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 lookahead search algorithm that alleviates these difficulties by limiting the search to a set of sampled scenarios. The execution of all policies on the sampled scenarios is summarized using a Determinized Sparse Partially Observable Tree (DESPOT), which is a sparsely sampled belief tree. Our algorithm, named Regularized DESPOT (R-DESPOT), searches the DESPOT for a policy that optimally balances the size of the policy and the accuracy on its value estimate obtained through sampling. We give an output-sensitive performance bound for all policies derived from the DESPOT, and show that R-DESPOT works well if a small optimal policy exists. We also give an anytime approximation to R-DESPOT. Experiments show strong results, compared with two of the fastest online POMDP algorithms.

Uncontrolled intersections account for a significant fraction of roadway crashes due to ambiguous right-of-way rules, occlusions, and unpredictable driver behavior. While autonomous vehicle research has explored uncertainty-aware decision making, few systems exist to retrofit human-operated vehicles with assistive navigation support. We present a driver-assist framework for right-of-way reasoning at uncontrolled intersections, formulated as a Partially Observable Markov Decision Process (POMDP). Using a custom simulation testbed with stochastic traffic agents, pedestrians, occlusions, and adversarial scenarios, we evaluate four decision-making approaches: a deterministic finite state machine (FSM), and three probabilistic planners: QMDP, POMCP, and DESPOT. Results show that probabilistic planners outperform the rule-based baseline, achieving up to 97.5 percent collision-free navigation under partial observability, with POMCP prioritizing safety and DESPOT balancing efficiency and runtime feasibility. Our findings highlight the importance of uncertainty-aware planning for driver assistance and motivate future integration of sensor fusion and environment perception modules for real-time deployment in realistic traffic environments.

Most popular and effective approaches to online solving Partially Observable Markov Decision Processes (POMDPs, Kaelbling et al. (1998)), e.g., Partially Observable Monte Carlo Planning (POMCP) by Silver and Veness (2010) and Determinized Sparse Partially Observable Tree (DESPOT) by Ye et al. (2017), rely on Monte Carlo Tree Search (MCTS). These approaches are based on online simulations performed in a simulation environment (i.e. a black-box twin of the real POMDP environment) and estimate the value of actions. However, they require domain-specific policy heuristics, suggesting best actions at each state, for efficient exploration. Macro-actions (He et al. (2011); Bertolucci et al. (2021)) are popular policy heuristics that are particularly efficient for long planning horizons. A macro-action is essentially a sequence of suggested actions from a given state that can effectively guide the simulation phase towards actions with high utilities. However, such heuristics are heavily dependent on domain features and are typically handcrafted for each specific domain. Defining these heuristics is an arduous process that requires significant domain knowledge, especially in complex domains. An alternative approach, like the one by Cai and Hsu (2022), is to learn such heuristics via neural networks, which are, however, uninterpretable and data-inefficient. This paper extends the methodology proposed by Meli et al. (2024) to the learning, via Inductive Logic Programming (ILP, Muggleton (1991)), of Event Calculus (EC) theories C. Veronese, D. Meli & A. Farinelli.

This study addresses the challenge of stroke diagnosis and treatment under uncertainty, a critical issue given the rapid progression and severe consequences of stroke conditions such as aneurysms, arteriovenous malformations (AVM), and occlusions. Current diagnostic methods, including Digital Subtraction Angiography (DSA), face limitations due to high costs and its invasive nature. To overcome these challenges, we propose a novel approach using a Partially Observable Markov Decision Process (POMDP) framework. Our model integrates advanced diagnostic tools and treatment approaches with a decision-making algorithm that accounts for the inherent uncertainties in stroke diagnosis. Our approach combines noisy observations from CT scans, Siriraj scores, and DSA reports to inform the subsequent treatment options. We utilize the online solver DESPOT, which employs tree-search methods and particle filters, to simulate potential future scenarios and guide our strategies. The results indicate that our POMDP framework balances diagnostic and treatment objectives, striking a tradeoff between the need for precise stroke identification via invasive procedures like DSA and the constraints of limited healthcare resources that necessitate more cost-effective strategies, such as in-hospital or at-home observation, by relying only relying on simulation rollouts and not imposing any prior knowledge. Our study offers a significant contribution by presenting a systematic framework that optimally integrates diagnostic and treatment processes for stroke and accounting for various uncertainties, thereby improving care and outcomes in stroke management.

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.

Partially Observable Markov Decision Processes (POMDPs) are a powerful framework for planning under uncertainty. They allow to model state uncertainty as a belief probability distribution. Approximate solvers based on Monte Carlo sampling show great success to relax the computational demand and perform online planning. However, scaling to complex realistic domains with many actions and long planning horizons is still a major challenge, and a key point to achieve good performance is guiding the action-selection process with domain-dependent policy heuristics which are tailored for the specific application domain. We propose to learn high-quality heuristics from POMDP traces of executions generated by any solver. We convert the belief-action pairs to a logical semantics, and exploit data- and time-efficient Inductive Logic Programming (ILP) to generate interpretable belief-based policy specifications, which are then used as online heuristics. We evaluate thoroughly our methodology on two notoriously challenging POMDP problems, involving large action spaces and long planning horizons, namely, rocksample and pocman. Considering different state-of-the-art online POMDP solvers, including POMCP, DESPOT and AdaOPS, we show that learned heuristics expressed in Answer Set Programming (ASP) yield performance superior to neural networks and similar to optimal handcrafted task-specific heuristics within lower computational time. Moreover, they well generalize to more challenging scenarios not experienced in the training phase (e.g., increasing rocks and grid size in rocksample, incrementing the size of the map and the aggressivity of ghosts in pocman).

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 lookahead search algorithm that alleviates these difficulties by limiting the search to a set of sampled scenarios. The execution of all policies on the sampled scenarios is summarized using a Determinized Sparse Partially Observable Tree (DESPOT), which is a sparsely sampled belief tree. Our algorithm, named Regularized DESPOT (R-DESPOT), searches the DESPOT for a policy that optimally balances the size of the policy and the accuracy on its value estimate obtained through sampling. We give an output-sensitive performance bound for all policies derived from the DESPOT, and show that R-DESPOT works well if a small optimal policy exists.

The partially observable Markov decision process (POMDP) provides a principled general framework for planning under uncertainty, but solving POMDPs optimally is computationally intractable, due to the "curse of dimensionality" and the "curse of history". To overcome these challenges, we introduce the Determinized Sparse Partially Observable Tree (DESPOT), a sparse approximation of the standard belief tree, for online planning under uncertainty. A DESPOT focuses online planning on a set of randomly sampled scenarios and compactly captures the "execution" of all policies under these scenarios. We show that the best policy obtained from a DESPOT is near-optimal, with a regret bound that depends on the representation size of the optimal policy. Leveraging this result, we give an anytime online planning algorithm, which searches a DESPOT for a policy that optimizes a regularized objective function. Regularization balances the estimated value of a policy under the sampled scenarios and the policy size, thus avoiding overfitting. The algorithm demonstrates strong experimental results, compared with some of the best online POMDP algorithms available. It has also been incorporated into an autonomous driving system for real-time vehicle control. The source code for the algorithm is available online.

The partially observable Markov decision process (POMDP) provides a principled general framework for planning under uncertainty, but solving POMDPs optimally is computationally intractable, due to the "curse of dimensionality" and the "curse of history". To overcome these challenges, we introduce the Determinized Sparse Partially Observable Tree (DESPOT), a sparse approximation of the standard belief tree, for online planning under uncertainty. A DESPOT focuses online planning on a set of randomly sampled scenarios and compactly captures the "execution" of all policies under these scenarios. We show that the best policy obtained from a DESPOT is near-optimal, with a regret bound that depends on the representation size of the optimal policy. Leveraging this result, we give an anytime online planning algorithm, which searches a DESPOT for a policy that optimizes a regularized objective function. Regularization balances the estimated value of a policy under the sampled scenarios and the policy size, thus avoiding overfitting. The algorithm demonstrates strong experimental results, compared with some of the best online POMDP algorithms available. It has also been incorporated into an autonomous driving system for real-time vehicle control. The source code for the algorithm is available online.

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 lookahead search algorithm that alleviates these difficulties by limiting the search to a set of sampled scenarios. The execution of all policies on the sampled scenarios is summarized using a Determinized Sparse Partially Observable Tree (DESPOT), which is a sparsely sampled belief tree. Our algorithm, named Regularized DESPOT (R-DESPOT), searches the DESPOT for a policy that optimally balances the size of the policy and the accuracy on its value estimate obtained through sampling. We give an output-sensitive performance bound for all policies derived from the DESPOT, and show that R-DESPOT works well if a small optimal policy exists. We also give an anytime approximation to R-DESPOT. Experiments show strong results, compared with two of the fastest online POMDP algorithms.