Benjamin Hudson

Benjamin Hudson, Laurent Charlin, Emma Frejinger

Decision-making problems often feature uncertainty stemming from heterogeneous and context-dependent human preferences. To address this, we propose a sequential learning-and-optimization pipeline to learn preference distributions and leverage them to solve downstream problems, for example risk-averse formulations. We focus on human choice settings that can be formulated as (integer) linear programs. In such settings, existing inverse optimization and choice modelling methods infer preferences from observed choices but typically produce point estimates or fail to capture contextual shifts, making them unsuitable for risk-averse decision-making. Using a bounded-variance score function gradient estimator, we train a predictive model mapping contextual features to a rich class of parameterizable distributions. This approach yields a maximum likelihood estimate. The model generates scenarios for unseen contexts in the subsequent optimization phase. In a synthetic ridesharing environment, our approach reduces average post-decision surprise by up to 114$\times$ compared to a risk-neutral approach with perfect predictions and up to 25$\times$ compared to leading risk-averse baselines.

Benjamin Hudson, Qingbiao Li, Matthew Malencia et al.

Solutions to the Traveling Salesperson Problem (TSP) have practical applications to processes in transportation, logistics, and automation, yet must be computed with minimal delay to satisfy the real-time nature of the underlying tasks. However, solving large TSP instances quickly without sacrificing solution quality remains challenging for current approximate algorithms. To close this gap, we present a hybrid data-driven approach for solving the TSP based on Graph Neural Networks (GNNs) and Guided Local Search (GLS). Our model predicts the regret of including each edge of the problem graph in the solution; GLS uses these predictions in conjunction with the original problem graph to find solutions. Our experiments demonstrate that this approach converges to optimal solutions at a faster rate than three recent learning based approaches for the TSP. Notably, we reduce the mean optimality gap on the 100-node problem set from 1.534% to 0.705%, a 2x improvement. When generalizing from 20-node instances to the 100-node problem set, we reduce the optimality gap from 18.845% to 2.622%, a 7x improvement.