Accelerated Learning with Linear Temporal Logic using Differentiable Simulation

ICLR 2026 Conference SubmissionAnonymous Authors
reinforcement learningtemporal logicdifferentiable simulation
Abstract:

Ensuring that reinforcement learning (RL) controllers satisfy safety and reliability constraints in real-world settings remains challenging: state-avoidance and constrained Markov decision processes often fail to capture trajectory-level requirements or induce overly conservative behavior. Formal specification languages such as linear temporal logic (LTL) offer correct-by-construction objectives, yet their rewards are typically sparse, and heuristic shaping can undermine correctness. We introduce, to our knowledge, the first end-to-end framework that integrates LTL with differentiable simulators, enabling efficient gradient-based learning directly from formal specifications. Our method relaxes discrete automaton transitions via soft labeling of states, yielding differentiable rewards and state representations that mitigate the sparsity issue intrinsic to LTL while preserving objective soundness. We provide theoretical guarantees connecting Büchi acceptance to both discrete and differentiable LTL returns and derive a tunable bound on their discrepancy in deterministic and stochastic settings. Empirically, across complex, nonlinear, contact-rich continuous-control tasks, our approach substantially accelerates training and achieves up to twice the returns of discrete baselines. We further demonstrate compatibility with reward machines, thereby covering co-safe LTL and LTLf without modification. By rendering automaton-based rewards differentiable, our work bridges formal methods and deep RL, enabling safe, specification-driven learning in continuous domains.

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Overview

Overall Novelty Assessment

The paper contributes an end-to-end framework integrating linear temporal logic with differentiable simulators for gradient-based reinforcement learning. It resides in the 'Differentiable LTL for Reinforcement Learning' leaf, which contains only three papers total, indicating a relatively sparse research direction within the broader taxonomy. This leaf sits under 'Differentiable Temporal Logic Frameworks', distinguishing itself from automaton-based methods and planning-only approaches. The small sibling count suggests this specific integration of differentiable simulation with LTL is an emerging area rather than a crowded subfield.

The taxonomy reveals neighboring directions including 'Differentiable STL-Based Optimization' (focused on signal temporal logic rather than LTL) and 'Automaton-Based Policy Synthesis' (using discrete automata without differentiable relaxations). The paper's approach diverges from automaton-based methods by avoiding explicit discrete state machines, instead rendering transitions differentiable through soft labeling. It also differs from STL-based work by targeting LTL specifications specifically. The taxonomy's scope notes clarify that non-differentiable automaton methods and planning-only approaches belong elsewhere, positioning this work at the intersection of formal methods and gradient-based learning.

Among eleven candidates examined across three contributions, no clearly refuting prior work was identified. The core framework contribution examined ten candidates with zero refutations, suggesting limited direct overlap in the examined literature. The soft labeling technique examined zero candidates (likely due to its technical specificity), while the theoretical guarantees contribution examined one candidate without finding refutation. This analysis covers a top-K semantic search plus citation expansion, not an exhaustive survey. The absence of refutations among this limited set suggests the specific combination of differentiable simulation, soft automaton transitions, and Büchi-based guarantees may represent a novel synthesis.

Based on the limited search scope of eleven candidates, the work appears to occupy a sparsely populated research direction with few direct competitors in the examined literature. The taxonomy structure confirms this is an emerging area rather than a mature subfield. However, the analysis cannot rule out relevant prior work outside the top-K semantic matches or in adjacent communities not captured by the search strategy.

Taxonomy

Core-task Taxonomy Papers
25
3
Claimed Contributions
11
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Reinforcement learning from linear temporal logic specifications using differentiable simulation. The field addresses how agents can learn policies that satisfy complex temporal logic constraints, with the taxonomy revealing several complementary approaches. Differentiable Temporal Logic Frameworks render LTL formulas amenable to gradient-based optimization, enabling end-to-end learning through smooth approximations of discrete logic operators. Automaton-Based Policy Synthesis constructs finite-state machines from specifications to guide exploration and reward shaping. Temporal Logic Planning and Control emphasizes model-based methods that integrate LTL into motion planning pipelines, while Safe Policy Learning with Temporal Logic focuses on constraint satisfaction during training. Direct LTL Reward Shaping translates formulas into scalar rewards without explicit automata, and Learning from Demonstrations with LTL leverages expert trajectories annotated with temporal properties. Emerging branches include Diffusion Models with Temporal Logic, which apply generative modeling to specification-driven tasks, and cross-domain applications in robotics and traffic simulation. A central tension exists between differentiable approaches that enable efficient gradient descent and automaton-based methods that provide formal guarantees but may suffer from state-space explosion. Works like Accelerated LTL Learning[0] and LTLDoG[3] exemplify the differentiable paradigm, using smooth relaxations to backpropagate through temporal logic constraints, whereas Colearning Logic Policies[1] and Hierarchical Formal Specs[15] explore hybrid strategies that combine symbolic reasoning with neural policy learning. Accelerated LTL Learning[0] sits squarely within the Differentiable LTL for Reinforcement Learning cluster, emphasizing computational efficiency through simulation-based gradient estimation. Compared to LTLDoG[3], which focuses on differentiable operators for general RL tasks, and Colearning Logic Policies[1], which jointly learns logic structures and policies, Accelerated LTL Learning[0] appears to prioritize scalability via differentiable simulation techniques. Open questions remain around balancing expressiveness, sample efficiency, and the interpretability of learned policies under complex temporal specifications.

Claimed Contributions

End-to-end framework integrating LTL with differentiable simulators

The authors present the first framework that combines linear temporal logic specifications with differentiable physics simulators to enable gradient-based reinforcement learning. This integration allows efficient learning from formal specifications while maintaining correctness guarantees.

10 retrieved papers
Soft labeling technique for differentiable automaton transitions

The authors introduce a soft labeling approach that converts discrete automaton transitions into probabilistic ones, creating differentiable reward functions and state representations. This technique addresses the reward sparsity problem inherent in LTL-based learning without compromising the correctness of the objectives.

0 retrieved papers
Theoretical guarantees connecting Büchi acceptance to differentiable LTL returns

The authors establish formal theoretical results that relate Büchi acceptance conditions to both discrete and differentiable LTL return formulations. They derive a tunable upper bound on the discrepancy between these two formulations that holds in both deterministic and stochastic environments.

1 retrieved paper

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

End-to-end framework integrating LTL with differentiable simulators

The authors present the first framework that combines linear temporal logic specifications with differentiable physics simulators to enable gradient-based reinforcement learning. This integration allows efficient learning from formal specifications while maintaining correctness guarantees.

Contribution

Soft labeling technique for differentiable automaton transitions

The authors introduce a soft labeling approach that converts discrete automaton transitions into probabilistic ones, creating differentiable reward functions and state representations. This technique addresses the reward sparsity problem inherent in LTL-based learning without compromising the correctness of the objectives.

Contribution

Theoretical guarantees connecting Büchi acceptance to differentiable LTL returns

The authors establish formal theoretical results that relate Büchi acceptance conditions to both discrete and differentiable LTL return formulations. They derive a tunable upper bound on the discrepancy between these two formulations that holds in both deterministic and stochastic environments.

Accelerated Learning with Linear Temporal Logic using Differentiable Simulation | Novelty Validation