Shen Li

Shen Li, Theodoros Stouraitis, Michael Gienger et al.

Consistent state estimation is challenging, especially under the epistemic uncertainties arising from learned (nonlinear) dynamic and observation models. In this work, we propose a set-based estimation algorithm, named Gaussian Process-Zonotopic Kalman Filter (GP-ZKF), that produces zonotopic state estimates while respecting both the epistemic uncertainties in the learned models and aleatoric uncertainties. Our method guarantees probabilistic consistency, in the sense that the true states are bounded by sets (zonotopes) across all time steps, with high probability. We formally relate GP-ZKF with the corresponding stochastic approach, GP-EKF, in the case of learned (nonlinear) models. In particular, when linearization errors and aleatoric uncertainties are omitted and epistemic uncertainties are simplified, GP-ZKF reduces to GP-EKF. We empirically demonstrate our method's efficacy in both a simulated pendulum domain and a real-world robot-assisted dressing domain, where GP-ZKF produced more consistent and less conservative set-based estimates than all baseline stochastic methods.

Ankit Shah, Shen Li, Julie Shah

Reward engineering is crucial to high performance in reinforcement learning systems. Prior research into reward design has largely focused on Markovian functions representing the reward. While there has been research into expressing non-Markov rewards as linear temporal logic (LTL) formulas, this has focused on task specifications directly defined by the user. However, in many real-world applications, task specifications are ambiguous, and can only be expressed as a belief over LTL formulas. In this paper, we introduce planning with uncertain specifications (PUnS), a novel formulation that addresses the challenge posed by non-Markovian specifications expressed as beliefs over LTL formulas. We present four criteria that capture the semantics of satisfying a belief over specifications for different applications, and analyze the qualitative implications of these criteria within a synthetic domain. We demonstrate the existence of an equivalent Markov decision process (MDP) for any instance of PUnS. Finally, we demonstrate our approach on the real-world task of setting a dinner table automatically with a robot that inferred task specifications from human demonstrations.