Real-world problems often require reasoning about hybrid beliefs, over both discrete and continuous random variables. Yet, such a setting has hardly been investigated in the context of planning. Moreover, existing online Partially Observable Markov Decision Processes (POMDPs) solvers do not support hybrid beliefs directly. In particular, these solvers do not address the added computational burden due to an increasing number of hypotheses with the planning horizon, which can grow exponentially. As part of this work, we present a novel algorithm, Hybrid Belief Monte Carlo Planning (HB-MCP) that utilizes the Monte Carlo Tree Search (MCTS) algorithm to solve a POMDP while maintaining a hybrid belief. We illustrate how the upper confidence bound (UCB) exploration bonus can be leveraged to guide the growth of hypotheses trees alongside the belief trees. We then evaluate our approach in highly aliased simulated environments where unresolved data association leads to multi-modal belief hypotheses.

翻译：现实世界问题通常需要对混合信念进行推理，涉及离散和连续随机变量。然而，这种设定在规划领域鲜有研究。此外，现有的在线部分可观测马尔可夫决策过程（POMDP）求解器并不直接支持混合信念。特别地，这些求解器无法应对因规划时间范围内假设数量增加而带来的额外计算负担——这种增长可能呈指数级。在本工作中，我们提出了一种新算法——混合信念蒙特卡洛规划（HB-MCP），它利用蒙特卡洛树搜索（MCTS）算法来求解POMDP，同时维持混合信念。我们阐释了如何利用上置信界（UCB）探索奖励来引导假设树随信念树同步生长。随后，我们在高度混叠的模拟环境中评估了该方法，其中未解决的数据关联会导致多模态信念假设。