Finding an object in a partially known and cluttered environment is critical for many robotics tasks.

Deterministic partially observable Markov decision processes (DetPOMDPs) often arise in planning problems where the agent is uncertain about its environmental state but can act and observe de-terministically. In this paper, we propose DetM-CVI, an adaptation of the Monte Carlo V alue Iteration (MCVI) algorithm for DetPOMDPs, which builds policies in the form of finite-state controllers (FSCs). DetMCVI solves large problems with a high success rate, outperforming existing baselines for DetPOMDPs. We also verify the performance of the algorithm in a real-world mobile robot forest mapping scenario.

Taking into account future risk is essential for an autonomously operating robot to find online not only the best but also a safe action to execute. In this paper, we build upon the recently introduced formulation of probabilistic belief-dependent constraints. We present an anytime approach employing the Monte Carlo Tree Search (MCTS) method in continuous domains. Unlike previous approaches, our method assures safety anytime with respect to the currently expanded search tree without relying on the convergence of the search. We prove convergence in probability with an exponential rate of a version of our algorithms and study proposed techniques via extensive simulations. Even with a tiny number of tree queries, the best action found by our approach is much safer than the baseline. Moreover, our approach constantly finds better than the baseline action in terms of objective. This is because we revise the values and statistics maintained in the search tree and remove from them the contribution of the pruned actions.

Online planning under uncertainty in partially observable domains is an essential capability in robotics and AI. The partially observable Markov decision process (POMDP) is a mathematically principled framework for addressing decision-making problems in this challenging setting. However, finding an optimal solution for POMDPs is computationally expensive and is feasible only for small problems. In this work, we contribute a novel method to simplify POMDPs by switching to an alternative, more compact, observation space and simplified model to speedup planning with formal performance guarantees. We introduce the notion of belief tree topology, which encodes the levels and branches in the tree that use the original and alternative observation space and models. Each belief tree topology comes with its own policy space and planning performance. Our key contribution is to derive bounds between the optimal Q-function of the original POMDP and the simplified tree defined by a given topology with a corresponding simplified policy space. These bounds are then used as an adaptation mechanism between different tree topologies until the optimal action of the original POMDP can be determined. Further, we consider a specific instantiation of our framework, where the alternative observation space and model correspond to a setting where the state is fully observable. We evaluate our approach in simulation, considering exact and approximate POMDP solvers and demonstrating a significant speedup while preserving solution quality. We believe this work opens new exciting avenues for online POMDP planning with formal performance guarantees.

This paper focuses on the task of hallucination detection, which aims to determine the truthfulness of LLM-generated statements. To address this problem, a popular class of methods utilize the LLM's self-consistencies in its beliefs in a set of logically related augmented statements generated by the LLM, which does not require external knowledge databases and can work with both white-box and black-box LLMs. However, in many existing approaches, the augmented statements tend to be very monotone and unstructured, which makes it difficult to integrate meaningful information from the LLM beliefs in these statements. Also, many methods work with the binarized version of the LLM's belief, instead of the continuous version, which significantly loses information. To overcome these limitations, in this paper, we propose Belief Tree Propagation (BTProp), a probabilistic framework for LLM hallucination detection. BTProp introduces a belief tree of logically related statements by recursively decomposing a parent statement into child statements with three decomposition strategies, and builds a hidden Markov tree model to integrate the LLM's belief scores in these statements in a principled way. Experiment results show that our method improves baselines by 3%-9% (evaluated by AUROC and AUC-PR) on multiple hallucination detection benchmarks. Code is available at https://github.com/UCSB-NLP-Chang/BTProp.

POMDPs provide a principled framework for planning under uncertainty, but are computationally intractable, due to the "curse of dimensionality" and the "curse of history". This paper presents an online POMDP algorithm that alleviates these difficulties by focusing the search on a set of randomly sampled scenarios.

Continuous POMDPs with general belief-dependent rewards are notoriously difficult to solve online. In this paper, we present a complete provable theory of adaptive multilevel simplification for the setting of a given externally constructed belief tree and MCTS that constructs the belief tree on the fly using an exploration technique. Our theory allows to accelerate POMDP planning with belief-dependent rewards without any sacrifice in the quality of the obtained solution. We rigorously prove each theoretical claim in the proposed unified theory. Using the general theoretical results, we present three algorithms to accelerate continuous POMDP online planning with belief-dependent rewards. Our two algorithms, SITH-BSP and LAZY-SITH-BSP, can be utilized on top of any method that constructs a belief tree externally. The third algorithm, SITH-PFT, is an anytime MCTS method that permits to plug-in any exploration technique. All our methods are guaranteed to return exactly the same optimal action as their unsimplified equivalents. We replace the costly computation of information-theoretic rewards with novel adaptive upper and lower bounds which we derive in this paper, and are of independent interest. We show that they are easy to calculate and can be tightened by the demand of our algorithms. Our approach is general; namely, any bounds that monotonically converge to the reward can be easily plugged-in to achieve significant speedup without any loss in performance. Our theory and algorithms support the challenging setting of continuous states, actions, and observations. The beliefs can be parametric or general and represented by weighted particles. We demonstrate in simulation a significant speedup in planning compared to baseline approaches with guaranteed identical performance.

In this work, we propose the Informed Batch Belief Trees (IBBT) algorithm for motion planning under motion and sensing uncertainties. The original stochastic motion planning problem is divided into a deterministic motion planning problem and a graph search problem. We solve the deterministic planning problem using sampling-based methods such as PRM or RRG to construct a graph of nominal trajectories. Then, an informed cost-to-go heuristic for the original problem is computed based on the nominal trajectory graph. Finally, we grow a belief tree by searching over the graph using the proposed heuristic. IBBT interleaves between batch state sampling, nominal trajectory graph construction, heuristic computing, and search over the graph to find belief space motion plans. IBBT is an anytime, incremental algorithm. With an increasing number of batches of samples added to the graph, the algorithm finds motion plans that converge to the optimal one. IBBT is efficient by reusing results between sequential iterations. The belief tree searching is an ordered search guided by an informed heuristic. We test IBBT in different planning environments. Our numerical investigation confirms that IBBT finds non-trivial motion plans and is faster compared with previous similar methods.

In this work, we develop the Batch Belief Trees (BBT) algorithm for motion planning under motion and sensing uncertainties. The algorithm interleaves between batch sampling, building a graph of nominal trajectories in the state space, and searching over the graph to find belief space motion plans. By searching over the graph, BBT finds sophisticated plans that will visit (and revisit) information-rich regions to reduce uncertainty. One of the key benefits of this algorithm is the modified interplay between exploration and exploitation. Instead of an exhaustive search (exploitation) after one exploration step, the proposed algorithm uses batch samples to explore the state space and, in addition, does not require exhaustive search before the next iteration of batch sampling, which adds flexibility.The algorithm finds motion plans that converge to the optimal one as more samples are added to the graph. We test BBT in different planning environments. Our numerical investigation confirms that BBT finds non-trivial motion plans and is faster compared with previous similar methods.