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Private Lift Games Pseudocode

Sample of Meta Input

Meta inputs the opportunity data of a Lift study. This is not shared with the advertiser. We assume the id_ column is aligned across publisher (meta) and advertiser using Private ID protocol that runs before MPC game.

  • Each row represents a person.
  • The id_ column can be in a different format based on the type of person id used by the participating advertiser.
  • opportunity column is optional.
  • test_flag indicates whether the person is in the test group or control group of the Lift study.
  • opportunity_timestamp represents the unixtime when the person was served an opportunity.
id_,opportunity,test_flag,opportunity_timestamp
0,0,0,0
1,1,0,1605360340
2,0,0,0
3,1,0,1605360341
4,1,1,1605360337
5,1,0,160536033538

Sample of Advertiser Input

The advertiser inputs the conversion data of a Lift study. This is not shared with Meta.

  • Because ids should be matched by PID process before play the Lift games, we expect a one-to-one mapping between the ids in this input and the ids in Meta's input.
  • Both "event_timestamps" and "values" are capped and padded to have 4 values. This means currently we support up to 4 conversions per user.
id_,event_timestamps,values,feature_foo,feature_bar
0,[0,0,0,1605360335],[0,0,0,33],aaa,111
1,0,0,0,0
2,0,0,0,0
3,[0,0,1605564241,1606014035],[0,0,32,59],bbb,222
4,0,0,0,0
5,0,0,0,0

Conversion Lift Game

Inputs and Outputs

  • Meta Input: List of id_, opportunity (optional), test_flag, opportunity_timestamp
  • Advertiser Input: List of id_, event_timestamps, values, any features (optional)
  • Meta Output: Xor share of Output statistics
  • Advertiser Output: Xor share of Output statistics

Output statistics

testPopulation, //# of all the people in the test group
controlPopulation, //# of all the people in the control group
testConversions, //# of valid conversion made by the test population
controlConversions, //# of valid conversion made by the control population
testValue, //sum of the value of valid conversions in the test group
controlValue, //sum of value of valid conversions in the control group
testSquared, //user-grain sum of the squares of the values of valid conversions in the test group
controlSquared, //user-grain sum of the squares of the values of valid conversions in the control group

Meta and Advertiser jointly compute in 2 PC

for each row in lists:
    if (opportunity (if present) and test_flag)
        testPopulation++
        for each event_timestamp and value:
            if (opportunity_timestamp < event_timestamp + 10)
                testConversions++
                testValue += value
                testValueSquared += value * value
    if (opportunity (if present) and not test_flag)
        controlPopulation++
        for each event_timestamp and value:
            if (opportunity_timestamp < event_timestamp + 10)
                controlConversions++
                controlValue += value
                controlValueSquared += value * value

We run the computation for the overall dataset and then again for each "cohort." Each "cohort" is defined as a unique combination of all features provided by the partner. Output XOR share of the Output Statistics to each party.

Aggregator Game

Inputs and outputs

  • Meta Input:
    X shards of XOR share of output metrics from previous step
        testPopulation,
        controlPopulation,
        testConversions,
        controlConversions,
        testValue,
        controlValue,
        testSquared,
        controlSquared
    with X >= 1
  • Advertiser Input: Same format as Meta Input
  • Meta Output: Output metrics with all zeroes
  • Advertiser Output: Aggregated output metrics

Meta and Advertiser jointly compute in 2 PC

for each shard S in all shards:
   for each metric M in S:
        aggregated.M += Xor M.value

Output aggregated Output Statistics to both parties or Advertiser only if they request so.