary .......... ................................. 120