Task guided agents demonstrate strong performance in a wide range of complex tasks. However, most existing task representation algorithms are tailored to specific contexts and struggle to generalize across diverse scenarios. Moreover, they typically depend on gradient signals from reinforcement learning controllers to update their weights, which can degrade both representation quality and learning efficiency. To overcome these limitations, we propose LOTUS, a temporal logic inspired universal task representation framework that can be seamlessly integrated into any RL algorithm to enhance agent performance across diverse task settings. Specifically, we design a novel task representation architecture capable of modeling relationships and extracting task semantics from LTL formulas. We further introduce a more effective update mechanism that treats the LTL encoder as a policy, thereby improving representation capacity. To enhance stability and robustness, LOTUS leverages the bisimulation metric, which provides theoretical guarantees for LTL representation, including behavioral equivalence, optimality fidelity, and trajectory robustness. Experimental results show that LOTUS outperforms most existing methods in learning efficiency, generalization capability, and representation quality. Specifically, LOTUS accelerates convergence over 20% in single-task scenarios, achieves a 15%-45% higher success rate in unseen manipulation tasks, and improves generalization performance over 25% in complex multi-task environments with increased sub-goal depth or conjunctions. The corresponding code, videos, and appendix are available at: https://lotus-website.github.io/.
Many visual reinforcement learning (RL) algorithms learn representations by matching latent distances to a behavioral distance induced by reward and transition similarity. In practice, the choice of the latent distance can strongly affect performance: using a fixed, pre-specified global norms (e.g., $\ell_p$ norms or other hand-designed metrics) may be overly restrictive to capture the behavioral distance. In contrast, unconstrained pairwise distances may admit degenerate solutions that drive the metric loss down without improving the representation. To address this gap, we introduce **PAMD: Pairwise Adaptive Mahalanobis Distance**, which parameterizes a positive-definite, pair-conditioned metric for measuring latent state similarity. PAMD is a simple plug-in for existing bisimulation-based methods, offering a more expressive yet structured alternative to fixed, pre-specified latent distances. We empirically validate our method on visual MuJoCo continuous-control tasks, where final performance of several recent bisimulation-based RL algorithms is substantially improved when equipped with the distance we propose.
Joint-embedding predictive (JEPA-style) objectives learn representations by predicting future latents. In doing so they can discard features that are exogenous (uncontrollable by the agent) yet control-relevant, even when those features are trivially encodable. This occurs because the objective optimizes temporal predictability rather than control-relevance. We isolate this failure mode in a controlled 2x2 experimental design that varies feature controllability and relevance independently, using a predictability knob that decouples a feature's temporal predictability from its control-relevance. Comparing six objectives: reconstruction, JEPA, action-conditioned JEPA, controllability-based JEPA, inverse dynamics under a random policy, and reward-grounded JEPA, we observe that all evaluated reward-free predictive objectives leave the exogenous control-relevant feature near chance accuracy, while a reward-grounded variant retains it selectively. The remedy is label-efficient and robust: as little as 2% of reward-labeled transitions recovers the feature, the effect holds across two environments with different surface forms, and it persists across latent dimensions from 16 to 1024. Comparing the learned latent geometry against bisimulation theory's prediction, the JEPA latent realizes only a small fraction of the class separation a supervised reference attains.
Yivan Zhang, Ziyan Luo, Manuel Baltierics.LG cs.AI math.CT
State abstraction plays a key role in scaling reinforcement learning to complex but structured systems. In studying such systems, a wide range of behavioral structures have been studied in reinforcement learning, including value functions, invariants, bisimulation relations, and behavioral metrics. However, a general principle for determining what structures are provably preserved under state abstraction is still lacking. In this paper, we present a unified framework for defining and analyzing behavioral structures in reinforcement learning. Our framework provides a compositional way to specify behavioral semantics based on local, one-step descriptions of system dynamics. Using this framework, we establish results showing how behavioral structures can be safely transferred between abstract and concrete systems. We further show how to construct quantitative metrics from logical behavioral semantics with soundness guarantees. Together, these results provide a principled foundation for reasoning about behaviors under state abstraction in reinforcement learning and offer reusable definition and proof principles for a broad class of behavioral structures in reinforcement learning.