Large language models (LLMs) excel at explicit reasoning, but their implicit computational strategies remain underexplored. Decades of psychophysics research show that humans intuitively process and integrate noisy signals using near-optimal Bayesian strategies in perceptual tasks. We ask whether LLMs exhibit similar behaviour and perform optimal multimodal integration without explicit training or instruction. Adopting the psychophysics paradigm, we infer computational principles of LLMs from systematic behavioural studies. We introduce a behavioural benchmark - BayesBench: four magnitude estimation tasks (length, location, distance, and duration) over text and image, inspired by classic psychophysics, and evaluate a diverse set of nine LLMs alongside human judgments for calibration. Through controlled ablations of noise, context, and instruction prompts, we measure performance, behaviour and efficiency in multimodal cue-combination. Beyond accuracy and efficiency metrics, we introduce a Bayesian Consistency Score that detects Bayes-consistent behavioural shifts even when accuracy saturates. Our results show that while capable models often adapt in Bayes-consistent ways, accuracy does not guarantee robustness. Notably, GPT-5 Mini achieves perfect text accuracy but fails to integrate visual cues efficiently. This reveals a critical dissociation between capability and strategy, suggesting accuracy-centric benchmarks may over-index on performance while missing brittle uncertainty handling. These findings reveal emergent principled handling of uncertainty and highlight the correlation between accuracy and Bayesian tendencies. We release our psychophysics benchmark and consistency metric (https://bayes-bench.github.io) as evaluation tools and to inform future multimodal architecture designs.

The aim of inverse reinforcement learning (IRL) is to infer an agent's preferences from observing their behaviour. Usually, preferences are modelled as a reward function, $R$, and behaviour is modelled as a policy, $\pi$. One of the central difficulties in IRL is that multiple preferences may lead to the same observed behaviour. That is, $R$ is typically underdetermined by $\pi$, which means that $R$ is only partially identifiable. Recent work has characterised the extent of this partial identifiability for different types of agents, including optimal and Boltzmann-rational agents. However, work so far has only considered agents that discount future reward exponentially: this is a serious limitation, especially given that extensive work in the behavioural sciences suggests that humans are better modelled as discounting hyperbolically. In this work, we newly characterise partial identifiability in IRL for agents with non-exponential discounting: our results are in particular relevant for hyperbolical discounting, but they also more generally apply to agents that use other types of (non-exponential) discounting. We significantly show that generally IRL is unable to infer enough information about $R$ to identify the correct optimal policy, which entails that IRL alone can be insufficient to adequately characterise the preferences of such agents.

The aim of Inverse Reinforcement Learning (IRL) is to infer a reward function $R$ from a policy $\pi$. This problem is difficult, for several reasons. First of all, there are typically multiple reward functions which are compatible with a given policy; this means that the reward function is only *partially identifiable*, and that IRL contains a certain fundamental degree of ambiguity. Secondly, in order to infer $R$ from $\pi$, an IRL algorithm must have a *behavioural model* of how $\pi$ relates to $R$. However, the true relationship between human preferences and human behaviour is very complex, and practically impossible to fully capture with a simple model. This means that the behavioural model in practice will be *misspecified*, which raises the worry that it might lead to unsound inferences if applied to real-world data. In this paper, we provide a comprehensive mathematical analysis of partial identifiability and misspecification in IRL. Specifically, we fully characterise and quantify the ambiguity of the reward function for all of the behavioural models that are most common in the current IRL literature. We also provide necessary and sufficient conditions that describe precisely how the observed demonstrator policy may differ from each of the standard behavioural models before that model leads to faulty inferences about the reward function $R$. In addition to this, we introduce a cohesive framework for reasoning about partial identifiability and misspecification in IRL, together with several formal tools that can be used to easily derive the partial identifiability and misspecification robustness of new IRL models, or analyse other kinds of reward learning algorithms.

Inverse reinforcement learning (IRL) aims to infer an agent's preferences (represented as a reward function R) from their behaviour (represented as a policy π). To do this, we need a behavioural model of how π relates to R. In the current literature, the most common behavioural models are optimality, Boltzmann-rationality, and causal entropy maximisation. However, the true relationship between a human's preferences and their behaviour is much more complex than any of these behavioural models. This means that the behavioural models are misspecified, which raises the concern that they may lead to systematic errors if applied to real data. In this paper, we analyse how sensitive the IRL problem is to misspecification of the behavioural model. Specifically, we provide necessary and sufficient conditions that completely characterise how the observed data may differ from the assumed behavioural model without incurring an error above a given threshold. In addition to this, we also characterise the conditions under which a behavioural model is robust to small perturbations of the observed policy, and we analyse how robust many behavioural models are to misspecification of their parameter values (such as e.g. the discount rate). Our analysis suggests that the IRL problem is highly sensitive to misspecification, in the sense that very mild misspecification can lead to very large errors in the inferred reward function. Inverse reinforcement learning (IRL) is a subfield of machine learning that aims to develop techniques for inferring an agent's preferences based on their actions in a sequential decision-making problem (Ng & Russell, 2000). There are many motivations for IRL. One motivation is to use it as a tool for imitation learning, where the objective is to replicate the behaviour of an expert in some task (e.g. In this context, it is not essential that the inferred preferences reflect the actual intentions of the expert, as long as they improve the imitation learning process. Another motivation for IRL is to use it as a tool for preference elicitation, where the objective is to understand an agent's goals or desires (e.g. In this context, it is of central importance that the inferred preferences reflect the actual preferences of the observed agent.

In our recent AAAI 2023 paper, Misspecification in Inverse Reinforcement Learning (Skalse and Abate, 2023), we study the question of how robust the inverse reinforcement learning problem is to misspecification of the underlying behavioural model (namely, how the agent's preferences relate to its behaviour). We provide a mathematical framework for reasoning about this question, and use that framework (based on equivalence classes and orders) to derive necessary and sufficient conditions describing what types of misspecification each of the standard behavioural models are (or are not) robust to. Moreover, we provide several results and formal tools, which can be used to study the misspecification robustness of any behavioural models that may be newly developed. Below, we will first explain the motivation for this work. Then, we will explain our results and, finally, describe ways to extend them. Inverse reinforcement learning (IRL) is an area of machine learning concerned with inferring what objective an agent is pursuing, based on the actions taken by that agent.

The aim of Inverse Reinforcement Learning (IRL) is to infer a reward function $R$ from a policy $\pi$. To do this, we need a model of how $\pi$ relates to $R$. In the current literature, the most common models are optimality, Boltzmann rationality, and causal entropy maximisation. One of the primary motivations behind IRL is to infer human preferences from human behaviour. However, the true relationship between human preferences and human behaviour is much more complex than any of the models currently used in IRL. This means that they are misspecified, which raises the worry that they might lead to unsound inferences if applied to real-world data. In this paper, we provide a mathematical analysis of how robust different IRL models are to misspecification, and answer precisely how the demonstrator policy may differ from each of the standard models before that model leads to faulty inferences about the reward function $R$. We also introduce a framework for reasoning about misspecification in IRL, together with formal tools that can be used to easily derive the misspecification robustness of new IRL models.

Semi-supervised learning improves the performance of supervised machine learning by leveraging methods from unsupervised learning to extract information not explicitly available in the labels. Through the design of a system that enables a robot to learn inspection strategies from a human operator, we present a hybrid semi-supervised system capable of learning interpretable and verifiable models from demonstrations. The system induces a controller program by learning from immersive demonstrations using sequential importance sampling. These visual servo controllers are parametrised by proportional gains and are visually verifiable through observation of the position of the robot in the environment. Clustering and effective particle size filtering allows the system to discover goals in the state space. These goals are used to label the original demonstration for end-to-end learning of behavioural models. The behavioural models are used for autonomous model predictive control and scrutinised for explanations. We implement causal sensitivity analysis to identify salient objects and generate counterfactual conditional explanations. These features enable decision making interpretation and post hoc discovery of the causes of a failure. The proposed system expands on previous approaches to program synthesis by incorporating repellers in the attribution prior of the sampling process. We successfully learn the hybrid system from an inspection scenario where an unmanned ground vehicle has to inspect, in a specific order, different areas of the environment. The system induces an interpretable computer program of the demonstration that can be synthesised to produce novel inspection behaviours. Importantly, the robot successfully runs the synthesised program on an unseen configuration of the environment while presenting explanations of its autonomous behaviour.

This article introduces a reflexion about behavioural specification for interactive and participative agent-based simulation in virtual reality. Within this context, it is neces sary to reach a high level of expressivness in order to enforce interactions between the designer and the behavioural model during the in-line prototyping. This requires to consider the need of semantic very early in the design process. The Intentional agent model is here exposed as a possible answer. It relies on a mixed imperative and declarative approach which focuses on the link between decision and action. The design of a tool able to simulate virtual environment implying agents based on this model is discuss