Quantifying the Sensitivity of Inverse Reinforcement Learning to Misspecification

Inverse reinforcement learning (IRL) aims to infer an agent's *preferences* (represented as a reward function $R$) from their *behaviour* (represented as a policy $\pi$). To do this, we need a *behavioural model* of how $\pi$ 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.