How much data is enough?

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How much data is enough? Generating reliable
policies w/MDPs

• Joel Tetreault
• University of Pittsburgh
• LRDC
• July 14, 2006

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Problem

• Problems with designing spoken dialogue systems
• How to handle noisy data or miscommunications?
• Hand-tailoring policies for complex dialogues?
• What features to use?
• Previous work used machine learning to improve
  the dialogue manager of spoken dialogue systems
• Singh et al., 02 Walker, 00 Henderson et
  al., 05
• However, very little empirical work Paek et al.,
  05 Frampton 05 on comparing the utility of
  adding specialized features to construct a better
  dialogue state

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Goal

• How does one choose which features best
  contribute to a better model of dialogue state?
• Goal show the comparative utility of adding
  three different features to a dialogue state
• 4 features concept repetition, frustration,
  student performance, student moves
• All are important to tutoring systems, but also
  are important to dialogue systems in general

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Previous Work

• In complex domains, annotation and testing is
  time-consuming so it is important to properly
  choose best features beforehand
• Developed a methodology for using Reinforcement
  Learning to determine whether adding complex
  features to a dialogue state will beneficially
  alter policies Tetreault Litman, EACL 06
• Extensions
• Methodology to determine which features are the
  best
• Also show our results generalize over different
  action choices (feedback vs. questions)

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Outline

• Markov Decision Processes (MDP)
• MDP Instantiation
• Experimental Method
• Results
• Policies
• Feature Comparison

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Markov Decision Processes

• What is the best action an agent should take at
  any state to maximize reward at the end?
• MDP Input
• States
• Actions
• Reward Function

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MDP Output

• Policy optimal action for system to take in each
  state
• Calculated using policy iteration which depends
  on
• Propagating final reward to each state
• the probabilities of getting from one state to
  the next given a certain action
• Additional output V-value the worth of each
  state

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MDPs in Spoken Dialogue
MDP works offline
MDP
Training data
Policy
Dialogue System
User Simulator
Human User
Interactions work online
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ITSPOKE Corpus

• 100 dialogues with ITSPOKE spoken dialogue
  tutoring system Litman et al. 04
• All possible dialogue paths were authored by
  physics experts
• Dialogues informally follow question-answer
  format
• 60 turns per dialogue on average
• Each student session has 5 dialogues bookended by
  a pretest and posttest to calculate how much
  student learned

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Corpus Annotations

• Manual annotations
• Tutor Moves (similar to Dialog Acts)
• Forbes-Riley et al., 05
• Student Frustration and Certainty
• Litman et al. 04 Liscombe et al. 05
• Automated annotations
• Correctness (based on students response to last
  question)
• Concept Repetition (whether a concept is
  repeated)
• Correctness (past performance)

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MDP State Features
Features Values
Correctness Correct (C), Incorrect (I)
Certainty Certain (cer), Neutral (neu), Uncertain (unc)
Concept Repetition New Concept (0), Repeated (R)
Frustration Frustrated (F) , Neutral (N)
Correctness 50-100 (H)igh, 0-49 (L)ow
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MDP Action Choices
Action Example Turn
SAQ (Short Answer Question) What is the direction of that force relative to your fist?
CAQ (Complex Answer Question) What is the definition of Newtons Second Law?
Mix If it doesnt hit the center of the pool what do you know about the magnitude of its displacement from the center of the pool when it lands? Can it be zero? Can it be nonzero?
NoQ So you can compare it to my response
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MDP Reward Function

• Reward Function use normalized learning gain to
  do a median split on corpus
• 10 students are high learners and the other 10
  are low learners
• High learner dialogues had a final state with a
  reward of 100, low learners had one of -100

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Methodology

• Construct MDPs to test the inclusion of new
  state features to a baseline
• Develop baseline state and policy
• Add a feature to baseline and compare polices
• A feature is deemed important if adding it
  results in a change in policy from a baseline
  policy given 3 metrics
• of Policy Differences (Diffs)
• Policy Change (PC)
• Expected Cumulative Reward (ECR)
• For each MDP verify policies are reliable
  (V-value convergence)

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Hypothetical Policy Change Example
0 Diffs
5 Diffs
B1 State Policy B1Certainty State
1 C CAQ C,Cer C,Neu C,Unc
2 I SAQ I,Cer I,Neu I,Unc
Cert 1 Policy ?
CAQ CAQ CAQ
SAQ SAQ SAQ
Cert 2 Policy ?
Mix CAQ Mix
Mix CAQ Mix
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Tests
B2
Concept
B1
Frustration
Correctness
Certainty
Baseline 2
Baseline 1
Correct
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Baseline

• Actions SAQ, CAQ, Mix, NoQ
• Baseline State Correctness

Baseline network
SAQCAQMixNoQ
C
I
FINAL
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Baseline 1 Policies
State State Size Policy
1 C 1308 NoQ
2 I 872 Mix

• Trend if you only have student correctness as a
  model of student state, give a hint or other
  state act to the student, otherwise give a Mix of
  complex and short answer questions

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But are our policies reliable?

• Best way to test is to run real experiments with
  human users with new dialogue manager, but that
  is months of work
• Our tact check if our corpus is large enough to
  develop reliable policies by seeing if V-values
  converge as we add more data to corpus
• Method run MDP on subsets of our corpus
  (incrementally add a student (5 dialogues) to
  data, and rerun MDP on each subset)

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Baseline Convergence Plot
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Methodology Adding more Features

• Create more complicated baseline by adding
  certainty feature (new baseline B2)
• Add other 4 features (concept repetition,
  frustration, performance, student move)
  individually to new baseline
• Check V-value and policy convergence
• Analyze policy changes
• Use Feature Comparison Metrics to determine the
  relative utility of the three features

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Tests
B2
Concept
B1
Frustration
Correctness
Certainty
Baseline 2
Baseline 1
Correct
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Certainty

• Previous work (Bhatt et al., 04) has shown the
  importance of certainty in ITS
• A student who is certain and correct, may require
  a harder question since he or she is doing well,
  but one that is correct but showing some doubt is
  a sign they are becoming confused, give an easier
  question

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B2 Baseline Certainty Policies
B1 State Policy B1Certainty State Certainty Policy
1 C NoQ C,Cer C,Neu C,Unc Mix SAQ Mix
2 I Mix I,Cer I,Neu I,Unc Mix NoQ Mix
Trend if neutral, give SAQ or NoQ, else give Mix
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Baseline 2 Convergence Plots
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Baseline 2 Diff Plots
Diff For each subset corpus, compare policy with
policy generated with full corpus
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Tests
B2
Concept
B1
Frustration
Correctness
Certainty
Baseline 2
Baseline 1
Correct
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Feature Comparison (3 metrics)

• Diffs
• Number of new states whose policies differ from
  the original
• Insensitive to how frequently a state occurs
• Policy Change (P.C.)
• Take into account the frequency of each
  state-action sequence

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Feature Comparison

• Expected Cumulative Reward (E.C.R.)
• One issue with P.C. is that frequently occurring
  states have low V-values and thus may bias the
  score
• Use the expected value of being at the start of
  the dialogue to compare features
• ECR average V-value of all start states

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Feature Comparison Results
State Feature Diffs P.C. E.C.R
Student Move 10 82.2 43.21
Concept Repetition 10 80.2 39.52
Frustration 8 66.4 31.30
Percent Correctness 4 44.3 28.47

• Trend of SMove gt Concept Repetition gt Frustration
  gt Percent Correctness stays the same over all
  three metrics
• Baseline Also tested the effects of a binary
  random feature
• If enough data, a random feature should not alter
  policies
• Average diff of 5.1

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How reliable are policies?
Frustration
Concept
Possible data size is small and with increased
data we may see more fluctuations
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Confidence Bounds

• Hypothesis instead of looking at the V-values
  and policy differences directly, look at the
  confidence bounds of each V-value
• As data increases, confidence of V-value should
  shrink to reflect a better model of the world
• Additionally, the policies should converge as
  well

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Confidence Bounds

• CBs can also be used to distinguish how much
  better an additional state feature is over a
  baseline state space
• That is, if the lower bound of a new state space
  is greater than the upper bound of the baseline
  state space

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Crossover Example
More complicated Model
ECR
Baseline
Data
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Confidence Bounds App 2

• Automatic model switching
• If you know a model, at its worst (ie. Its
  lower bound is better than another models upper
  bound) then you can automatically switch to the
  more complicated model
• Good for online RL applications

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Confidence Bound Methodology

• For each data slice, calculate upper and lower
  bounds on the V-value
• Take transition matrix for slice and sample from
  each row using direch. statistical formula 1000
  times
• do this b/c real world data is not exactly
  approximating what data is like in the real
  world, but may be close
• So get 1000 new transition matrices that are all
  very similar
• Run MDP on all 1000 transition matrices to get a
  range of ECRs
• Rows with not a lot of data are very volatile so
  expect large range of ECRs, but as data
  increases, transition matrices should stabilize
  such that most of the new matrices produce
  similar policies and values as the original
• Take upper and lower bounds at 2.5 percentile

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Experiment

• Original action/state setup did not show anything
  promising
• State/action space too large for data?
• Not best MDP instantiation
• Looked at a variety of MDP configurations
• Refined reward metric
• Adding discourse segmentation

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essay Instantiation with 0305 data
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essay Baseline1
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essay Baseline2
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essay B2SMove
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Feature Comparison Results
State Feature Diffs P.C. E.C.R
Student Move 5 43.4 49.17
Concept Repetition 3 25.5 42.56
Frustration 1 0.03 32.99
Percent Correctness 3 11.19 28.50

• Reduced state size Certainty CertNeutral,
  Uncert
• Trend that SMove and Concept Repetition are the
  best features
• B2 ECR 31.92

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Baseline 1
Upper 23.65 Lower 0.24
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Baseline 2
Upper 57.16 Lower 39.62
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B2 Concept Repetition
Upper 64.30 Lower 49.16
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B2Percent Correctness
Upper 48.42 Lower 32.86
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B2Student Move
Upper 61.36 Lower 39.94
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Discussion

• Baseline 2 has crossover effect and policy
  stability
• More complex features (B2 X) have crossover
  effect, but not sure if polices are stable (some
  stabilize at 17 students)
• Indicates that 100 dialogues isnt enough for
  even this simple MDP? (but is enough for
  baseline 2 to feel confident about?)