Solving Partially Observable Markov Decision Processes (POMDPs) with continuous actions is challenging, particularly for high-dimensional action spaces. To alleviate this difficulty, we propose a new sampling-based online POMDP solver, called Adaptive Discretization using Voronoi Trees (ADVT). It uses Monte Carlo Tree Search in combination with an adaptive discretization of the action space as well as optimistic optimization to efficiently sample high-dimensional continuous action spaces and compute the best action to perform. Specifically, we adaptively discretize the action space for each sampled belief using a hierarchical partition which we call a Voronoi tree. A Voronoi tree is a Binary Space Partitioning (BSP) that implicitly maintains the partition of a cell as the Voronoi diagram of two points sampled from the cell. This partitioning strategy keeps the cost of partitioning and estimating the size of each cell low, even in high-dimensional spaces where many sampled points are required to cover the space well. ADVT uses the estimated sizes of the cells to form an upper-confidence bound of the action values of the cell, and in turn uses the upper-confidence bound to guide the Monte Carlo Tree Search expansion and further discretization of the action space. This strategy enables ADVT to better exploit local information in the action space, leading to an action space discretization that is more adaptive, and hence more efficient in computing good POMDP solutions, compared to existing solvers. Experiments on simulations of four types of benchmark problems indicate that ADVT outperforms and scales substantially better to high-dimensional continuous action spaces, compared to state-of-the-art continuous action POMDP solvers.

该论文介绍了一种新的基于采样的在线POMDP求解器，名为Adaptive Discretization using Voronoi Trees（ADVT）。它使用Monte Carlo tree search与适应性离散化的行动空间，以及乐观优化来高效地采样高维连续行动空间并计算最佳行动，该策略使ADVT更好地利用行动空间中的局部信息，从而导致行动空间的离散化更加适应，因此在计算好的POMDP解方面更加有效。

使用 Voronoi 树进行自适应离散化来处理连续动作 POMDP