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

The original review had presented entropy as a way to quantify uncertainty in medical reasoning, describing it as offering a concise summary of uncertainty that nonetheless lacks a built-in mechanism for action. That admission, the Singapore authors contend, is precisely where the trouble begins. In clinical practice, uncertainty is not merely a quantity to be measured; it is a condition to be navigated, weighed against risks, benefits, and patient values, and ultimately resolved into a decision: treat, test, observe, or reassure. A framework that summarizes uncertainty without specifying how to act on it, they argue, risks creating what they call an illusion of precision, presenting clinicians with a single descriptive number that feels rigorous but resists translation into a concrete clinical act.

The technical heart of the critique lies in a comparison between entropy and Bayesian inference, the dominant framework for reasoning under uncertainty in medicine and statistics. Bayesian models produce state-specific probabilities: the probability, for instance, that a patient with chest pain is having a myocardial infarction versus a benign cause. These actionable probabilities can then be compared against established decision thresholds, most famously formalized by Pauker and Kassirer in the New England Journal of Medicine in 1980. The threshold approach defines a testing threshold and a treatment threshold; if the probability of disease falls below the former, the clinician forgoes testing, and if it rises above the latter, treatment proceeds without further diagnostic workup. This architecture converts probability directly into action, providing a rational bridge between belief and behavior.

Entropy, by contrast, collapses an entire probability distribution into a single scalar. In information theory, the Shannon entropy of a diagnostic hypothesis set is maximal when all possibilities are equally likely and minimal when one diagnosis dominates. A high-entropy differential diagnosis tells the clinician that the situation is genuinely uncertain, but it does not say which diagnosis is most probable, what test would most efficiently reduce the uncertainty, or whether further investigation is even warranted given the stakes. Two patients could carry identical entropy values while demanding radically different management: one with a high-mortality condition hovering near a treatment threshold, the other with a trivial condition with little actionable consequence. The letter’s authors argue that this loss of state-specific information is not a minor technicality but an ontological mismatch between the descriptive reach of entropy and the prescriptive demands of clinical judgment.

The critique also engages with the literature on value of information, a family of methods for prioritizing research and testing by quantifying how much a new piece of information would be worth in terms of improved outcomes. Value of information analysis, as codified by Jackson and colleagues in Epidemiologic Methods in 2021, builds explicitly on decision-theoretic foundations, linking the acquisition of information to expected gains in health. Bayesian probability combined with threshold logic naturally accommodates these calculations: knowing a probability and the payoff matrix of actions allows one to compute the expected value of perfect or sample information. Entropy alone, stripped of state-specific probabilities and payoff structures, cannot perform this function. A clinician told that a case has an entropy of 1.7 bits has learned little about what to do next, whereas a clinician told that the probability of disease is 45 percent against a testing threshold of 30 percent knows immediately that more information is worth acquiring.

What makes the letter particularly provocative is its pivot from decision theory to pedagogy. The authors acknowledge that the original review rightly locates entropy’s true promise in standardization and scalability, especially for artificial intelligence systems trained on vast clinical datasets. In that context, entropy can serve as a useful computational statistic, a way for machine learning systems to flag cases of high diagnostic ambiguity, route them to specialists, or measure model confidence. But the authors warn that the vision of an “entropy-based medicine” must be weighed against its potential educational consequences. Medicine has long oscillated between the aspiration to quantify everything and the recognition that its core practice remains an interpretive, human activity. If trainees learn that good clinical reasoning means minimizing a calculated uncertainty value, the letter suggests, they may lose sight of a more important competency: the cultivated ability to tolerate uncertainty and still act responsibly.

That argument draws on a growing body of medical education scholarship, most prominently the 2016 New England Journal of Medicine perspective by Simpkin and Schwartzstein titled “Tolerating uncertainty — the next medical revolution?” That piece argued that discomfort with uncertainty drives a range of pathology in modern medicine, from excessive diagnostic testing and defensive medicine to communication failures and burnout. Uncertainty tolerance, far from being a soft skill, is framed as a professional capacity intimately linked to clinical judgment, effective patient communication, and patient safety. The Singapore authors build directly on this framing: an “entropy-minimization” mindset, they caution, could distract trainees from the deeper goal of becoming comfortable living with ambiguity. In a busy clinical environment, the temptation to chase a single number that promises clarity is strong, and a pedagogy built around minimizing entropy could reinforce precisely the reflexive, test-driven behavior that educators have spent years trying to moderate.

The debate also carries implications for how artificial intelligence tools will be explained and governed in medicine. As machine learning systems become embedded in triage, imaging interpretation, and predictive analytics, measures of model uncertainty such as entropy will increasingly be surfaced to clinicians, perhaps as confidence scores or risk flags. The letter’s warning suggests that how these numbers are taught, contextualized, and displayed will matter enormously. A confidence metric presented without a decision threshold or a treatment implication invites either blind deference or reflexive dismissal. Used well, however, uncertainty quantification can prompt exactly the right kind of reflection: a pause before acting on a low-confidence prediction, a request for a second opinion, or a conversation with the patient about the limits of what is known. The difference lies not in the mathematics but in the professional culture that surrounds it.

None of this amounts to a rejection of information theory in medicine. The letter is explicit in crediting the original review with a valuable service: introducing a complex concept to a general medical audience and sparking a necessary dialogue on the nature of clinical uncertainty. Its authors position their critique as a call for deeper conversation rather than a dismissal, insisting that before the profession embraces new quantitative tools, it must clarify their proper place in a practice that remains both a science and an art. The historical parallel is instructive. Bayesian reasoning took decades to move from statistical journals into bedside teaching, and only became genuinely useful to clinicians once it was paired with threshold frameworks, likelihood ratios, and pretest probability estimation. Entropy, if it follows a similar path, will need its own translation layer: ways of connecting a global uncertainty measure to the specific probabilities, stakes, and values that drive individual decisions.

For now, the Singapore letter stands as a compact but pointed intervention in one of the most consequential conversations in contemporary medicine: how a profession built on judgment should metabolize the quantitative machinery of the information age. Its message resonates well beyond internal medicine, touching any field wrestling with the promise of AI-assisted uncertainty quantification, from radiology to public health modeling. The core claim is deceptively simple. Measuring uncertainty is not the same as managing it, and a number that summarizes doubt without pointing toward action may, in the hands of an overburdened clinician or a trainee still forming professional habits, do more to obscure good judgment than to support it. As hospitals and developers race to embed uncertainty metrics in clinical workflows, this letter insists that the decisive questions are not computational but philosophical and pedagogical: what do we want clinicians to learn when we teach them to measure what they do not know?

Subject of Research: The limitations of entropy as a quantitative measure of clinical uncertainty in medical decision-making, judgment, and education.

Article Title: Beyond Entropy: Decision Thresholds, Judgment, and Pedagogy

Article References: Sadasiv, M. S., & Chow, M. (2026). Beyond Entropy: Decision Thresholds, Judgment, and Pedagogy. Journal of General Internal Medicine. https://doi.org/10.1007/s11606-026-10746-3

Image Credits: AI Generated

DOI: 10.1007/s11606-026-10746-3

Keywords: entropy, clinical decision-making, uncertainty, Bayesian inference, decision thresholds, medical education, clinical judgment, artificial intelligence, decision theory, value of information, diagnostic uncertainty, internal medicine