Optimistic Feasible Search for Closed-Loop Fair Threshold Decision-Making

• URL: http://arxiv.org/abs/2512.22313v1
• Date: Fri, 26 Dec 2025 10:44:40 GMT
• Title: Optimistic Feasible Search for Closed-Loop Fair Threshold Decision-Making
• Authors: Wenzhang Du,
• Abstract summary: We study online learning of a one-dimensional threshold policy from bandit feedback.<n>We propose Optimistic Feasible Search (OFS), a simple grid-based method that maintains confidence bounds for reward and constraint residuals.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Closed-loop decision-making systems (e.g., lending, screening, or recidivism risk assessment) often operate under fairness and service constraints while inducing feedback effects: decisions change who appears in the future, yielding non-stationary data and potentially amplifying disparities. We study online learning of a one-dimensional threshold policy from bandit feedback under demographic parity (DP) and, optionally, service-rate constraints. The learner observes only a scalar score each round and selects a threshold; reward and constraint residuals are revealed only for the chosen threshold. We propose Optimistic Feasible Search (OFS), a simple grid-based method that maintains confidence bounds for reward and constraint residuals for each candidate threshold. At each round, OFS selects a threshold that appears feasible under confidence bounds and, among those, maximizes optimistic reward; if no threshold appears feasible, OFS selects the threshold minimizing optimistic constraint violation. This design directly targets feasible high-utility thresholds and is particularly effective for low-dimensional, interpretable policy classes where discretization is natural. We evaluate OFS on (i) a synthetic closed-loop benchmark with stable contraction dynamics and (ii) two semi-synthetic closed-loop benchmarks grounded in German Credit and COMPAS, constructed by training a score model and feeding group-dependent acceptance decisions back into population composition. Across all environments, OFS achieves higher reward with smaller cumulative constraint violation than unconstrained and primal-dual bandit baselines, and is near-oracle relative to the best feasible fixed threshold under the same sweep procedure. Experiments are reproducible and organized with double-blind-friendly relative outputs.

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