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.
IST Austria (Institute of Science and Technology Austria)（奥地利科学技术研究所）；Indian Institute of Technology, Bombay（印度理工学院孟买分校）
We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, rece…
Decision-making policies for agents are often synthesized with the constraint that a formal specification of behaviour is satisfied. Here we focus on infinite-horizon properties. On the one hand, Linear Temporal Logic (LTL) is a popular example of a formalism for qualitative specifications. On the other hand, Steady-State Policy Synthesis (SSPS) has recently received considerable attention as it provides a more quantitative and more behavioural perspective on specifications, in terms of the frequency with which states are visited. Finally, rewards provide a classic framework for quantitative p…
Lehigh University（理海大学）；MIT Lincoln Laboratory（麻省理工学院林肯实验室）
This paper explores continuous-time control synthesis for target-driven navigation to satisfy complex high-level tasks expressed as linear temporal logic (LTL). We propose a model-free framework using deep reinforcement learning (DRL) where the underlying dynamic system is unknown (an opaque box). Unlike prior work, this paper considers scenarios where the given LTL specification might be infeasible and therefore cannot be accomplished globally. Instead of modifying the given LTL formula, we provide a general DRL-based approach to satisfy it with minimal violation. To do this, we transform a p…
Multi-agent partially observable Markov decision processes (MPOMDPs) provide a framework to represent heterogeneous autonomous agents subject to uncertainty and partial observation. In this paper, given a nominal policy provided by a human operator or a conventional planning method, we propose a technique based on barrier functions to design a minimally interfering safety-shield ensuring satisfaction of high-level specifications in terms of linear distribution temporal logic (LDTL). To this end, we use sufficient and necessary conditions for the invariance of a given set based on discrete-time…
In this work we investigate on the concept of "restraining bolt", envisioned in Science Fiction. Specifically we introduce a novel problem in AI. We have two distinct sets of features extracted from the world, one by the agent and one by the authority imposing restraining specifications (the "restraining bolt"). The two sets are apparently unrelated since of interest to independent parties, however they both account for (aspects of) the same world. We consider the case in which the agent is a reinforcement learning agent on the first set of features, while the restraining bolt is specified log…
Aragón Institute of Engineering Research (I3A)（阿拉贡工程研究所（I3A））；University of Zaragoza（萨拉戈萨大学）；Université Paris-Saclay（巴黎萨克雷大学）；ENS Paris-Saclay（巴黎萨克雷高等师范学院）
This work considers the path planning problem for a team of identical robots evolving in a known environment. The robots should satisfy a global specification given as a Linear Temporal Logic (LTL) formula over a set of regions of interest. The proposed method exploits the advantages of Petri net models for the team of robots and Büchi automata modeling the specification. The approach in this paper consists in combining the two models into one, denoted Composed Petri net and use it to find a sequence of action movements for the mobile robots, providing collision free trajectories to fulfill th…
The University of Iowa（爱荷华大学）；Apex.AI Inc（Apex.AI公司）；University of Science and Technology of China（中国科学技术大学）
This work considers online optimal motion planning of an autonomous agent subject to linear temporal logic (LTL) constraints. The environment is dynamic in the sense of containing mobile obstacles and time-varying areas of interest (i.e., time-varying reward and workspace properties) to be visited by the agent. Since user-specified tasks may not be fully realized (i.e., partially infeasible), this work considers hard and soft LTL constraints, where hard constraints enforce safety requirement (e.g. avoid obstacles) while soft constraints represent tasks that can be relaxed to not strictly follo…
The synthesis problem for partially observable Markov decision processes (POMDPs) is to compute a policy that satisfies a given specification. Such policies have to take the full execution history of a POMDP into account, rendering the problem undecidable in general. A common approach is to use a limited amount of memory and randomize over potential choices. Yet, this problem is still NP-hard and often computationally intractable in practice. A restricted problem is to use neither history nor randomization, yielding policies that are called stationary and deterministic. Previous approaches to …
In this paper, we propose a model-free reinforcement learning method to synthesize control policies for motion planning problems with continuous states and actions. The robot is modelled as a labeled discrete-time Markov decision process (MDP) with continuous state and action spaces. Linear temporal logics (LTL) are used to specify high-level tasks. We then train deep neural networks to approximate the value function and policy using an actor-critic reinforcement learning method. The LTL specification is converted into an annotated limit-deterministic Büchi automaton (LDBA) for continuously sh…
Linear temporal logic and automaton-based run-time verification provide a powerful framework for designing task and motion planning algorithms for autonomous agents. The drawback to this approach is the computational cost of operating on high resolution discrete abstractions of continuous dynamical systems. In particular, the computational bottleneck that arises is converting perceived environment variables into a labeling function on the states of a Kripke structure or analogously the transitions of a labeled transition system. This paper presents the design and empirical evaluation of an app…
Masaryk University（马萨里克大学）；Massachusetts Institute of Technology (MIT)（麻省理工学院（MIT））
We consider the problem of automatic generation of control strategies for robotic vehicles given a set of high-level mission specifications, such as "Vehicle x must eventually visit a target region and then return to a base," "Regions A and B must be periodically surveyed," or "None of the vehicles can enter an unsafe region." We focus on instances when all of the given specifications cannot be reached simultaneously due to their incompatibility and/or environmental constraints. We aim to find the least-violating control strategy while considering different priorities of satisfying different p…
Lehigh University（理海大学）；The University of Iowa（爱荷华大学）；University of Science and Technology of China（中国科学技术大学）
This paper studies optimal motion planning subject to motion and environment uncertainties. By modeling the system as a probabilistic labeled Markov decision process (PL-MDP), the control objective is to synthesize a finite-memory policy, under which the agent satisfies complex high-level tasks expressed as linear temporal logic (LTL) with desired satisfaction probability. In particular, the cost optimization of the trajectory that satisfies infinite horizon tasks is considered, and the trade-off between reducing the expected mean cost and maximizing the probability of task satisfaction is ana…
We propose a new task-specification language for Markov decision processes that is designed to be an improvement over reward functions by being environment independent. The language is a variant of Linear Temporal Logic (LTL) that is extended to probabilistic specifications in a way that permits approximations to be learned in finite time. We provide several small environments that demonstrate the advantages of our geometric LTL (GLTL) language and illustrate how it can be used to specify standard reinforcement-learning tasks straightforwardly.
Often times, we specify tasks for a robot using temporal language that can also span different levels of abstraction. The example command ``go to the kitchen before going to the second floor'' contains spatial abstraction, given that ``floor'' consists of individual rooms that can also be referred to in isolation ("kitchen", for example). There is also a temporal ordering of events, defined by the word "before". Previous works have used Linear Temporal Logic (LTL) to interpret temporal language (such as "before"), and Abstract Markov Decision Processes (AMDPs) to interpret hierarchical abstrac…
University of California, Berkeley（加州大学伯克利分校）；Radboud University Nijmegen（奈梅亨拉德堡德大学）
Partially-Observable Markov Decision Processes (POMDPs) are a well-known stochastic model for sequential decision making under limited information. We consider the EXPTIME-hard problem of synthesising policies that almost-surely reach some goal state without ever visiting a bad state. In particular, we are interested in computing the winning region, that is, the set of system configurations from which a policy exists that satisfies the reachability specification. A direct application of such a winning region is the safe exploration of POMDPs by, for instance, restricting the behavior of a rein…
Do It for HER: First-Order Temporal Logic Reward Specification in Reinforcement Learning (Extended Version)
DEIB, Politecnico di Milano（博洛尼亚工程学院，米兰理工大学）；Politecnico di Milano（米兰理工大学）；INESC-ID/Instituto Superior Técnico Universidade de Lisboa（里斯本大学超级学院/葡萄牙信息科学与技术研究所）；Dipartimento di Informatica Università degli Studi di Milano（米兰大学信息学院）
The University of Texas at Austin（得克萨斯大学奥斯汀分校）；Radboud University（拉德堡德大学）；Albert-Ludwigs-Universität Freiburg（阿尔伯特-路德维希大学弗莱堡分校）；Concept Engineering GmbH（康赛普特工程有限公司）
We study strategy synthesis for partially observable Markov decision processes (POMDPs). The particular problem is to determine strategies that provably adhere to (probabilistic) temporal logic constraints. This problem is computationally intractable and theoretically hard. We propose a novel method that combines techniques from machine learning and formal verification. First, we train a recurrent neural network (RNN) to encode POMDP strategies. The RNN accounts for memory-based decisions without the need to expand the full belief space of a POMDP. Secondly, we restrict the RNN-based strategy …
Albert-Ludwigs-Universität Freiburg（弗莱堡大学）；Concept Engineering GmbH（Concept Engineering有限公司）；RWTH Aachen University（亚琛工业大学）；Radboud University（拉德堡德大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
We study synthesis problems with constraints in partially observable Markov decision processes (POMDPs), where the objective is to compute a strategy for an agent that is guaranteed to satisfy certain safety and performance specifications. Verification and strategy synthesis for POMDPs are, however, computationally intractable in general. We alleviate this difficulty by focusing on planning applications and exploiting typical structural properties of such scenarios; for instance, we assume that the agent has the ability to observe its own position inside an environment. We propose an abstracti…
There have been many studies on automated test generation for mobile Graphical User Interface (GUI) applications. These studies successfully demonstrate how to detect fatal exceptions and achieve high code and activity coverage with fully automated test generation engines. However, it is unclear how many GUI functions these engines manage to test. Furthermore, these engines implement only implicit test oracles. We propose Fully Automated Reinforcement LEArning-Driven Specification-Based Test Generator for Android (FARLEAD-Android). FARLEAD-Android accepts a GUI-level formal specification as a …
Sapienza University of Rome（罗马大学）；The Open University of Israel（以色列开放大学）
Devising a strategy to make a system mimicking behaviors from another system is a problem that naturally arises in many areas of Computer Science. In this work, we interpret this problem in the context of intelligent agents, from the perspective of LTLf, a formalism commonly used in AI for expressing finite-trace properties. Our model consists of two separated dynamic domains, D_A and D_B, and an LTLf specification that formalizes the notion of mimicking by mapping properties on behaviors (traces) of D_A into properties on behaviors of D_B. The goal is to synthesize a strategy that step-by-ste…
Model-free continuous control for robot navigation tasks using Deep Reinforcement Learning (DRL) that relies on noisy policies for exploration is sensitive to the density of rewards. In practice, robots are usually deployed in cluttered environments, containing many obstacles and narrow passageways. Designing dense effective rewards is challenging, resulting in exploration issues during training. Such a problem becomes even more serious when tasks are described using temporal logic specifications. This work presents a deep policy gradient algorithm for controlling a robot with unknown dynamics…
Rice University（莱斯大学）；University of Colorado, Boulder（科罗拉多大学博尔德分校）
Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite tra…
The University of Texas at Austin（得克萨斯大学奥斯汀分校）；Radboud University（拉德堡德大学）
Recurrent neural networks (RNNs) have emerged as an effective representation of control policies in sequential decision-making problems. However, a major drawback in the application of RNN-based policies is the difficulty in providing formal guarantees on the satisfaction of behavioral specifications, e.g. safety and/or reachability. By integrating techniques from formal methods and machine learning, we propose an approach to automatically extract a finite-state controller (FSC) from an RNN, which, when composed with a finite-state system model, is amenable to existing formal verification tool…
SAP Labs, India（思爱普实验室（印度））；IIT Kanpur, India（印度坎普尔理工学院）
We address the path planning problem for a team of robots satisfying a complex high-level mission specification given in the form of an Linear Temporal Logic (LTL) formula. The state-of-the-art approach to this problem employs the automata-theoretic model checking technique to solve this problem. This approach involves computation of a product graph of the Buchi automaton generated from the LTL specification and a joint transition system which captures the collective motion of the robots and then computation of the shortest path using Dijkstra's shortest path algorithm. We propose MT*, an algo…
Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）
Path planning for a robot is one of the major problems in the area of robotics. When a robot is given a task in the form of a Linear Temporal Logic (LTL) specification such that the task needs to be carried out repetitively, we want the robot to follow the shortest cyclic path so that the number of times the robot completes the mission within a given duration gets maximized. In this paper, we address the LTL path planning problem in a dynamic environment where the newly arrived dynamic obstacles may invalidate some of the available paths at any arbitrary point in time. We present DT*, an SMT-b…
Finite linear temporal logic ($\mathsf{LTL}_f$) is a powerful formal representation for modeling temporal sequences. We address the problem of learning a compact $\mathsf{LTL}_f$ formula from labeled traces of system behavior. We propose a novel neural network operator and evaluate the resulting architecture, Neural$\mathsf{LTL}_f$. Our approach includes a specialized recurrent filter, designed to subsume $\mathsf{LTL}_f$ temporal operators, to learn a highly accurate classifier for traces. Then, it discretizes the activations and extracts the truth table represented by the learned weights. Th…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Synthesizing a program that realizes a logical specification is a classical problem in computer science. We examine a particular type of program synthesis, where the objective is to synthesize a strategy that reacts to a potentially adversarial environment while ensuring that all executions satisfy a Linear Temporal Logic (LTL) specification. Unfortunately, exact methods to solve so-called LTL synthesis via logical inference do not scale. In this work, we cast LTL synthesis as an optimization problem. We employ a neural network to learn a Q-function that is then used to guide search, and to co…
Technical University of Kaiserslautern（凯泽斯劳滕工业大学）；Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）
Virtually all verification and synthesis techniques assume that the formal specifications are readily available, functionally correct, and fully match the engineer's understanding of the given system. However, this assumption is often unrealistic in practice: formalizing system requirements is notoriously difficult, error-prone, and requires substantial training. To alleviate this severe hurdle, we propose a fundamentally novel approach to writing formal specifications, named specification sketching for Linear Temporal Logic (LTL). The key idea is that an engineer can provide a partial LTL for…
Linear temporal logic (LTL) offers a simplified way of specifying tasks for policy optimization that may otherwise be difficult to describe with scalar reward functions. However, the standard RL framework can be too myopic to find maximally LTL satisfying policies. This paper makes two contributions. First, we develop a new value-function based proxy, using a technique we call eventual discounting, under which one can find policies that satisfy the LTL specification with highest achievable probability. Second, we develop a new experience replay method for generating off-policy data from on-pol…
