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Repairing Decision-Making Programs Under Uncertainty Samuel Drews Aws Albarghouthi Loris DAntoni University of Wisconsin-Madison Example Fairness Condition decision- making program Example Fairness Condition sensitive feature (e.g.

  1. Repairing Decision-Making Programs Under Uncertainty Samuel Drews Aws Albarghouthi Loris D’Antoni University of Wisconsin-Madison

  3. Example Fairness Condition decision- making program

  4. Example Fairness Condition sensitive feature (e.g. minority)

  5. Example Fairness Condition probabilistic precondition

  6. FairSquare [OOPSLA 17] Unfairness proof Fairness proof

  7. FairSquare [OOPSLA 17] Unfairness proof Fairness proof

  8. Probabilistic program repair: definition 8 Input The postcondition does not hold

  9. Probabilistic program repair: definition 9 Input Output Program in repair model The postcondition does not hold The postcondition holds , Difference between and is minimal

  14. Challenge: What should the output of be on each input?

  17. 17 DIGITS: DIstribution-Guided InducTive Synthesis Sampling Samples Synthesizer from Candidate Candidate Repair accepted/rejected Probabilistic Verifier

  18. 18 DIGITS: DIstribution-Guided InducTive Synthesis Sample n inputs from precondition inp 1 inp 2 … inp n …

  19. 19 DIGITS: DIstribution-Guided InducTive Synthesis Sample n inputs from precondition inp 1 inp 2 … inp n … T T T … T T T T … F T T F … T T T F … F T F T T … .. .. .. … …

  20. 20 DIGITS: DIstribution-Guided InducTive Synthesis For each labeling, synthesize one Sample n inputs program consistent with it and from precondition check postcondition inp 1 inp 2 … inp n … T T T … T T T T … F T T F … T T T F … F T F T T … .. .. .. … …

  21. 21 DIGITS: DIstribution-Guided InducTive Synthesis For each labeling, synthesize one Sample n inputs program consistent with it and from precondition check postcondition inp 1 inp 2 … inp n … T T T … T T T T … F T T F … T T T F … F T F T T … .. .. .. … … …

  22. 22 DIGITS: DIstribution-Guided InducTive Synthesis For each labeling, synthesize one Sample n inputs program consistent with it and from precondition check postcondition inp 1 inp 2 … inp n … T T T … T T T T … F T T F … T T T F … F T F T T … .. .. .. … … …

  23. 23 DIGITS: DIstribution-Guided InducTive Synthesis For each labeling, synthesize one Sample n inputs program consistent with it and from precondition check postcondition inp 1 inp 2 … inp n … T T T … T Output that T T T … F has minimal T T F … T T T F … F T F T T … .. .. .. … … …

  27. 27 Does DIGITS work? 18 repair problems: decision trees, support vector machines 10 minute best-effort period All repaired!

  28. 28 Does DIGITS work?

  29. 29 Does DIGITS converge? Yes * * terms and conditions apply: repair model has finite VC-dimension postcondition has some extra continuity property (see paper)

  30. 30 VC dimension of a set of programs image: V. Kecman, 2001

  31. 31 VC dimension of a set of programs image: V. Kecman, 2001

  32. 32 Does DIGITS work? Assume: • there exists an optimal solution • repair model has finite VC-dimension

  33. 33 Does DIGITS work? Assume: • there exists an optimal solution • repair model has finite VC-dimension For every , if we run DIGITS on samples, then with probability we find a solution with .

  39. Trie Structure Sample one point at a time

  40. Trie Structure Sample one point at a time

  41. Trie Structure Sample one point at a time

  42. Trie Structure Sample one point at a time

  43. Trie Structure Sample one point at a time

  44. Trie Structure Sample one point at a time

  45. Trie Structure Sample one point at a time

  46. Trie Structure Sample one point at a time Prune the trie and generalize

  47. Trie Savings

  48. DIGITS Sampling Samples Synthesizer from Candidate Candidate Repair accepted/rejected Probabilistic Verifier

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