A Smoothed Analysis of the Greedy Algorithm for the Linear Contextual Bandit Problem
This addresses fairness issues in high-stakes decisions like criminal justice or healthcare, offering a way to avoid harming individuals during learning, though it is incremental as it builds on existing greedy algorithm analysis.
The paper tackles the fairness concern in contextual bandit settings where exploration harms individuals, by analyzing the greedy algorithm's performance with adversarial contexts. It shows that small perturbations allow the greedy algorithm to achieve no regret, potentially with constant initial data, indicating that exploration and exploitation need not conflict generically in linear settings.
Bandit learning is characterized by the tension between long-term exploration and short-term exploitation. However, as has recently been noted, in settings in which the choices of the learning algorithm correspond to important decisions about individual people (such as criminal recidivism prediction, lending, and sequential drug trials), exploration corresponds to explicitly sacrificing the well-being of one individual for the potential future benefit of others. This raises a fairness concern. In such settings, one might like to run a "greedy" algorithm, which always makes the (myopically) optimal decision for the individuals at hand - but doing this can result in a catastrophic failure to learn. In this paper, we consider the linear contextual bandit problem and revisit the performance of the greedy algorithm. We give a smoothed analysis, showing that even when contexts may be chosen by an adversary, small perturbations of the adversary's choices suffice for the algorithm to achieve "no regret", perhaps (depending on the specifics of the setting) with a constant amount of initial training data. This suggests that "generically" (i.e. in slightly perturbed environments), exploration and exploitation need not be in conflict in the linear setting.