March 20, 2004 Symposium on Reasoning and Learning in Cognitive Systems

Mixing Automatic and Deliberative Learning During

Problem Solving

Randolph M. Jones

Soar Technology &

Colby College

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Background

• There are alternative ways we might incorporate multi-step learning into a model– One approach would be to automate explicit

instruction of desired task behavior• Even this is difficult

– This talk focuses on models that can discover new problem-solving knowledge and strategies on their own

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Knowledge Tuning and Acquisition

• There are two primary ways a model can learn new strategies– Acquiring new task knowledge that allows more

complete or efficient coverage of a problem space– Tuning existing task knowledge so it is retrieved more

oportunistically

• Knowledge acquisition in its own right is also important– But this work suggests that knowledge acquisition

depends on knowledge tuning

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Knowledge Tuning

• Basic representational structure of knowledge “chunk” remains unchanged

• Retrieval/selection patterns associated with the knowledge do change

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Knowledge Acquisition

• Entirely new structured representations of long-term knowledge are added to the model’s knowledge base

• Or existing “chunks” of knowledge undergo structural changes

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Task Example: Solving Physics Problems

• Learning to solve physics problems involves learning new equations relevant to the problems, and learning the situations in which those equations should be used

• Students who “self-explain” study examples show greater improved performance than those who don’t (Chi et al., 1989)– Are they tuning knowledge or acquiring knowledge?

• Cascade (VanLehn, Jones, & Chi, 1992) models the “self-explanation effect” observed in humans learning to solve physics problems

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Task Example: Simple Addition

• There are a variety of strategies that can be used to perform elementary addition, some more efficient than others

• Children are usually instructed using a basic strategy, but invent a particular set of more efficient strategies on their own (Siegler & Jenkins, 1989)– Are they tuning knowledge or acquiring knowledge?

• GIPS (Jones & VanLehn, 1994) models the series of strategy shifts exhibited by children

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Cascade: Typical Problem

10 kg

30What is the tension in the string?

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Problem Solving

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Cascade: Typical Problem

30 45A B

C

What is the magnitude of each force?

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Cascade: Typical Example

• Let the knot be “the body”• FA, FB, FC are all the forces

acting on the body• The body is at rest, so

FA+FB+FC=0

• By projection, FAX+FBX=0

• By projection, FAY+FBY+FCY=0

• FAX=–FA cos 30 = –0.8666FA

• etc.

FA FB

FC

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Cascade: Modeling Goal

• Explain the learning process and other factors that cause students who carefully study examples to learn more effectively than students who do not

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Cascade: Knowledge Representation

• Long-term task knowledge is a set of physics equations, geometric equations, and rules for representing free-body diagrams– Implemented in Prolog

• Default problem-solving strategy is exhaustive depth-first search with backtracking– Straightforward application of Prolog

• Problem-solving goals are quantities (variables) for which the problem solver must compute a value

• Selection knowledge allows heuristic search by using past solution paths as analogies to the current problem

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Cascade: Learning Processes• Knowledge tuning

– Analogical Search Control– When Cascade succeeds in computing a value for a sought quantity,

it records a triple including the name of the problem, the sought quantity, and the equation that was used to compute the value

– The caching process occurs automatically and frequently, every time a subgoal is achieved

– On subsequent problems, Cascade • Attempts to map the current problem quantities and relations to the

analog problem• Searches for cached triples that mention problem analogs to the current

problem, together with an analogous sought quantity• Attempts the retrieved equation before falling back on the default

ordering of knowledge (if backtracking occurs)

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Cascade: Learning Processes

• Knowledge acquisition– Explanation-based Learning of Correctness

– If Cascade cannot solve a problem (after exhaustive search), it begins the search again, this time attempting a “repair” at the first point that backtracking is encountered

• Repairs occur by attempting to apply relevant “overly general rules” to the problem

• On success, Cascade stores a specialization of the overly general rule with the rest of the task knowledge

– The rule learning process occurs deliberatively and infrequently, only after the model has recognized an impasse in problem solving

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Problem Solving

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Cascade: Learning Interactions

• Knowledge acquisition only works if the model is repairing “the right gap” in a potential solution space

• The model can be guided toward the right gap:– By the directions in a worked example– By the quality of knowledge tuning

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Cascade: Learning InteractionsInitial problem state

Solution

Dead ends

False paths

Knowledge gap

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Cascade: Experimental Results

• No Analogical Search Control– Learns 3 correct rules– Solves 9 problems correctly

• No EBLC on examples– Learns 13 correct rules– Learns 4 incorrect rules– Solves 21 problems correctly (many using a backup

transformational analogy strategy)

• ASC & EBLC– Learns 22 correct rules– Solves 23 problems correctly

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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GIPS: Typical Problem

“Sum” Strategy

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GIPS: Modeling Goal

• Model how children independently invent the “Min” strategy with experience– “Min” is a more efficient strategy, suggesting

that it may be produced primarily by knowledge tuning

– However, there appear to be structural changes to the steps the children are taking to solve problems

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Problem Solving

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GIPS: Knowledge Representation

• Task knowledge is represented as STRIPS-like operators with preconditions, constraints, add conditions, and delete conditions

– Problem-solving algorithm is “flexible” means-ends analysis• TRANSFORM goal: Use features describing current state and goal to

retrieve a candidate operator to APPLY for the next step in the transformation

• APPLY goal: Execute the operator if possible, else set up a new TRANSFORM to the preconditions of the operator

• Retrieval/selection knowledge is encoded as probability estimates (for logical sufficiency and logical necessity) attached to each potential triggering feature for each operator

– State and Goal relations

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Problem Solving

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Example Bayesian Concept

• “Liftable”FEATURE LS LNsize is small 3.0 0.0weight is light 2.0 0.3has handle 2.0 0.3attached to floor 0.0 3.0color is red 1.0 1.0

• Note this example has propositional features, but features in GIPS are relational– GIPS uses a graph-based “maximal partial match” procedure to

map combinations of relations to “propositions”

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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GIPS: Learning Processes• Knowledge tuning

– Every time an APPLY goal leads to success or failure, GIPS updates the appropriate probability estimates for each state and goal feature present when the APPLY goal was created

• A = “Action A is the right thing to do next”

• F = “Feature F is true in the problem situation”

– A similar process occurs every time an operator executes (or not)

)(

)()|()|(

FP

APAFPFAP

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GIPS: Learning Processes

• Knowledge acquisition– When feature values for an operator’s

“execution concept” receive particularly strong “logical necessity” values, a deliberative process explicitly adds the new feature as a condition of the operator

• Another process removes features from the operator conditions

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The SUM-to-MIN Strategy Shift

I just counted “X”and X is the addend.(I have to count.)

I see X fingersand X is the addend.(I don’t have to count! I can use the counter for something else!)

X is the addend.(I don’t have to raise any fingers.)

March 20, 2004 Mixing Automatic and Deliberative Learning During

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GIPS Learning Interactions

• Bayesian updates happen continuously and automatically, leading to performance shifts based on retrieval of operators

• Based on accumulating evidence, the model periodically tries more drastic structural changes to operator preconditions, which have larger effects on subsequent retrieval patterns (because operator preconditions are used as subgoal retrieval cues and determine satisfaction of APPLY goals)

March 20, 2004 Mixing Automatic and Deliberative Learning During

Problem Solving

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Lessons

• It is difficult to acquire new knowledge without first tuning old knowledge

• Tuning old knowledge implies that you have some old knowledge to tune

• For complex learning, we need to focus on learning in the context of significant prior knowledge

• Tuning can help guide the search for building new operators (Cascade) as well as for adjusting the structural representations of existing operators (GIPS)– You only want to acquire new knowledge after you have

accumulated some evidence (from tuning) that the knew knowledge is appropriate and useful