Back-propagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods

@inproceedings{Leung2021BackpropagationTS,
  title={Back-propagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods},
  author={Karen Leung and Nikos Ar{\'e}chiga and Marco Pavone},
  booktitle={WAFR},
  year={2021}
}
This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics… 
Signal Temporal Logic Synthesis as Probabilistic Inference
TLDR
The notion of random STL (RSTL), which extends deterministic STL with random predicates, is introduced, which leads to a synthesis-as-inference approach and allows for differentiable, gradient-based synthesis while extending the class of possible uncertain semantics.
Robust Counterexample-guided Optimization for Planning from Differentiable Temporal Logic
TLDR
This paper presents an algorithm for finding robust plans that satisfy STL specifications, using automatically differentiable temporal logic to iteratively optimize its plan in response to counterexamples found during the falsification process.
Semi-Supervised Trajectory-Feedback Controller Synthesis for Signal Temporal Logic Specifications
TLDR
This work proposes a semi-supervised controller synthesis technique that is attuned to human-like behaviors while satisfying desired STL specifications and demonstrates that having imitationbased regularization leads to higher qualitative and quantitative performance compared to optimizing an STL objective only as done in prior work.
Multi-Agent Motion Planning From Signal Temporal Logic Specifications
TLDR
Results show that the method based on timed waypoints supports multi-agent planning from complex specification over long planning horizons, and significantly outperforms state-of-the-art abstraction-based and MPC-based motion planning methods.
Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints
We propose a framework based on Recurrent Neural Networks (RNNs) to determine an optimal control strategy for a discrete-time system that is required to satisfy specifications given as Signal
Model-Based Safe Policy Search from Signal Temporal Logic Specifications Using Recurrent Neural Networks
TLDR
This work proposes a policy search approach to learn controllers from specifications given as Signal Temporal Logic (STL) formulae, and uses control barrier functions (CBFs) with the learned model to improve the safety of the system.
Learning A Risk-Aware Trajectory Planner From Demonstrations Using Logic Monitor
TLDR
This work uses a logic monitor that keeps track of the environmental agents’ behaviors and provides a risk metric that the controlled agent can incorporate during planning, and introduces LogicRiskNet, a learning structure that can be constructed from temporal logic formulas describing rules governing a safe agent’s behaviors.
Learning Provably Robust Motion Planners Using Funnel Libraries
TLDR
The ability of the approach to provide strong guarantees on two simulated examples: navigation of an autonomous vehicle under external disturbances on a five-lane highway with multiple vehicles, and navigation of a drone across an obstacle field in the presence of wind disturbances is demonstrated.
Vehicle Trajectory Prediction Using Generative Adversarial Network With Temporal Logic Syntax Tree Features
TLDR
A framework based on generative adversarial networks that uses tools from formal methods, namely signal temporal logic and syntax trees, allows us to leverage information on rule obedience as features in neural networks and improves prediction accuracy without biasing towards lawful behavior.
Knowledge-Integrated Informed AI for National Security
TLDR
Findings are shared from a thorough exploration of AI approaches that exploit data as well as principled and/or practical knowledge, which are referred to as “knowledge-integrated informed AI” and how the advantages stand to benefit the national security domain.
...
...

References

SHOWING 1-10 OF 36 REFERENCES
Safe Control under Uncertainty with Probabilistic Signal Temporal Logic
TLDR
This work proposes the new Probabilistic Signal Temporal Logic (PrSTL), an expressive language to define stochastic properties and enforce probabilistic guarantees on them, and presents an efficient algorithm to reason about safe controllers given the constraints derived from the PrSTL specification.
Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints
We propose a framework based on Recurrent Neural Networks (RNNs) to determine an optimal control strategy for a discrete-time system that is required to satisfy specifications given as Signal
Monitoring Temporal Properties of Continuous Signals
TLDR
A variant of temporal logic tailored for specifying desired properties of continuous signals, based on a bounded subset of the real-time logic mitl, augmented with a static mapping from continuous domains into propositions is introduced.
Smooth operator: Control using the smooth robustness of temporal logic
TLDR
This work formalizes the requirements as formulas in Metric Temporal Logic (MTL), and designs a controller that maximizes the robustness of the MTL formula, thus enabling the use of powerful gradient descent optimizers.
Reinforcement learning with temporal logic rewards
  • Xiao LiC. VasileC. Belta
  • Computer Science
    2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
  • 2017
TLDR
It is shown in simulated trials that learning is faster and policies obtained using the proposed approach outperform the ones learned using heuristic rewards in terms of the robustness degree, i.e., how well the tasks are satisfied.
Learning from Demonstrations using Signal Temporal Logic
TLDR
Signal Temporal Logic is used to evaluate and rank the quality of demonstrations, and it is shown that this approach outperforms the state-of-the-art Maximum Causal Entropy Inverse Reinforcement Learning.
TuLiP: a software toolbox for receding horizon temporal logic planning
TLDR
TuLiP applies the receding horizon framework, allowing the synthesis problem to be broken into a set of smaller problems, and consequently alleviating the computational complexity of the synthesis procedure, while preserving the correctness guarantee.
Multi-objective optimal control for proactive decision making with temporal logic models
TLDR
This paper distill high-dimensional state trajectories of human–robot interaction into concise, symbolic behavioral summaries that can be learned from data, and designs a novel decision-making scheme that maintains a belief distribution over models of human behavior, and proactively plans informative actions.
Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications
TLDR
A new average-based robustness for Signal Temporal Logic (STL) and a framework for optimal control of a dynamical system under STL constraints is presented and its usefulness in control synthesis problems is illustrated through case studies.
Temporal logic motion planning for dynamic robots
...
...