Decision-Aware Approximation Improves Evidential Optimization

In evidential combinatorial optimization, traditional methods for approximating belief functions (mass functions) focus on maintaining the mathematical closeness to the original function. However, this approach can lead to suboptimal decisions when the approximated function is used in a problem like finding the shortest path. This research proposes a novel "decision-aware approximation" method. Instead of minimizing the distance between mass functions, this new approach targets the regret of the decision, aiming to preserve the quality of the decision induced by the approximated function. This means the approximation is optimized to ensure that choosing based on the cheaper, approximated function still yields a good outcome under the true, more complex function. Experiments, including a minimal shortest path problem, show that traditional distance-optimal approximations can flip the optimal decision, whereas the decision-aware merge preserves it. The paper provides theoretical bounds and extends the method to an online version, demonstrating its effectiveness in reducing decision errors compared to representation-aware compression.