The Constitutional Filter: Bayesian Estimation of Compliant Agents

Simon Kohaut; Felix Divo; Benedict Flade; Devendra Singh Dhami; Julian Eggert; Kristian Kersting

cs.RODec 24, 2024

The Constitutional Filter: Bayesian Estimation of Compliant Agents

Authors: Simon Kohaut, Felix Divo, Benedict Flade, Devendra Singh Dhami, Julian Eggert, Kristian Kersting

Organizations: Artificial Intelligence and Machine Learning Group, Department of Computer Science, TU Darmstadt, 64283 Darmstadt, Germany · Honda Research Institute Europe GmbH, Carl-Legien-Str. 30, 63073 Offenbach, Germany · Uncertainty in Artificial Intelligence Group, Department of Mathematics and Computer Science, TU Eindhoven, 5600 MB Eindhoven, Netherlands · Hessian AI ·

Abstract

Predicting agents impacted by legal policies, physical limitations, and operational preferences is inherently difficult. In recent years, neuro-symbolic methods have emerged, integrating machine learning and symbolic reasoning models into end-to-end learnable systems. Hereby, a promising avenue for expressing high-level constraints over multi-modal input data in robotics has opened up. This work introduces an approach for Bayesian estimation of agents expected to comply with a human-interpretable neuro-symbolic model we call its Constitution. Hence, we present the Constitutional Filter (CoFi), leading to improved tracking of agents by leveraging expert knowledge, incorporating deep learning architectures, and accounting for environmental uncertainties. CoFi extends the general, recursive Bayesian estimation setting, ensuring compatibility with a vast landscape of established techniques such as Particle Filters. To underpin the advantages of CoFi, we evaluate its performance on real-world marine traffic data. Beyond improved performance, we show how CoFi can learn to trust and adapt to the level of compliance of an agent, recovering baseline performance even if the assumed Constitution clashes with reality.

Figures & tables

Fig. 1 : The Constitutional Filter’s estimation cycle: A Constitution for a remote-controlled, unmanned aircraft system is shown on the left. The right-hand side shows the tracked drone and the likely compliant areas shaded in blue.

Panel of Figure 2 — Fig. 2 : StaR Maps parameters in an Advanced Aerial Mobility setting : Here, the expected values of two basic probabilistic spatial relations are shown in an urban environment, namely over and distance (used in Figure 1 ).

Fig. 3 : The Constitutional Filter’s architecture: CoFi extends recursive Bayesian estimation using a neuro-symbolic model of the tracked agent’s decision-making constraints, integrating background knowledge, perception, and a probabilistic environment representation.

Panel of Figure 4 — Fig. 4 : Statistical relational maps for marine traffic: Expectations of StaR Map relations employed in Listing 5 at New York’s harbor, considering land, waterways, anchorage areas, and depth. Distances are shown in kilometers.

Fig. 5 : A marine vessel’s constitution, modeling compliance with safety and traffic rules.

Panel of Figure 6 — Fig. 6 : Marine traffic over constitutional probabilities: Here, we show real-world AIS traces from (a) often compliant cargo and (b) often incompliant towing vessels on top of the probabilities for each to satisfy the constitution.

Fig. 7 : Trust depending on observations: Not every tracked agent can be expected to satisfy the assumed constitution. Here, the average value of

P(C_{t}|\mathbf{x}_{t},\mathbf{z}_{t})

is shown aggregated for different vessel types.

Fig. 8 : A majority of vessels can be trusted: Here, the rate at which a specific value of

\tau

is optimal (given observed trust features) is shown for the entire dataset. Note how CoFi rarely needs to fall back to its internal Particle Filter.

Fig. 9 : CoFi adapting to appropriate trust: We show the relative mean absolute error, comparing CoFi’s performance with the baseline Particle Filter. Once a vessel profits from

\tau>0

, CoFi achieves greatly improved accuracy.

Bayesian Filtering

Bayesian filtering recursively estimates hidden states and their uncertainty from noisy, sequential observations in changing systems.

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The Constitutional Controller: Doubt-Calibrated Steering of Compliant Agents

Simon Kohaut, Felix Divo, Navid Hamid, Benedict Flade+3

Artificial Intelligence and Machine Learning Lab, Department of Computer Science, TU Darmstadt, 64283 Darmstadt, Germany · Honda Research Institute Europe GmbH, Carl-Legien-Str. 30, 63073 Offenbach, Germany · Uncertainty in Artificial Intelligence Group, Department of Mathematics and Computer Science, TU Eindhoven, 5600 MB Eindhoven, Netherlands+3

Robotic Control Robot Safety Neuro-Symbolic Reasoning Probabilistic Logic

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Ensuring reliable and rule-compliant behavior of autonomous agents in uncertain environments remains a fundamental challenge in modern robotics. Our work shows how neuro-symbolic systems, which integrate probabilistic, symbolic white-box reasoning models with deep learning methods, offer a powerful solution to this challenge. They enable the simultaneous consideration of explicit rules and neural models trained on noisy data, combining the strengths of structured reasoning with flexible representations. To this end, we introduce the Constitutional Controller (CoCo), a novel framework designed to enhance the safety and reliability of agents by reasoning over deep probabilistic logic programs that represent constraints, such as those found in shared traffic spaces. Furthermore, we propose the concept of self-doubt, implemented as a probability density conditioned on doubt features such as travel velocity, employed sensors, or health factors. In a real-world aerial mobility study, we demonstrate CoCo's advantages for intelligent autonomous systems to learn appropriate doubts and navigate complex, uncertain environments safely and compliantly.

Abstract

Bayesian Filtering

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