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Communication Dans Un Congrès Année : 2022

The price of unfairness in linear bandits with biased feedback

Résumé

In this paper, we study the problem of fair sequential decision making with biased linear bandit feedback. At each round, a player selects an action described by a covariate and by a sensitive attribute. The perceived reward is a linear combination of the covariates of the chosen action, but the player only observes a biased evaluation of this reward, depending on the sensitive attribute. To characterize the difficulty of this problem, we design a phased elimination algorithm that corrects the unfair evaluations, and establish upper bounds on its regret. We show that the worst-case regret is smaller than $\mathcal{O}(\kappa_*^{1/3}\log(T)^{1/3}T^{2/3})$, where $\kappa_*$ is an explicit geometrical constant characterizing the difficulty of bias estimation. We prove lower bounds on the worst-case regret for some sets of actions showing that this rate is tight up to a possible sub-logarithmic factor. We also derive gap-dependent upper bounds on the regret, and matching lower bounds for some problem instance. Interestingly, these results reveal a transition between a regime where the problem is as difficult as its unbiased counterpart, and a regime where it can be much harder.
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Dates et versions

hal-03611628 , version 1 (17-03-2022)
hal-03611628 , version 2 (01-06-2022)
hal-03611628 , version 3 (29-11-2022)

Identifiants

Citer

Solenne Gaucher, Alexandra Carpentier, Christophe Giraud. The price of unfairness in linear bandits with biased feedback. NeurIPS 2022, Nov 2022, New Orleans, United States. ⟨hal-03611628v3⟩
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