Modular Deep Reinforcement Learning for Continuous Motion Planning with Temporal Logic

Alessandro Abate; Mingyu Cai; Mohammadhosein Hasanbeig; Shaoping Xiao; Zhen Kan

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Modular Deep Reinforcement Learning for Continuous Motion Planning with Temporal Logic

Mingyu Cai, Mohammadhosein Hasanbeig, Shaoping Xiao, Alessandro Abate, Zhen Kan

Machine Learning · Submitted 24 Feb 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Rigorous analysis shows that any RL method that optimizes the expected discounted return is guaranteed to find an optimal policy whose traces maximize the satisfaction probability.

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arXiv ID2102.12855 (version 7)

Pith IDCIDROVVW, Pith's permanent record of this paper and its review

CitationAlessandro Abate, Mingyu Cai, Mohammadhosein Hasanbeig, Shaoping Xiao, Zhen Kan. "Modular Deep Reinforcement Learning for Continuous Motion Planning with Temporal Logic." arXiv:2102.12855 (2021). https://pith.science/paper/CIDROVVW

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What the abstract itself states, as probabilities: claims first 0.13 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.10 · mentions code or data availability 0.02.

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arXiv listing abstract v7. Results and the main claim are underlined; show every role.

This paper investigates the motion planning of autonomous dynamical systems modeled by Markov decision processes (MDP) with unknown transition probabilities over continuous state and action spaces. Linear temporal logic (LTL) is used to specify high-level tasks over infinite horizon, which can be converted into a limit deterministic generalized B\"uchi automaton (LDGBA) with several accepting sets. The novelty is to design an embedded product MDP (EP-MDP) between the LDGBA and the MDP by incorporating a synchronous tracking-frontier function to record unvisited accepting sets of the automaton, and to facilitate the satisfaction of the accepting conditions. The proposed LDGBA-based reward shaping and discounting schemes for the model-free reinforcement learning (RL) only depend on the EP-MDP states and can overcome the issues of sparse rewards. Rigorous analysis shows that any RL method that optimizes the expected discounted return is guaranteed to find an optimal policy whose traces maximize the satisfaction probability. A modular deep deterministic policy gradient (DDPG) is then developed to generate such policies over continuous state and action spaces. The performance of our framework is evaluated via an array of OpenAI gym environments.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This paper investigates the motion planning of autonomous dynamical systems modeled by Markov decision processes (MDP) with unknown transition probabilities over continuous state and action spaces.	background 0.96	0.35	0.03	asserted 0.94
s1	Linear temporal logic (LTL) is used to specify high-level tasks over infinite horizon, which can be converted into a limit deterministic generalized B\"uchi automaton (LDGBA) with several accepting sets.	method 0.57	0.23	0.03	asserted 1.00
s2	The novelty is to design an embedded product MDP (EP-MDP) between the LDGBA and the MDP by incorporating a synchronous tracking-frontier function to record unvisited accepting sets of the automaton, and to facilitate the satisfaction of the accepting conditions.	contribution 0.97	0.91	0.11	asserted 1.00
s3	The proposed LDGBA-based reward shaping and discounting schemes for the model-free reinforcement learning (RL) only depend on the EP-MDP states and can overcome the issues of sparse rewards.	contribution 0.56	0.87	0.10	asserted 1.00
s4	Rigorous analysis shows that any RL method that optimizes the expected discounted return is guaranteed to find an optimal policy whose traces maximize the satisfaction probability.	result 0.78	0.85	0.44	asserted 1.00
s5	A modular deep deterministic policy gradient (DDPG) is then developed to generate such policies over continuous state and action spaces.	method 0.86	0.91	0.05	asserted 1.00
s6	The performance of our framework is evaluated via an array of OpenAI gym environments.	method 0.91	0.92	0.04	asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.57.

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arXiv listing abstract v7

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full text
figures and tables
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P abstract

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C citations
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The paper

Original abstract

This paper investigates the motion planning of autonomous dynamical systems modeled by Markov decision processes (MDP) with unknown transition probabilities over continuous state and action spaces. Linear temporal logic (LTL) is used to specify high-level tasks over infinite horizon, which can be converted into a limit deterministic generalized B\"uchi automaton (LDGBA) with several accepting sets. The novelty is to design an embedded product MDP (EP-MDP) between the LDGBA and the MDP by incorporating a synchronous tracking-frontier function to record unvisited accepting sets of the automaton, and to facilitate the satisfaction of the accepting conditions. The proposed LDGBA-based reward shaping and discounting schemes for the model-free reinforcement learning (RL) only depend on the EP-MDP states and can overcome the issues of sparse rewards. Rigorous analysis shows that any RL method that optimizes the expected discounted return is guaranteed to find an optimal policy whose traces maximize the satisfaction probability. A modular deep deterministic policy gradient (DDPG) is then developed to generate such policies over continuous state and action spaces. The performance of our framework is evaluated via an array of OpenAI gym environments.

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4 arXiv papers cite this in 4 sentences

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Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

With appropriate dependent reward and discount functions, rigorous analysis shows that any method that optimizes the expected discount return of the RL-based approach is guaranteed to find the optimal policy that maximizes the satisfaction probability of the LTL specifications.

Reinforcement Learning Based Temporal Logic Control with Maximum Probabilistic Satisfaction · 0.90

Papers citing it · 1 sentence without a confident label

Cites it as background 3 papers

Reinforcement learning (RL) has recently emerged as a prominent tool to synthesize optimal control policies for stochastic systems, modeled as Markov Decision Processes (MDPs), with complex control objectives captured by formal languages, such as Linear Temporal Logic (LTL) [ref] .

Accelerated Reinforcement Learning for Temporal Logic Control Objectives · Introduction · 0.99
Temporal formalisms such as Linear Temporal Logic (LTL) [ref] provide a rich semantics to unambiguously specify liveness and safety properties, sequencing constraints, response guarantees in safety-critical hardware, software, and communication systems [ref] , dynamical systems [ref] , etc.

NeuroNL2LTL: A Neurosymbolic Framework for Natural Language Translation of Linear Temporal Logic · Introduction · 0.98
Other learning-based related works include modeling with Gaussian processes ( [ref] ), or use neural networks ( [ref] ) to accomplish reachability, verification or temporal logic specifications.

Non-Parametric Neuro-Adaptive Control Subject to Task Specifications · Related work · 0.96

What it cites · 13 sentences without a confident label

Contests 1 paper

However, the maximum probability of task satisfaction cannot be guaranteed and the standard DDPG algorithm cannot distinguish the sub-task module in [ref] , resulting in an unsatisfactory success rate.

Continuous Motion Planning with Temporal Logic Specifications using Deep Neural Networks · Introduction · contest 0.88

Uses the method or tool of 2 papers

Inspired by [ref] and [ref] , the complex LTL task $ϕ$ can be divided into simple composable modules.

Modular Deep Reinforcement Learning with Temporal Logic Specifications · Modular Deep Deterministic Policy Gradient · 0.81
To deal with continuous-state and continuous-action MDPs, a deep deterministic policy gradient (DDPG) [ref] is adopted in this work to approximate the current deterministic policy via a parameterized function $π(x|θ^u.)$ called actor.

Continuous control with deep reinforcement learning · Modular Deep Deterministic Policy Gradient · 1.00

Compares with 1 paper

The modular DDPG with the EP-MDP in this work is capable of recording the unvisited accepting sets for each round, which outperforms the result of [ref] .

Continuous Motion Planning with Temporal Logic Specifications using Deep Neural Networks · Modular Deep Deterministic Policy Gradient · 1.00

Cites as background 2 papers

Along this line of research, the most relevant works include [ref] .

Modular Deep Reinforcement Learning with Temporal Logic Specifications · Introduction · 0.88
Along this line of research, the most relevant works include [ref] .

Continuous Motion Planning with Temporal Logic Specifications using Deep Neural Networks · Introduction · 0.88

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