Certified Reinforcement Learning with Logic Guidance

This paper proposes the first model-free Reinforcement Learning (RL) framework to synthesise policies for unknown, and continuous-state Markov Decision Processes (MDPs), such that a given linear temporal property is satisfied. We convert the given property into a Limit Deterministic Buchi Automaton (LDBA), namely a finite-state machine expressing the property. Exploiting the structure of the LDBA, we shape a synchronous reward function on-the-fly, so that an RL algorithm can synthesise a policy resulting in traces that probabilistically satisfy the linear temporal property. This probability (certificate) is also calculated in parallel with policy learning when the state space of the MDP is finite: as such, the RL algorithm produces a policy that is certified with respect to the property. Under the assumption of finite state space, theoretical guarantees are provided on the convergence of the RL algorithm to an optimal policy, maximising the above probability. We also show that our method produces ''best available'' control policies when the logical property cannot be satisfied. In the general case of a continuous state space, we propose a neural network architecture for RL and we empirically show that the algorithm finds satisfying policies, if there exist such policies. The performance of the proposed framework is evaluated via a set of numerical examples and benchmarks, where we observe an improvement of one order of magnitude in the number of iterations required for the policy synthesis, compared to existing approaches whenever available.Comment: This article draws from arXiv:1801.08099, arXiv:1809.0782

Learning Task Specifications from Demonstrations

Real world applications often naturally decompose into several sub-tasks. In many settings (e.g., robotics) demonstrations provide a natural way to specify the sub-tasks. However, most methods for learning from demonstrations either do not provide guarantees that the artifacts learned for the sub-tasks can be safely recombined or limit the types of composition available. Motivated by this deficit, we consider the problem of inferring Boolean non-Markovian rewards (also known as logical trace properties or specifications) from demonstrations provided by an agent operating in an uncertain, stochastic environment. Crucially, specifications admit well-defined composition rules that are typically easy to interpret. In this paper, we formulate the specification inference task as a maximum a posteriori (MAP) probability inference problem, apply the principle of maximum entropy to derive an analytic demonstration likelihood model and give an efficient approach to search for the most likely specification in a large candidate pool of specifications. In our experiments, we demonstrate how learning specifications can help avoid common problems that often arise due to ad-hoc reward composition.Comment: NIPS 201

NNgTL: Neural Network Guided Optimal Temporal Logic Task Planning for Mobile Robots

In this work, we investigate task planning for mobile robots under linear temporal logic (LTL) specifications. This problem is particularly challenging when robots navigate in continuous workspaces due to the high computational complexity involved. Sampling-based methods have emerged as a promising avenue for addressing this challenge by incrementally constructing random trees, thereby sidestepping the need to explicitly explore the entire state-space. However, the performance of this sampling-based approach hinges crucially on the chosen sampling strategy, and a well-informed heuristic can notably enhance sample efficiency. In this work, we propose a novel neural-network guided (NN-guided) sampling strategy tailored for LTL planning. Specifically, we employ a multi-modal neural network capable of extracting features concurrently from both the workspace and the B\"{u}chi automaton. This neural network generates predictions that serve as guidance for random tree construction, directing the sampling process toward more optimal directions. Through numerical experiments, we compare our approach with existing methods and demonstrate its superior efficiency, requiring less than 15% of the time of the existing methods to find a feasible solution.Comment: submitte