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：在现实世界中运行的自主智能体常常需要应对部分可观测性，这一问题通常通过部分可观测马尔可夫决策过程（POMDP）进行建模。然而，传统的POMDP模型依赖于对观测源具有完全知识的假设，即完全可观测的数据关联。为克服这一局限性，我们提出一种规划算法，该算法维护多个数据关联假设，这些假设以信念混合的形式表示，其中每个分量对应一个不同的数据关联假设。然而，该方法会导致假设数量呈指数增长，从而带来显著的计算开销。为应对这一挑战，我们引入一种基于剪枝的方法来处理模糊数据关联下的规划问题。我们的核心贡献在于推导出基于完整假设集的价值函数与基于剪枝后假设子集的价值函数之间的界限，这使我们能够在计算效率与性能之间建立权衡关系。我们展示了如何利用这些界限对任意剪枝启发式方法进行事后验证，并提出一种新颖的方法来确定应剪除哪些假设，以确保损失在预定义限度内。我们在仿真环境中评估了所提方法，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。