The work, published open access in the journal Applied Intelligence, targets Hierarchical Task Network planning, or HTN planning, a technique prized in artificial intelligence for its speed and its ability to encode rich domain knowledge as recipes. In classical HTN planning, an agent starts with a high-level task, such as delivering a package or capturing a scientific image, and repeatedly decomposes it into smaller subtasks using predefined methods until only directly executable primitive actions remain. This hierarchical structure mirrors how humans organise complex decision-making, which is precisely why the Stuttgart team saw it as a natural home for risk reasoning. Yet, as they document in a sweeping review of prior work, no existing HTN approach models risk in terms of probabilistic action costs, and none reasons about the risk attitude of the planning agent. Existing planners either ignore costs entirely, minimise expected cost in a risk-neutral way, or handle uncertainty over action effects rather than costs, leaving a conceptual gap between what decision theory prescribes and what planning algorithms actually compute.

The theoretical backbone of the new approach comes from expected utility theory, formalised in the mid-twentieth century by von Neumann and Morgenstern. Under this framework, an agent’s tolerance for risk is expressed as a utility function that transforms uncertain monetary or temporal costs into real-valued utilities. A risk-neutral agent uses a linear function and simply minimises expected cost. A risk-seeking agent uses a convex exponential function that rewards the small chance of a cheap, lucky outcome. A risk-averse agent uses a concave function that disproportionately punishes the tail risk of an expensive disaster. The Stuttgart team defines a family of exponential utility functions in which a coefficient called alpha controls the intensity of the attitude: the larger alpha becomes, the more extreme the agent’s risk-seeking or risk-averse behaviour. Crucially, these functions allow the expected utility of a plan to be computed segment by segment, a property called segmentation that makes the mathematics tractable inside a hierarchical planner.

Turning this theory into a working algorithm required solving several technical puzzles that had blocked earlier attempts. First, expected utilities can be negative as well as positive, whereas classical cost-optimal planners assume strictly positive action costs, so existing heuristics could not simply be reused. Second, the exponential utility functions multiply across plan segments, but the A* search algorithm at the heart of the planner adds values. The researchers’ elegant workaround is a logarithmic transformation: by taking the logarithm of the expected utility of each primitive action, the multiplicative aggregation becomes additive, restoring compatibility with A* while preserving the sign of the utility through an attitude-determining coefficient. Third, hierarchical domains often contain cycles, where decomposing a task can lead back to the same task, and a naive maximisation procedure could loop forever through a cycle, inflating expected utility without bound. The team’s preprocessing phase detects such cycles by tracking decomposition paths and assigns negative infinity to the last method in each cycle, forcing the search to prefer alternative decompositions when they exist.

The resulting system, implemented as a prototype planner called RISKIE built on top of the established PANDA planning framework, operates in two phases. In the preprocessing phase, the planner grounds the domain into a graph structure called a Ground Cost-Variable Task Decomposition Graph and computes, bottom-up, an estimate of the expected utility of every task and method. Because a compound task may appear in many different decomposition paths, some of which contain cycles and some of which do not, each task stores a vector of expected utility values rather than a single number, and the maximum is used during search. In the plan generation phase, A* explores partial plans, ordering them by the sum of the expected utilities of their already-refined primitive actions plus a heuristic estimate for the compound tasks still to be decomposed. The authors prove formally that this heuristic is admissible in the maximisation setting, meaning it never underestimates the achievable expected utility, and they establish termination, soundness, completeness, and optimality of the overall algorithm, together with worst-case and best-case complexity bounds.

To test the approach, the researchers evaluated RISKIE on four risk-involving domains: a Self-Driving Car domain modelled in earlier work, a Satellite domain adapted from a classical planning benchmark, and extended versions of the Rover and Transport benchmark domains from the 2020 International Planning Competition. In the Self-Driving Car domain, a vehicle must navigate roads with construction zones, congested pedestrian crossings, and icy stretches, choosing among options such as accelerating without electronic stability control, decelerating with it, or activating stability control but accelerating anyway. In the extended Rover domain, rovers can delegate data transmission to space drones that are fast but prone to crashes, signal loss, and transmission failures. In the extended Transport domain, trucks can choose between ordinary roads and a speedway network that is potentially faster but riskier. Each domain was modelled in three planning languages, including an extension of the standard hierarchical language HDDL that the authors call rHDDL, which allows probability distributions over operator costs to be expressed directly.

The behavioural results are striking. In the Self-Driving Car domain, an extremely risk-averse agent with alpha equal to 0.9 chooses the only route whose every action has a guaranteed outcome, taking the long road and decelerating with stability control engaged on the icy stretch. The extreme risk-seeking agent, by contrast, takes the short road and accelerates on the ice without stability control, accepting an eighty percent chance of slipping for a twenty percent chance of saving four hours. The risk-neutral agent takes the route with the lowest expected cost and is indifferent among several icy-road options. In the Satellite domain, risk-seeking agents power all three instruments simultaneously, accepting the risk of a power failure to skip two switching actions, while risk-averse agents operate instruments one at a time, producing longer but safer plans. In the Transport and Rover domains, the pattern flips: risk-averse agents produce shorter plans because the risky options, speedways and drones, require extra steps, illustrating that the relationship between risk attitude and plan length is domain-dependent rather than universal.

The comparative evaluation pitted RISKIE against four state-of-the-art HTN planners spanning the full spectrum of cost awareness: SH and HyperTensioN, which ignore costs entirely, and SHOP2 and PANDA, which optimise costs in a risk-neutral fashion. Across 440 experiments covering eleven risk-attitude settings per problem instance, RISKIE solved every instance in every domain within a ten-minute timeout, achieving coverage on par with or better than the established planners despite optimising a considerably more complex objective. By construction, RISKIE’s plans always matched or exceeded the expected utility of plans produced by the other planners when scored with the same utility function. Plan-overlap analysis revealed that the risk-neutral configuration of RISKIE agreed most often with the conventional planners, as expected, while risk-seeking configurations frequently diverged, producing plans no baseline planner could find. An ablation study confirmed that varying alpha meaningfully changes behaviour in domains rich with risky alternatives, while in domains offering only binary risk choices, all attitudes converge on the same plan.

The authors are candid about limitations and open challenges. The current approach assumes a static risk attitude and utility functions that permit segmentation; arbitrary utility functions could, in the worst case, require enumerating every possible plan trajectory. Scalability bottlenecks emerge when the branching factor is high or when the heuristic becomes uninformative, and the team points to landmark guidance and greedy pre-passes as promising remedies. Dynamic risk attitudes that shift with remaining battery or elapsed time, and multi-agent settings where a self-driving car must adapt to the risk preferences of surrounding human drivers, remain future work. Still, the significance of the contribution is hard to overstate: for the first time, a hierarchical AI planner can be handed a risk attitude the way a human client hands a financial adviser a risk profile, and it will return a provably optimal plan for that personality. As autonomous vehicles, satellites, and robots move from laboratories into the messy, probabilistic real world, planners that understand risk may become not a luxury but a necessity.

Subject of Research: Risk-aware hierarchical task network planning using expected utility theory

Article Title: Solving risk-aware HTN planning problems: algorithmic, formal, and empirical results

Article References: Alnazer, E., Georgievski, I., & Aiello, M. (2026). Solving risk-aware HTN planning problems: algorithmic, formal, and empirical results. Applied Intelligence, 56(15), Article 468. https://doi.org/10.1007/s10489-026-07450-4

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07450-4

Keywords: HTN planning, risk-aware planning, expected utility, AI planning, autonomous vehicles, decision theory, heuristic search, probabilistic action costs, RISKIE planner, risk attitudes, A* search, Applied Intelligence