Deductive (explanation-based) learning
Prof. Gheorghe Tecuci
Learning Agents Laboratory
Computer Science Department
George Mason University
 2002, G.Tecuci, Learning Agents Laboratory
1
Overview
The explanation-based learning problem
The explanation-based learning method
The utility problem
Discussion
Recommended reading
 2002, G.Tecuci, Learning Agents Laboratory
2
Explanation-based learning problem
Given
A training example
A positive example of a concept to be learned.
Learning goal
A specification of the desirable features of the concept to be learned
from the training example.
Background knowledge
Prior knowledge that allows proving (explaining) that the training
example is indeed a positive example of the concept.
Determine
A concept definition representing a deductive generalization of the
training example that satisfies the learning goal.
Purpose of learning
Improve the problem solving efficiency of the agent.
 2002, G.Tecuci, Learning Agents Laboratory
3
Explanation-based learning problem: illustration
Given
Training Example - The description of a particular cup:
OWNER(OBJ1, EDGAR) & COLOR(OBJ1, RED) & IS(OBJ1, LIGHT) & PART-OF(CONCAVITY1,
OBJ1) & ISA(CONCAVITY1, CONCAVITY) & IS(CONCAVITY1, UPWARD-POINTING) & PARTOF(BOTTOM1, OBJ1) & ISA(BOTTOM1, BOTTOM) & IS(BOTTOM1, FLAT) &
PART-OF(BODY1, OBJ1) & ISA(BODY1, BODY) & IS(BODY1, SMALL) &
PART-OF(HANDLE1, OBJ1) & ISA(HANDLE1, HANDLE) & LENGTH(HANDLE1, 5)
Learning goal
Find a sufficient concept definition for CUP, expressed in terms of the features used
in the training example (LIGHT, HANDLE, FLAT, etc.)
Background Knowledge
"x, LIFTABLE(x) & STABLE(x) & OPEN-VESSEL(x)  CUP(x)
"x "y, IS(x, LIGHT) & PART-OF(y, x) & ISA(y, HANDLE)  LIFTABLE(x)
"x "y, PART-OF(y, x) & ISA(y, BOTTOM) & IS(y, FLAT)  STABLE(x)
"x "y, PART-OF(y,x) & ISA(y, CONCAVITY) & IS(y, UPWARD-POINTING)  OPEN-VESSEL(x)
Determine
A deductive generalization of the training example that satisfies the learning goal
"x"y1"y2"y3, [PART-OF(y1, x) & ISA(y1, CONCAVITY) & IS(y1, UPWARD-POINTING) &
PART-OF(y2, x) & ISA(y2, BOTTOM) & IS(y2, FLAT) & IS(x, LIGHT) &
PART-OF(y3, x) & ISA(y3, HANDLE) => CUP(x)]
 2002, G.Tecuci, Learning Agents Laboratory
4
Overview
The explanation-based learning problem
The explanation-based learning method
The utility problem
Discussion
Recommended reading
 2002, G.Tecuci, Learning Agents Laboratory
5
Explanation-based learning method
Explain
Construct an explanation that proves that the training
example is an example of the concept to be learned.
Generalize
Generalize the found explanation as much as possible so
that the proof still holds, and extract from it a concept
definition that satisfies the learning goal.
 2002, G.Tecuci, Learning Agents Laboratory
6
Explain - Prove that the training example is a cup:
CUP(OBJ1)
STABLE(OBJ1)
OPEN-VESSEL(OBJ1)
LIFTABLE(OBJ1)
PART-OF
IS(BOTTOM1,
(BOTTOM1,
FLAT)
OBJ1)
ISA(BOTTOM1,BOTTOM)
PART-OF
IS(CONCAVITY1,
(CONCAVITY1,
UPWARD-POINTING)
OBJ1)
ISA(CONCAVITY1,CONCAVITY)
IS(OBJ1,LIGHT) ISA(HANDLE1,
HANDLE)
PART-OF(HANDLE1, OBJ1)
The leaves of the proof tree are those features of the training example
that allows one to recognize it as a cup. By building the proof one
isolates the relevant features of the training example.
 2002, G.Tecuci, Learning Agents Laboratory
7
LIGHT
CONCAVITY
ISA
CONCAVITY-1
ISA
IS
PART-OF
IS
UPWARD-POINTING
BOTTOM1
RED
IS
PART-OF
OBJ1
PART-OF BODY1
PART-OF
COLOR
BOTTOM
OWNER
EDGAR
FLAT
ISA
BODY
IS
SMALL
HANDLE1 ISA
HANDLE
LENGTH
5
The semantic network representation of the cup example.
The enclosed features are the relevant ones.
 2002, G.Tecuci, Learning Agents Laboratory
8
Generalize the proof tree as much as possible so that the proof still holds:
- replace each rule instance with its general pattern;
- find the most general unification of these patterns.
CUP(x1)
STABLE(x1)
OPEN-VESSEL(x1)
STABLE(x3)
LIFTABLE(x1)
LIFTABLE(x4)
OPEN-VESSEL(x2)
PART-OF(y2,x3)
IS(y2,FLAT)
ISA(y2,BOTTOM)
PART-OF(y1,x2)
IS(y1,UPWARD-POINTING)
IS(x4,LIGHT)
ISA(y1,CONCAVITY)
OPEN-VESSEL (x1)

OPEN-VESSEL (x2)
ISA(y3,HANDLE)
PART-OF(y3,x4)
STABLE (x1)

STABLE (x3)
LIFTABLE (x1)

LIFTABLE (x4)
Therefore x1=x2=x3=x4=x
 2002, G.Tecuci, Learning Agents Laboratory
9
CUP(x1)
STABLE(x1)
OPEN-VESSEL(x1)
LIFTABLE(x1)
PART-OF(y2,x1)
IS(y2,FLAT)
ISA(y2,BOTTOM)
PART-OF(y1,x1)
IS(y1,UPWARD-POINTING)
ISA(y1,CONCAVITY)
IS(x1,LIGHT)
ISA(y3,HANDLE)
PART-OF(y3,x1)
The leaves of this generalized proof tree represent an operational definition of the
concept CUP:
"x1"y1"y2"y3, [PART-OF(y1, x1) & ISA(y1, CONCAVITY) &
IS(y1, UPWARD-POINTING) & PART-OF(y2, x1) &
ISA(y2, BOTTOM) & IS(y2, FLAT) & IS(x1, LIGHT) &
PART-OF(y3, x1) & ISA(y3, HANDLE) => CUP(x1)]
 2002, G.Tecuci, Learning Agents Laboratory
10
Discussion
How does this learning method improve the efficiency of
the problem solving process?
 2002, G.Tecuci, Learning Agents Laboratory
11
The goal of this learning strategy is to improve the efficiency in problem solving.
The agent is able to perform some task but in an inefficient manner. We would like
to teach the agent to perform the task faster.
Consider, for instance, an agent that is able to recognize cups. The agent receives a
description of a cup that includes many features. The agent will recognize that this
object is a cup by performing a complex reasoning process, based on its prior
knowledge. This process is illustrated by the proof tree which demonstrates that
object o1 is indeed a cup: The object o1 is light and has a handle. Therefore it is
liftable. An so on … being liftable, stable and an open vessel, it is a cup. However,
the agent can learn from this process to recognize a cup faster.
The next step in the learning process is to generalize the proof tree. While the initial
tree proves that the specific object o1 is a cup, the generalized tree proves that any
object x which is light, has a handle and some other features is a cup. Therefore, to
recognize that an object o2 is a cup, the agent only needs to look for the presence
of these features discovered as important. It no longer needs to build a complex
proof tree. Therefore cup recognition is done much faster.
Finally, notice that the agent needs only one example to learn from. However, it
needs a lot of prior knowledge to prove that this example is a cup. Providing such
prior knowledge to the agent is a very complex task.
 2002, G.Tecuci, Learning Agents Laboratory
12
Overview
The explanation-based learning problem
The explanation-based learning method
The utility problem
Discussion
Recommended reading
 2002, G.Tecuci, Learning Agents Laboratory
13
The utility problem: discussion
Let us assume that we have learned an operational definition of the
concept “cup”.
What happens with the efficiency of recognizing cups covered by
the learned rule?
Why?
What happens with the efficiency of recognizing cups when the
input is not covered by the learned rule?
Why?
When does the efficiency increase?
How to assure the increase of the efficiency?
 2002, G.Tecuci, Learning Agents Laboratory
14
The utility problem: a solution
Cost/benefit formula to estimates the utility of the learned rule on the
efficiency of the system:
Utility = (AvrSavings * ApplicFreq) - AvrMatchCost
where
AvrSavings = the average time savings when the rule is applicable
ApplicFreq = the probability that the rule is applicable when it is tested
AvrMatchCost = the average time cost of matching the rule
 2002, G.Tecuci, Learning Agents Laboratory
15
The utility problem: discussion of the solution
How to estimate ApplicFreq?
Maintain a statistic on the rule's use during subsequent problem solving.
How to estimate AvrMatchCost?
Measure rule’s matching cost during subsequent problem solving.
How to estimate AvrSavings?
Measure the savings requires running the problem solver with and
without the rule on each problem.
Is this practical?
Which would be a good heuristic?
Heuristic: One possible solution is to use an estimate of the rule's
average savings based on the savings that the rule would have
produced on the training example from which it was learned.
Conclusion: The system maintains a statistic on the rule's use during
subsequent problem solving, in order to determine its utility. If the rule
has a negative utility, it is discarded.
 2002, G.Tecuci, Learning Agents Laboratory
16
The utility of the learned rules
Explanation-based learning has been introduced as a method for improving the efficiency of a system.
Let us consider again the explanation-based system learning an operational definition of the concept CUP.
The system has learned a new rule for recognizing a certain kind of cup. This rule does not contain any new
knowledge. It is just a compilation of some other rules from the knowledge base.
Adding this new rule in the KB has the following effects on system's efficiency:
- increases the efficiency in recognizing cups covered by the learned rule;
- decreases the efficiency in recognizing cups that are not covered by the learned rule.
Adding the operational definition of cup into the KB will increase the global performance of the system only if
the first effect is more important then the second one.
Both these effects may be combined into a cost/benefit formula that indicates the utility of the rule with
respect to the efficiency of the system:
Utility = (AvrSavings * ApplicFreq) - AvrMatchCost
where
AvrSavings = the average time savings when the rule is applicable
ApplicFreq = the probability that the rule is applicable when it is tested
AvrMatchCost = the average time cost of matching the rule
After learning a rule, the system should maintain a statistic on the rule's use during subsequent problem
solving, in order to determine its utility. If the rule has a negative utility, it is discarded.
Unfortunately, although the match cost and the application frequency can be directly measured during
subsequent problem solving, it is more difficult to measure the savings. Doing so would require running the
problem solver with and without the rule on each problem. And this would have to be done for all rules.
One possible solution is to use an estimate of the rule's average savings based on the savings that the rule
would have produced on the training example from which it was learned.
 2002, G.Tecuci, Learning Agents Laboratory
17
Overview
The explanation-based learning problem
The explanation-based learning method
The utility problem
Discussion
Recommended reading
 2002, G.Tecuci, Learning Agents Laboratory
18
Exercise
Given
• A training Example
The following example of “supports”:
[ book(book1) & material(book1, rigid) & cup(cup1) & material(cup1, rigid) &
above(cup1, book1) & touches(cup1, book1) ] => supports(book1, cup1)
• Learning goal
Find a sufficient concept definition for “supports”, expressed in terms of the
features used in the training example.
• Background Knowledge
"x "y [on-top-of(y, x) & material(x, rigid)  supports(x, y)]
"x "y [above(x, y) & touches(x, y)  on-top-of(x, y)]
"x "y "z [above(x, y) & above(y, z)  above(x, z)]
Determine
A deductive generalization of the training example that satisfies the learning goal.
 2002, G.Tecuci, Learning Agents Laboratory
19
Discussion
Do we need a training example to learn an operational definition of
the concept?
Why?
Answer:
The learner does not need a training example. It can simply built
proof trees from top-down, starting with an abstract definition of
the concept and growing the tree until the leaves are operational
features.
However, without a training example the learner will learn many
operational definitions. The training example focuses the learner on
the most typical example.
 2002, G.Tecuci, Learning Agents Laboratory
20
Discussion
What is the classification accuracy of deductive learning?
What is the classification accuracy of an example classified as
positive? Why?
What is the classification accuracy of an example classified as
negative? Why?
How could one improve the classification accuracy?
 2002, G.Tecuci, Learning Agents Laboratory
21
Learning from several positive examples
Learn an operational definition from the first example. Consider this
as the first term of a disjunctive definition.
Eliminate all the examples already covered by this definition.
Learn another operational definition from an uncovered example.
Eliminate all the examples covered by this new definition and add it
as a new term in the disjunctive definition of the concept.
Continue this process until there is no training example left.
 2002, G.Tecuci, Learning Agents Laboratory
22
Discussion
How to use negative examples?
Develop a theory of why something is a negative example of
some concept and apply the standard method.
Does such an approach make sense when we already have a
theory that explains positive examples? Why?
Sometimes it is easier to explain that something is a negative
example.
Could you provide an example of such a case?
 2002, G.Tecuci, Learning Agents Laboratory
23
Discussion
How could we apply explanation-based learning to learn inference
rules from facts?
How could we apply explanation-based learning to learn macrooperators from action plans?
 2002, G.Tecuci, Learning Agents Laboratory
24
Learning inference rules: illustration
Given
• Training Example
An input fact: RICE-AREA(VIETNAM)
• Learning goal
Learn a general inference rule allowing the direct derivation of the input fact from facts
explicitly represented in the background knowledge (e.g., RAINFALL, CLIMATE, SOIL)
• Background Knowledge
RAINFALL(VIETNAM, HEAVY); CLIMATE(VIETNAM, SUBTROPICAL);
SOIL(VIETNAM, RED-SOIL); LOCATION(VIETNAM, SE-ASIA)
"x, CLIMATE(x, SUBTROPICAL)  TEMPERATURE(x, WARM)
"x, RAINFALL(x, HEAVY)  WATER-SUPPLY(x, HIGH)
"x, SOIL(x, RED-SOIL)  SOIL(x, FERTILE-SOIL)
"x, WATER-SUPPLY(x, HIGH) & TEMPERATURE(x, WARM) &
SOIL(x, FERTILE-SOIL)  RICE-AREA(x)
This background knowledge could be used in proving the input fact.
Determine
• A general inference rule that allows the direct derivation of the input from the facts stored in
the knowledge base:
"x, RAINFALL(x, HEAVY) & CLIMATE(x, SUBTROPICAL) & SOIL(x, RED-SOIL)
=> RICE-AREA(x)
 2002, G.Tecuci, Learning Agents Laboratory
25
Learning macro-operators: illustration
Consider the following situation that involves a robot that could go from one
room to another and could push boxes through the doors:
InRoom(Robot, Room1)
InRoom(Box, Room2)
Connects(Door1, Room1, Room2)
Connects(Door2, Room2, Room3)
Connects(Door3, Room1, Room4)
Room1
Robot
Door3
Room4
Room2
Door1
Box
Door2
Room3
Apply explanation-based learning to learn a general macro-operator from the
following example of problem solving episode
to achieve the goal:
InRoom(Box, Room1)
perform the actions:
GoThru(Robot, Door1, Room1, Room2)
PushThru(Robot, Box, Door1, Room2, Room1)
The knowledge of the system consists of the action models and inference rule
from the next slide.
 2002, G.Tecuci, Learning Agents Laboratory
26
Learning macro-operators: illustration (cont.)
GoThru(a, d, r1, r2)
; robot a goes through door d from room r1 to room r2
Preconditions: InRoom(a, r1)
; a is in room r1
Connects(d, r1, r2) ; door d connects room r1 with room r2
Effects:
InRoom(a, r2)
; a is in room r2
PushThru(a, o, d, r1, r2)
; a pushes box o through d from r1 to r2
Preconditions: InRoom(a, r1)
; a is in room r1
InRoom(o, r1)
; o is in room r1
Connects(d, r1, r2) ; door d connects room r1 with room r2
Effects:
InRoom(a, r2)
; a is in room r2
InRoom(o, r2)
; o is in room r2
Connects(d, r1, r2) => Connects(d, r2, r1)
; if d connects r1 with r2 then it also connects r2 with r1.
 2002, G.Tecuci, Learning Agents Laboratory
27
Learning macro-operators: illustration (cont.)
GoAndPushThru(a, o, d1, d2, r1, r2, r3)
; the robot goes from room r1 into room r2 and pushes the box into room r3
Preconditions: InRoom(a, r1)
InRoom(o, r2)
Connects(d1, r1, r2)
Connects(d2, r2, r3)
; a is in room r1
; o is in room r2
; door d1 connects room r1 with room r2
; door d2 connects room r2 with room r3
Effects:
; a is in room r3
; o is in room r3
 2002, G.Tecuci, Learning Agents Laboratory
InRoom(a, r3)
InRoom(o, r3)
28
Discussion
How does deductive learning compare with inductive learning?
What comparison criteria to consider?
Input examples
EIL – many, both positive and negative
EBL – only one positive example
Background knowledge
EIL – very little needed (e.g. generalization hierarchy)
EBL – complete and correct domain theory
Type of inference
EIL – inductive
EBL – deductive
Result of learning
EIL – improves system’s competence
EBL – improves system’s efficiency
 2002, G.Tecuci, Learning Agents Laboratory
29
General features of explanation-based learning
• Needs only one example
• Requires complete knowledge about the concept
(which makes this learning strategy impractical).
• Improves agent's efficiency in problem solving
• Shows the importance of explanations in learning
 2002, G.Tecuci, Learning Agents Laboratory
30
Recommended reading
Mitchell T.M., Machine Learning, Chapter 11: Analytical Learning,
pp. 307 - 333, McGraw Hill, 1997.
Mitchell T.M., Keller R.M., Kedar-Cabelli S.T., Explanation-Based Generalization: A
Unifying View, Machine Learning 1, pp. 47-80, 1986. Also in Readings in Machine
Learning, J.W.Shavlik, T.G.Dietterich (eds), Morgan Kaufmann, 1990.
DeJong G., Mooney R., Explanation-Based Learning: An Alternative View, Machine
Learning 2, 1986. Also in Readings in Machine Learning, J.W.Shavlik, T.G.Dietterich
(eds), Morgan Kaufmann, 1990.
Tecuci G. & Kodratoff Y., Apprenticeship Learning in Imperfect Domain Theories, in
Kodratoff Y. & Michalski R. (eds), Machine Learning, vol 3, Morgan Kaufmann,
1990.
S. Minton, Quantitative Results Concerning the Utility of Explanation-Based
Learning, in Artificial Intelligence, vol. 42, pp. 363-392, 1990. Also in Shavlik J. and
Dietterich T. (eds), Readings in Machine Learning, Morgan Kaufmann, 1990.
 2002, G.Tecuci, Learning Agents Laboratory
31