Recent work has formalized the reward hypothesis through the lens of expected utility theory, by interpreting reward as utility. Hausner's foundational work showed that dropping the continuity axiom leads to a generalization of expected utility theory where utilities are lexicographically ordered vectors of arbitrary dimension. In this paper, we extend this result by identifying a simple and practical condition under which preferences cannot be represented by scalar rewards, necessitating a 2-dimensional reward function. We provide a full characterization of such reward functions, as well as the general d-dimensional case, in Markov Decision Processes (MDPs) under a memorylessness assumption on preferences. Furthermore, we show that optimal policies in this setting retain many desirable properties of their scalar-reward counterparts, while in the Constrained MDP (CMDP) setting -- another common multiobjective setting -- they do not.

We propose a novel symbolic modeling framework for decision-making under risk that merges interpretability with the core insights of Prospect Theory. Our approach replaces opaque utility curves and probability weighting functions with transparent, effect-size-guided features. We mathematically formalize the method, demonstrate its ability to replicate well-known framing and loss-aversion phenomena, and provide an end-to-end empirical validation on synthetic datasets. The resulting model achieves competitive predictive performance while yielding clear coefficients mapped onto psychological constructs, making it suitable for applications ranging from AI safety to economic policy analysis.

As a unifying concept in economics, game theory, and operations research, even in the Robotics and AI field, the utility is used to evaluate the level of individual needs, preferences, and interests. Especially for decision-making and learning in multi-agent/robot systems (MAS/MRS), a suitable utility model can guide agents in choosing reasonable strategies to achieve their current needs and learning to cooperate and organize their behaviors, optimizing the system's utility, building stable and reliable relationships, and guaranteeing each group member's sustainable development, similar to the human society. Although these systems' complex, large-scale, and long-term behaviors are strongly determined by the fundamental characteristics of the underlying relationships, there has been less discussion on the theoretical aspects of mechanisms and the fields of applications in Robotics and AI. This paper introduces a utility-orient needs paradigm to describe and evaluate inter and outer relationships among agents' interactions. Then, we survey existing literature in relevant fields to support it and propose several promising research directions along with some open problems deemed necessary for further investigations.

Contextual utility theory integrates context-sensitive factors into utility-based decision-making models. It stresses the importance of understanding individual decision-makers' preferences, values, and beliefs and the situational factors that affect them. Contextual utility theory benefits explainable AI. First, it can improve transparency and understanding of how AI systems affect decision-making. It can reveal AI model biases and limitations by considering personal preferences and context. Second, contextual utility theory can make AI systems more personalized and adaptable to users and stakeholders. AI systems can better meet user needs and values by incorporating demographic and cultural data. Finally, contextual utility theory promotes ethical AI development and social responsibility. AI developers can create ethical systems that benefit society by considering contextual factors like societal norms and values. This work, demonstrates how contextual utility theory can improve AI system transparency, personalization, and ethics, benefiting both users and developers.

We consider the problem of modeling trajectories of drivers in a road network from the perspective of inverse reinforcement learning. As rational agents, drivers are trying to maximize some reward function unknown to an external observer as they make up their trajectories. We apply the concept of random utility from microeconomic theory to model the unknown reward function as a function of observable features plus an error term which represents features known only to the driver. We develop a parameterized generative model for the trajectories based on a random utility Markov decision process formulation of drivers decisions. We show that maximum entropy inverse reinforcement learning is a particular case of our proposed formulation when we assume a Gumbel density function for the unobserved reward error terms. We illustrate Bayesian inference on model parameters through a case study with real trajectory data from a large city obtained from sensors placed on sparsely distributed points on the street network.

In this first article, we highlight how intelligence and rationality are tightly coupled with the uncertainty present in the world. We also discuss how uncertainty plays a critical role in designing beneficial general-purpose artificial intelligence (AI), as described by the work of Stuart Russel and Peter Norvig on Modern AI [1][2]. Human intelligence, both social and individual, is what has been driving advances achieved by the human civilization. Having access to even greater intelligence in the form of machine artificial intelligence (AI) can potentially lead to even further advances, and will help us solve major problems such as eliminating poverty and disease, solving open scientific and mathematical problems, and offering personal assistance targeting billions of people worldwide. This is subject of course to the finite resources of land and raw material available on earth.

The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utilities, and therefore, to a partial (incomplete) preference order on the set of all belief function lotteries. If the belief function reference lotteries we use are Bayesian belief functions, then our representation theorem coincides with Jaffray's representation theorem for his linear utility theory for belief functions. We illustrate our framework using some examples discussed in the literature, and we propose a simple model based on an interval-valued pessimism index representing a decision-maker's attitude to ambiguity and indeterminacy. Finally, we compare our decision theory with those proposed by Jaffray, Smets, Dubois et al., Giang and Shenoy, and Shafer.

Understanding human driving behavior is important for autonomous vehicles. In this paper, we propose an interpretable human behavior model in interactive driving scenarios based on the cumulative prospect theory (CPT). As a non-expected utility theory, CPT can well explain some systematically biased or ``irrational'' behavior/decisions of human that cannot be explained by the expected utility theory. Hence, the goal of this work is to formulate the human drivers' behavior generation model with CPT so that some ``irrational'' behavior or decisions of human can be better captured and predicted. Towards such a goal, we first develop a CPT-driven decision-making model focusing on driving scenarios with two interacting agents. A hierarchical learning algorithm is proposed afterward to learn the utility function, the value function, and the decision weighting function in the CPT model. A case study for roundabout merging is also provided as verification. With real driving data, the prediction performances of three different models are compared: a predefined model based on time-to-collision (TTC), a learning-based model based on neural networks, and the proposed CPT-based model. The results show that the proposed model outperforms the TTC model and achieves similar performance as the learning-based model with much less training data and better interpretability.

Traditional cognitive theories systematically apply classical set-theoretic structures to model human judgements and decisions under uncertainty. This is particularly evident in theories of rational decision-making, like expected utility theory, where Bayesian, or Kolmogorovian [1], models of probability directly follow from axioms on agents' preferences [2, 3]. However, several cognitive puzzles have been discovered in empirical tests, which provide evidence of systematic deviations from Kolmogorovian probability structures (see, e.g., [4]). For example, Kahneman and Tversky identified a conjunction fallacy in human probability judgements, namely, the law of monotonicity of Kolmogorovian probability does not generally hold in this kind of judgements [5]. Also, in human decision-making, Tversky and Shafir proved that the law of total Kolmogorovian probability does not hold in the disjunction effect [6], while Allais and Ellsberg indicated that people do not always choose by maximizing an expected utility with respect to a Kolmogorovian probability measure [7]. As a consequence of the puzzles above, traditional theories using Kolmogorovian structures, though normatively compelling, are descriptively flawed, which led several authors to elaborate alternative proposals able to more efficiently and realistically represent human behaviour. This was the starting point of the bounded rationality research programme, initially proposed by Herbert Simon [8] and systematically applied by Kahneman and Tversky [5, 6] to describe concrete judgements and decisions. Bounded rationality models give good predictions in a variety of circumstances.

Some well-known paradoxes in decision making (e.g., the Allais paradox, the St. Peterburg paradox, the Ellsberg paradox, and the Machina paradox) reveal that choices conventional expected utility theory predicts could be inconsistent with empirical observations. So, solutions to these paradoxes can help us better understand humans decision making accurately. This is also highly related to the prediction power of a decision-making model in real-world applications. Thus, various models have been proposed to address these paradoxes. However, most of them can only solve parts of the paradoxes, and for doing so some of them have to rely on the parameter tuning without proper justifications for such bounds of parameters. To this end, this paper proposes a new descriptive decision-making model, expected utility with relative loss reduction, which can exhibit the same qualitative behaviours as those observed in experiments of these paradoxes without any additional parameter setting. In particular, we introduce the concept of relative loss reduction to reflect people's tendency to prefer ensuring a sufficient minimum loss to just a maximum expected utility in decision-making under risk or ambiguity.