Algorithmic Challenges in Ensuring Fairness at the Time of Decision

Abstract: Algorithmic decision-making in societal contexts, such as retail pricing, loan administration, recommendations on online platforms, etc., can be framed as stochastic optimization under bandit feedback, which typically requires experimentation with different decisions for the sake of learning. Such experimentation often results in perceptions of unfairness among people impacted by these decisions; for instance, there have been several recent lawsuits accusing companies that deploy algorithmic pricing practices of price gouging. Motivated by the changing legal landscape surrounding algorithmic decision-making, we introduce the well-studied fairness notion of envy-freeness within the context of stochastic convex optimization. Our notion requires that upon receiving decisions in the present time, groups do not envy the decisions received by any of the other groups, both in the present as well as the past. This results in a novel trajectory-constrained stochastic optimization problem that renders existing techniques inapplicable. The main technical contribution of this work is to show problem settings where there is no gap in achievable regret (up to logarithmic factors) when envy-freeness is imposed. In particular, in our main result, we develop a near-optimal envy-free algorithm that achieves $\tilde{O}(\sqrt{T})$ regret for smooth convex functions that satisfy the PL inequality. This algorithm has a coordinate-descent structure, in which we carefully leverage gradient information to ensure monotonic sampling along each dimension, while avoiding overshooting the constrained optimum with high probability. This latter aspect critically uses smoothness and the structure of the envy-freeness constraints, while the PL inequality allows for sufficient progress towards the optimal solution. We discuss several open questions that arise from this analysis, which may be of independent interest.