feat: Diverse recommendations bundles

[lfaucon]

To-do:

• [ ] Pursue experiments with
  • [ ] Adapt the random selection with clipping of score difference
  • [ ] Consider top 1900 videos (all videos that are recommendable, i.e. with tournesol score >= 20)
  • [ ] Maybe remove the part about incomplete entities (not rated on all criteria) because they may be selected by the randomized sampling with temperature.
• [ ] Add recency term in optimization objective
• [ ] Open a Pull Request modifying the solidago package adding the method noisy_greedy_submodular_optimization for optimization in a new submodule recommendation_bundle and tests.

Next steps:

• [ ] in Tournesol backend, cache regularly the list of videos with all criteria scores and

[lfaucon]

Use case

• Evaluate the method with bundles of 12
• Allow to select all 1900 recommendable videos

Without recency

In average, videos would appear in about 12 / 1900 = 0.6% of the bundles

Potential targets for choosing the temperature and temperature clipping parameters:

• A video of the top 5% apparaissent dans environ 3% (5 times more than average) des bundles. It would mean an average of 3 top 100 videos per bundle of 12
• videos of the top 5% should appear 10 times as much in bundles as the lower 50%

With recency

Target: top 20 of the month should appear in about 20% (10% - 30%) of the bundles. That means an average of 4 recent best videos in each bundle

 Which formula to use for recency?

1 / (t_0 + age) = 1 / t_0 . . . when age = 0 1 / (2*t_0) . . . when age = t_0

t_0 = ..... 15 j .... 0 j

age = 1 .... 1 / 16 j .... 1 / 1j age = 15 ... 1 / 30 j .... 1 / 15j age = 45 ... 1 / 60 j .... 1 / 45j