Diversity-Preserving K-Armed Bandits, Revisited

Hédi Hadiji (1) , Sébastien Gerchinovitz (2, 3) , Jean-Michel Loubes (2) , Gilles Stoltz (4, 5, 6)

1 L2S - Laboratoire des signaux et systèmes
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 IRT Saint Exupéry - Institut de Recherche Technologique
4 CELESTE - Statistique mathématique et apprentissage
5 LMO - Laboratoire de Mathématiques d'Orsay
6 HEC Paris - Recherche - Hors Laboratoire

We consider the bandit-based framework for diversity-preserving recommendations introduced by Celis et al. (2019), who approached it in the case of a polytope mainly by a reduction to the setting of linear bandits. We design a UCB algorithm using the specific structure of the setting and show that it enjoys a bounded distribution-dependent regret in the natural cases when the optimal mixed actions put some probability mass on all actions (i.e., when diversity is desirable). The regret lower bounds provided show that otherwise, at least when the model is mean-unbounded, a regret is suffered. We also discuss an example beyond the special case of polytopes.

Domains: Machine Learning [stat.ML]

Hédi Hadiji, Sébastien Gerchinovitz, Jean-Michel Loubes, Gilles Stoltz. Diversity-Preserving K-Armed Bandits, Revisited. 2024. ⟨hal-02957485v2⟩