Autonomous agents that operate in the real world must often deal with partial observability, which is commonly modeled as partially observable Markov decision processes (POMDPs). However, traditional POMDP models rely on the assumption of complete knowledge of the observation source, known as fully observable data association. To address this limitation, we propose a planning algorithm that maintains multiple data association hypotheses, represented as a belief mixture, where each component corresponds to a different data association hypothesis. However, this method can lead to an exponential growth in the number of hypotheses, resulting in significant computational overhead. To overcome this challenge, we introduce a pruning-based approach for planning with ambiguous data associations. Our key contribution is to derive bounds between the value function based on the complete set of hypotheses and the value function based on a pruned-subset of the hypotheses, enabling us to establish a trade-off between computational efficiency and performance. We demonstrate how these bounds can both be used to certify any pruning heuristic in retrospect and propose a novel approach to determine which hypotheses to prune in order to ensure a predefined limit on the loss. We evaluate our approach in simulated environments and demonstrate its efficacy in handling multi-modal belief hypotheses with ambiguous data associations.

翻译：在真实世界中运行的自主智能体通常需要处理部分可观测性，这通常被建模为部分可观测马尔可夫决策过程（POMDP）。然而，传统的POMDP模型依赖于对观测来源具有完全知识这一假设，即完全可观测的数据关联。为解决这一局限性，我们提出了一种规划算法，该算法维护多个数据关联假设，表示为信念混合，其中每个分量对应一个不同的数据关联假设。但这种方法可能导致假设数量呈指数增长，从而产生显著的计算开销。为应对这一挑战，我们引入了一种基于剪枝的方法来处理含模糊数据关联的规划问题。我们的关键贡献在于推导了基于完整假设集的价值函数与基于剪枝子集的价值函数之间的界限，从而能够在计算效率与性能之间建立权衡。我们展示了这些界限如何用于事后验证任意剪枝启发式方法，并提出了一种新方法来确定需要剪枝哪些假设，以确保损失符合预定限制。我们在模拟环境中评估了该方法，并证明了其在处理具有模糊数据关联的多模态信念假设方面的有效性。