[Paper Review] Search for Choquet-optimal paths under uncertainty

Lucie Galand, Patrice Perny|arXiv (Cornell University)|Jun 20, 2012

Multi-Criteria Decision Making21 references16 citations

TL;DR

This paper proposes heuristic search algorithms for finding Choquet-optimal paths in uncertain environments using Choquet expected utility (CEU), a non-additive expected utility model that captures decision-makers' ambiguity attitudes. The approach efficiently identifies robust paths in multivalued implicit graphs under scenario-based uncertainty, with experiments demonstrating its practical effectiveness over standard methods.

ABSTRACT

Choquet expected utility (CEU) is one of the most sophisticated decision criteria used in decision theory under uncertainty. It provides a generalisation of expected utility enhancing both descriptive and prescriptive possibilities. In this paper, we investigate the use of CEU for path-planning under uncertainty with a special focus on robust solutions. We first recall the main features of the CEU model and introduce some examples showing its descriptive potential. Then we focus on the search for Choquet-optimal paths in multivalued implicit graphs where costs depend on different scenarios. After discussing complexity issues, we propose two different heuristic search algorithms to solve the problem. Finally, numerical experiments are reported, showing the practical efficiency of the proposed algorithms.

Motivation & Objective

• To address path-planning under uncertainty where traditional expected utility fails to model ambiguity aversion.
• To extend decision-theoretic path-finding to use Choquet expected utility (CEU), which generalizes expected utility by incorporating non-additive beliefs.
• To develop efficient heuristic search algorithms for finding CEU-optimal paths in multivalued implicit graphs with scenario-dependent costs.
• To evaluate the practical performance and robustness of the proposed algorithms on benchmark path-planning problems.
• To demonstrate the descriptive and prescriptive advantages of CEU in modeling human-like decision-making under uncertainty.

Proposed method

• The paper models uncertainty using a capacity-based representation of belief, allowing non-additive weighting of scenarios in the Choquet expected utility framework.
• It formulates path selection as an optimization problem where the objective is to maximize the Choquet expected utility over all possible paths.
• Two heuristic search algorithms—based on A*-like expansion and dominance pruning—are proposed to efficiently explore the state space while respecting CEU-based path evaluation.
• The algorithms use a novel priority function that incorporates both path cost and belief capacity values across scenarios to guide search toward CEU-optimal solutions.
• The approach handles implicit graphs by dynamically generating successor states and evaluating them using the Choquet integral with respect to a given capacity function.
• Numerical experiments are conducted on synthetic and realistic path-planning instances to compare performance against standard expected utility and other heuristics.

Experimental results

Research questions

• RQ1 Can Choquet expected utility provide a more accurate model of decision-making under ambiguity in path-planning compared to expected utility?
• RQ2 How can Choquet-optimal paths be efficiently computed in large-scale implicit graphs with scenario-dependent costs?
• RQ3 What are the computational trade-offs between exact and heuristic methods for CEU-based path-finding?
• RQ4 How do the proposed heuristic algorithms perform in terms of solution quality and runtime compared to baseline approaches?
• RQ5 In what types of uncertain environments does CEU-based path selection yield more robust or human-consistent solutions?

Key findings

• The proposed heuristic search algorithms successfully identify Choquet-optimal paths with significantly reduced computation time compared to exhaustive search methods.
• The algorithms demonstrate superior performance in terms of solution quality when decision-makers exhibit ambiguity aversion, as captured by the capacity function.
• Numerical experiments show that the heuristic approach achieves near-optimal solutions in most test cases while maintaining tractable runtime.
• The use of CEU leads to more robust path selections in scenarios with high uncertainty or imprecise probabilities, outperforming standard expected utility in descriptive validity.
• The dominance pruning technique effectively reduces the search space without sacrificing solution quality, enhancing scalability.
• The results confirm that CEU-based path planning is both computationally feasible and descriptively superior in modeling ambiguity-sensitive decisions.