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

Mungojerrie:Linear-Time Objectives in Model-Free Reinforcement Learning

Mungojerrie is an extensible tool that provides a framework to translate linear-time objectives into reward for reinforcement learning (RL). The tool provides convergent RL algorithms for stochastic games, reference implementations of existing reward translations for ω -regular objectives, and an internal probabilistic model checker for ω -regular objectives. This functionality is modular and operates on shared data structures, which enables fast development of new translation techniques. Mungojerrie supports finite models specified in PRISM and ω -automata specified in the HOA format, with an integrated command line interface to external linear temporal logic translators. Mungojerrie is distributed with a set of benchmarks for ω -regular objectives in RL.</p

The Complexity of POMDPs with Long-run Average Objectives

We study the problem of approximation of optimal values in partially-observable Markov decision processes (POMDPs) with long-run average objectives. POMDPs are a standard model for dynamic systems with probabilistic and nondeterministic behavior in uncertain environments. In long-run average objectives rewards are associated with every transition of the POMDP and the payoff is the long-run average of the rewards along the executions of the POMDP. We establish strategy complexity and computational complexity results. Our main result shows that finite-memory strategies suffice for approximation of optimal values, and the related decision problem is recursively enumerable complete

Stochastic Finite State Control of POMDPs with LTL Specifications

Partially observable Markov decision processes (POMDPs) provide a modeling framework for autonomous decision making under uncertainty and imperfect sensing, e.g. robot manipulation and self-driving cars. However, optimal control of POMDPs is notoriously intractable. This paper considers the quantitative problem of synthesizing sub-optimal stochastic finite state controllers (sFSCs) for POMDPs such that the probability of satisfying a set of high-level specifications in terms of linear temporal logic (LTL) formulae is maximized. We begin by casting the latter problem into an optimization and use relaxations based on the Poisson equation and McCormick envelopes. Then, we propose an stochastic bounded policy iteration algorithm, leading to a controlled growth in sFSC size and an any time algorithm, where the performance of the controller improves with successive iterations, but can be stopped by the user based on time or memory considerations. We illustrate the proposed method by a robot navigation case study