Representation Learning for RL

Deep Reinforcement Learning (RL) is notoriously sample inefficient. One contributing factor is that RL agents are typically initialized from scratch, forcing them to acquire task-relevant knowledge through online interaction. Existing approaches obtain informative initializations through pre-collected datasets, high-fidelity simulators, or meta-learning over related tasks, but these prerequisites may be difficult to access or even unavailable. In this paper, we propose Programmatic Dynamics Priors for Value Network Initialization (ProDVI), a framework that leverages the commonsense and domain knowledge encoded in large language models to initialize RL agents without relying on these resources. Specifically, ProDVI prompts a code-generating language model to produce executable Python functions that encode coarse hypotheses about environment dynamics. These functions are then used to generate synthetic transitions. Based on these transitions, we construct an auxiliary dynamics prediction objective to pretrain the state-action encoder of the value network in an actor-critic framework. The learned representation provides dynamics-aware inductive biases before online RL begins. Importantly, the generated programs are used only for representation pretraining and are not required to faithfully simulate the target environment. While the generated programs may be inaccurate, their induced initialization can be corrected through online learning from real transitions and rewards. Experiments on OpenAI Gym and DeepMind Control Suite tasks show that ProDVI can effectively improve the sample efficiency of model-free RL algorithms.

Much like humans benefit from guidance while learning, reinforcement learning algorithms may benefit from additional supervision beyond rewards. Leveraging additional information during training to learn better representations and behaviors has been the focus of asymmetric reinforcement learning. This learning paradigm has proven effective under partial observability when additional state information is available, but also under full observability when more refined state information is available. Focusing on model-based reinforcement learning, we study the effect of asymmetric learning on observation representations and on privileged information representations. First, we identify a limitation in the privileged information representations learned by an asymmetric model-based algorithm known as the Informed Dreamer. Then, we propose a novel asymmetric representation learning objective using latent guidance, resulting in a new algorithm called the Reinformed Dreamer. Experiments across several benchmarks show a more consistent improvement over Dreamer than previous asymmetric approaches.

Learning a compact model of the world from interaction data is central to sample-efficient deep reinforcement learning. Spectral representation methods have become the leading paradigm for representation learning in continuous control by taking a matrix view of the transition kernel, with state-action pairs on one side and next states on the other, and learning a low-rank factorization through self-supervised contrastive objectives. We take this view one step further. The transition kernel is naturally a three-mode tensor over states, actions, and next states, and a CP decomposition gives one feature map per mode. We propose FaStR, which fits this decomposition with a noise contrastive objective, producing separate state, action, and next-state encoders that together form a single spectral representation. The factored form yields a smaller hypothesis class, and the sample size needed for representation learning shrinks by a factor that scales with the smaller of the state and action dimensions. Empirically, FaStR delivers its largest gains on high-dimensional locomotion tasks whose dynamics align with the factored structure, and the learned state encoder transfers intact across actuator shift while only the action encoder is retrained.

Recent advances in humanoid robotics have highlighted the importance of deployable loco-manipulation skills. Dribbling a soccer ball while evading active opponents requires simultaneous balance, precise ball control, and awareness of a dynamic adversary under onboard sensing and real-time constraints. Existing approaches typically separate perception and motion, which can be effective in controlled settings but may fail under occlusions, fast ball movements, and complex opponent interactions, since perception is not directly optimized for control. We propose an integrated approach in which a temporal depth encoder is embedded into a reinforcement learning policy through a task-specific projection layer. We apply this framework to a simulated Booster T1 humanoid robot and show that it is possible to learn vision-based, opponent-aware dribbling directly from depth observations, without explicit state estimation or privileged scene information. The learned policy achieves 100% success in nominal target-driven dribbling and 96% success with a single static obstacle, while reaching 46% success against an actively moving ball-attacker opponent. These results demonstrate that the proposed framework supports robust vision-based dribbling in nominal and moderately dynamic settings, and provides a strong foundation for handling more challenging moving-adversary scenarios.

Unsupervised pre-training on large-scale datasets has demonstrated significant potential for improving the sample efficiency and performance of Reinforcement Learning (RL). Given the large-scale action-free internet videos, existing methods utilize single-step transition prediction and image reconstruction to learn representations. However, these methods prefer to preserve large-proportion stationary information in the pixel space, neglecting small but crucial information. To preserve enough information in the representation, it is essential to pay equal attention to each element in videos. Specifically, we propose a temporal correlation space to distinguish each element. For implementation, we introduce the Multi-scale Temporal Contrastive Learning (MTCL) method to model multi-scale temporal correlations separately. This approach can balance the attention of different elements and yield more informative representations, effectively supporting policy learning in various downstream tasks. Experimental results demonstrate that our method improves sample efficiency and asymptotic performance across various downstream tasks.

Visual Reinforcement Learning (VRL) has achieved considerable success in solving control tasks. However, generalizing learned policies to new environments remains a major challenge, as agents often overfit to task-irrelevant features in the training environment. To solve this problem, we introduce the concept of decoupling observations into task-relevant and task-irrelevant representations. Building on this idea, we propose a self-supervised Task-Relevant Representation Decoupling (T2RD) algorithm for VRL. This algorithm consists of three components: task-relevant representation consistency, cross-reconstruction, and cross-dynamic prediction. The first two components achieve the decoupling of content and style features, but the resulting content representations are not necessarily task-relevant. To further refine task-relevant features from content representations, we design the third component that introduces dynamic prediction. T2RD achieves State-Of-The-Art (SOTA) generalization performance and sample efficiency in the DeepMind Control Suite and Robotic Manipulation tasks.

Reinforcement learning has achieved remarkable success in learning complex control policies, yet its applicability remains limited due to sample inefficiency and poor generalization across tasks. In this work, we propose RepMT-SAC, a framework for multi-task RL that enables efficient knowledge sharing and robust transfer to new tasks. RepMT-SAC uses spectral MDP decomposition to capture transferable dynamics, structuring the value function into a task-agnostic core with a minimal task-specific adjustment. This design allows for strong zero-shot performance on in-distribution tasks and rapid few-shot adaptation to out-of-distribution tasks. We evaluate RepMT-SAC on quadcopter trajectory-following tasks across in-distribution and out-of-distribution contexts, demonstrating that it outperforms baselines by up to 30%.

Scaling reinforcement learning (RL) to diverse multitask settings remains a central challenge. While recent advances in model-based RL achieve strong performance, they rely on planning and complex training pipelines, making it unclear which components are essential for scalability. We revisit this question and argue that the primary driver of scalable multitask RL is not model-based control, but representation learning. In particular, we show that combining predictive, model-based representations with high-capacity value function approximation is sufficient to achieve strong performance, even without planning. We evaluate a simple model-free algorithm, MR.Q, coupled with auxiliary predictive objectives into a scalable actor-critic architecture. This approach outperforms a recent world-model-based method and a range of deep RL baselines across a diverse suite of multitask continuous control tasks, while significantly reducing computational overhead and improving wall-clock efficiency. We observe consistent improvements with increased model capacity and show through ablations that predictive representation learning is critical for performance.

Reward transfer in Inverse Reinforcement Learning (IRL) is unreliable when policies must generalize to unseen combinations of environment dynamics and task goals. We propose Factorized Contrastive Abstractions for Transferable IRL (ConTraIRL), a framework that enables compositional reward transfer by learning decoupled latent representations of these two factors. ConTraIRL uses a dual-encoder architecture that maps observations into separate dynamics and goal latent spaces, trained with a dual contrastive objective. Temporal alignment encourages the dynamics encoder to learn goal-invariant structure, while the goal encoder captures dynamics-invariant features. This factorization supports reward inference under recombined dynamics-goal settings. Experiments on continuous control benchmarks demonstrate effective few-shot transfer to unseen dynamics-goal pairings, improving sample efficiency and reward recovery over transfer IRL baselines.

Representation learning is a powerful tool for spatio-temporal abstraction within reinforcement learning (RL). Two well established approaches are through the successor representation (SR) and the default representation (DR). The SR encodes states by the future trajectories they induce, capturing information flow decoupled from reward. The DR builds on this by weighting trajectories with reward, integrating credit-assignment structure into the representation. Eigenvectors of both representations have been used to support a range of downstream tasks -- including option discovery, reward shaping, transfer learning, and exploration. We introduce a structurally distinct formulation: the terminal representation (TR). The TR encodes reward-weighted trajectories similarly to the DR, but can be learned as a lower-dimensionality object, and can be used directly for the mentioned applications without eigenvector computations. Eigendecomposition also imposes the assumption of symmetric transition dynamics, which the TR can bypass. In this work we develop the theoretical foundations of the TR: its derivation, convergence of two learning algorithms, its use for zero-shot compositionality, and equivalences between alternative reward formulations. We further show the TR is embedded in the top DR eigenvector, allowing it to capture the same underlying knowledge without eigendecomposition. Additionally, we provide empirical evidence of the TR as a viable alternative to existing representations in subsidiary applications, while requiring less computational overhead to learn, store, and use.

In many practical reinforcement learning environments, observations are far higher-dimensional than the variables that matter for control. In this work, we ask: can we learn representations that capture only control-relevant features of the environment? We study this question through the empowerment objective, which maximizes an agent's influence over the environment and is widely used for unsupervised skill learning. We show that empowerment agents induce two distinct representations -- forward and backward -- that capture complementary aspects of the state, and both of which are invariant to control-irrelevant features. Thus, empowerment maximization leads agents to learn an implicit, control-centric model of the world. Our analysis highlights the importance of learning representations through interaction rather than from passive datasets: interaction aimed at maximizing control is essential for learning useful invariance properties, a perspective that aligns closely with the causal learning literature.

Hierarchical Reinforcement Learning (HRL) promises to solve long-horizon Reinforcement Learning (RL) tasks more efficiently than non-hierarchical counterparts by discovering and reusing temporally-extended skills. However, obtaining skills that are actually reusable remains an open challenge. Towards this end, we focus on abstractions that exploit the intuition of local dynamics: local transitions in different global contexts require similar kinds of action sequences. By aligning these contexts with the action sequences they require, we are able to learn which skills to reuse and where to reuse them. In principle, this information should benefit many HRL algorithms, where high-level policies have to reason about the low-level skills they use. The resulting algorithm CARL (Contrastive Action-based Representations for Reusable Local Control) shows both qualitative clustering of meaningful skills in complex humanoid environments and improved downstream performance on the OGBench benchmark when integrated with HIQL.

Deep reinforcement learning (RL) agents commonly rely on high-dimensional neural representations, despite growing evidence that task-relevant value and policy structure may be intrinsically low-dimensional. In this work, we present a simple yet effective representation-level prior that inserts a fixed orthonormal projection to constrain encoder features to a low-dimensional subspace, requiring no auxiliary objectives, pretraining, or changes to the underlying RL algorithm. Under a linear realizability assumption, we prove that when the bottleneck dimension exceeds the intrinsic rank of the optimal value function in feature space, the bottleneck preserves expressivity and leaves the induced gradient dynamics unchanged up to an equivalent low-dimensional parameterization. Empirically, we find that across both single and multi-task benchmarks, baseline performance is either matched or improved once the bottleneck dimension exceeds a small task-dependent threshold; in many cases, value representations can be compressed to extremely low dimensions without loss, and the minimal sufficient dimension depends far more on environment complexity than encoder width. In addition, we analyze representation geometry and find that orthogonal bottlenecks stabilize feature norms and are associated with higher effective rank. Together, these results support a representation-space interpretation of the manifold hypothesis in reinforcement learning and position orthogonal bottlenecks as a lightweight, architecture-agnostic mechanism for shaping RL representations.

Offline goal-conditioned reinforcement learning (GCRL) provides a practical framework for obtaining goal-reaching policies from fixed datasets. However, learning a reliable goal-conditioned value function in long-horizon tasks remains challenging. In this paper, we identify erroneous generalization in goal-conditioned value functions as a fundamental bottleneck, and demonstrate that appropriate inductive bias in the value function is crucial for addressing the bottleneck. Building on these findings, we propose Latent-Aligned Value Learning (LAVL), an offline GCRL algorithm that integrates latent-representation-based value generalization with hierarchical planning in a unified framework. Extensive experiments on OGBench demonstrate that LAVL consistently outperforms existing offline GCRL methods, achieving the highest performance on 20 out of 22 datasets. Notably, LAVL exhibits strong performance in long-horizon tasks and trajectory stitching datasets, where prior methods suffer significant performance degradation. Our code is available at https://github.com/oh-lab/LAVL.git.

3D open-world environments with adversarial opponents remain a core challenge for reinforcement learning due to their vast state spaces. Effective reasoning representations are essential in such settings. While existing self-supervised visual foresight reasoning approaches often suffer from multi-step error accumulation, many recent studies resort to injecting domain-specific knowledge for more stable guidance. Our key insight is that the photorealistic fidelity of visual reasoning representations is secondary; what truly matters is providing informative, task-relevant signals. To this end, we propose ResDreamer, a hierarchical world model in which each higher-level layer is trained to reconstruct the residuals of the layer below. This design enables progressive abstraction of increasingly sophisticated world dynamics and fosters the emergence of richer latent representations. Drawing inspiration from the "Bitter Lesson", ResDreamer trains its reasoning representations in a purely self-supervised manner. The higher-level residual representations are used to modulate lower-level predictions, allowing the world model to scale effectively with only linearly increasing cross-layer communication costs. Experiments show that ResDreamer achieves state-of-the-art sample efficiency and parameter efficiency. This scalable hierarchical visual foresight reasoning architecture paves the way for more capable online RL agents in open-ended, dynamic environments. The code is accessible at https://github.com/XuYuanFei01/ResDreamer.

For reinforcement learning in data-scarce domains like real-world robotics, intensive data reuse enhances efficiency but induces overfitting. While prior works focus on critic bias, representation-level instability in Self-Predictive Learning (SPL) under high Update-to-Data (UTD) regimes remains underexplored. To bridge this gap, we propose Robust Representation via Redundancy Reduction (R2R2), a regularization method within SPL. We theoretically identify that standard zero-centering conflicts with SPL's spectral properties and design a non-centered objective accordingly. We verify R2R2 on SPL-native algorithms like TD7. Furthermore, to demonstrate its orthogonality to prior advancements, we extend the state-of-the-art SimbaV2, which originally lacks SPL, by integrating a tailored SPL module, termed SimbaV2-SPL. Experiments across 11 continuous control tasks confirm that R2R2 effectively mitigates overfitting; specifically, at a UTD ratio of 20, it improves TD7 by ~22% and provides additional gains on top of SimbaV2-SPL, which itself establishes a new state-of-the-art. The code can be found at: https://github.com/songsang7/R2R2

Diffusion world models have recently become competitive for online model-based reinforcement learning, but current approaches expose a tension: pixel diffusion is effective but computationally expensive while the latest latent diffusion approach improves efficiency yet performs subpar. The latter also relies on separately trained latents rather than the end-to-end world-model objectives that have driven much of modern MBRL progress. In particular, JEPA-style predictive representation learning has emerged as an especially promising direction for world modeling and MBRL. Concurrently, diffusion-style objectives have gained traction across multiple domains, with iterative refinement as a promising approach for multimodal and stochastic targets. Taken together, these trends motivate Joint Embedding DIffusion (JEDI), the first online end-to-end latent diffusion world model. JEDI learns its latent space directly from the diffusion denoising loss with a JEPA framework, using denoising to learn and predict future latents rather than relying on reconstruction and pretrained models. We provide a theoretical motivation showing that conventional JEPA objectives induce a predictive information bottleneck, and that conditional diffusion denoising admits a closely related predictive-compression decomposition. Empirically, JEDI is competitive on Atari100k and outperforms the baseline with seperately trained latents where directly comparable. Relative to the pixel diffusion baseline, JEDI uses 43% less VRAM, over 3$\times$ faster world-model sampling, and 2.5$\times$ faster training. JEDI also exhibits a markedly different task-level performance profile from the pixel baseline, suggesting that end-to-end predictive latents change more than compute alone.

Offline goal-conditioned reinforcement learning (GCRL) is a practical reinforcement learning paradigm that aims to learn goal-conditioned policies from reward-free offline data. Despite recent advances in hierarchical architectures such as HIQL, long-horizon control in offline GCRL remains challenging due to the limited expressiveness of Gaussian policies and the inability of high-level policies to generate effective subgoals. To address these limitations, we propose the goal-conditioned mean flow policy, which introduces an average velocity field into hierarchical policy modeling for offline GCRL. Specifically, the mean flow policy captures complex target distributions for both high-level and low-level policies through a learned average velocity field, enabling efficient action generation via one-step sampling. Furthermore, considering the insufficiency of goal representation, we introduce a LeJEPA loss that repels goal representation embeddings during training, thereby encouraging more discriminative representations and improving generalization. Experimental results show that our method achieves strong performance across both state-based and pixel-based tasks in the OGBench benchmark.

Zero-shot unsupervised reinforcement learning (URL) offers a promising direction for building generalist agents capable of generalizing to unseen tasks without additional supervision. Among existing approaches, successor representations (SR) have emerged as a prominent paradigm due to their effectiveness in structured, low-dimensional settings. However, SR methods struggle to scale to high-dimensional visual environments. Through empirical analysis, we identify two key limitations of SR in visual URL: (1) SR objectives often lead to suboptimal representations that attend to dynamics-irrelevant regions, resulting in inaccurate successor measures and degraded task generalization; and (2) these flawed representations hinder SR policies from modeling multi-modal skill-conditioned action distributions and ensuring skill controllability. To address these limitations, we propose Saliency-Guided Representation with Consistency Policy Learning (SRCP), a novel framework that improves zero-shot generalization of SR methods in visual URL. SRCP decouples representation learning from successor training by introducing a saliency-guided dynamics task to capture dynamics-relevant representations, thereby improving successor measure and task generalization. Moreover, it integrates a fast-sampling consistency policy with URL-specific classifier-free guidance and tailored training objectives to improve skill-conditioned policy modeling and controllability. Extensive experiments on 16 tasks across 4 datasets from the ExORL benchmark demonstrate that SRCP achieves state-of-the-art zero-shot generalization in visual URL and is compatible with various SR methods.

In this paper, we develop a stratification-based semantics for Signal Temporal Logic (STL) in which each atomic predicate is interpreted as a membership test in a stratified space. This perspective reveals a novel correspondence principle between stratification theory and STL, showing that most STL formulas can be viewed as inducing a stratification of space-time. The significance of this interpretation is twofold. First, it offers a fresh theoretical framework for analyzing the structure of the embedding space generated by deep reinforcement learning (DRL) and relates it to the geometry of the ambient decision space. Second, it provides a principled framework that both enables the reuse of existing high-dimensional analysis tools and motivates the creation of novel computational techniques. To ground the theory, we (1) illustrate the role of stratification theory in Minigrid games and (2) apply numerical techniques to the latent embeddings of a DRL agent playing such a game where the robustness of STL formulas is used as the reward. In the process, we propose computationally efficient signatures that, based on preliminary evidence, appear promising for uncovering the stratification structure of such embedding spaces.

Multi-task representation learning (MTRL) is an approach that learns shared latent representations across related tasks, facilitating collaborative learning that improves the overall learning efficiency. This paper studies MTRL for multi-task reinforcement learning (RL), where multiple tasks have the same state-action space and transition probabilities, but different rewards. We consider T linear Markov Decision Processes (MDPs) where the reward functions and transition dynamics admit linear feature embeddings of dimension d. The relatedness among the tasks is captured by a low-rank structure on the reward matrices. Learning shared representations across multiple RL tasks is challenging due to the complex and policy-dependent nature of data that leads to a temporal progression of error. Our approach adopts a reward-free reinforcement learning framework to first learn a data-collection policy. This policy then informs an exploration strategy for estimating the unknown reward matrices. Importantly, the data collected under this well-designed policy enable accurate estimation, which ultimately supports the learning of an near-optimal policy. Unlike existing approaches that rely on restrictive assumptions such as Gaussian features, incoherence conditions, or access to optimal solutions, we propose a low-rank matrix estimation method that operates under more general feature distributions encountered in RL settings. Theoretical analysis establishes that accurate low-rank matrix recovery is achievable under these relaxed assumptions, and we characterize the relationship between representation error and sample complexity. Leveraging the learned representation, we construct near-optimal policies and prove a regret bound. Experimental results demonstrate that our method effectively learns robust shared representations and task dynamics from finite data.

In this paper, we present a Koopman autoencoder-based least-squares policy iteration (KAE-LSPI) algorithm in reinforcement learning (RL). The KAE-LSPI algorithm is based on reformulating the so-called least-squares fixed-point approximation method in terms of extended dynamic mode decomposition (EDMD), thereby enabling automatic feature learning via the Koopman autoencoder (KAE) framework. The approach is motivated by the lack of a systematic choice of features or kernels in linear RL techniques. We compare the KAE-LSPI algorithm with two previous works, the classical least-squares policy iteration (LSPI) and the kernel-based least-squares policy iteration (KLSPI), using stochastic chain walk and inverted pendulum control problems as examples. Unlike previous works, no features or kernels need to be fixed a priori in our approach. Empirical results show the number of features learned by the KAE technique remains reasonable compared to those fixed in the classical LSPI algorithm. The convergence to an optimal or a near-optimal policy is also comparable to the other two methods.

Forward-backward (FB) representations provide a powerful framework for learning the successor representation (SR) in continuous spaces by enforcing a low-rank factorization. However, a fundamental spectral mismatch often exists between the high-rank transition dynamics of continuous environments and the low-rank bottleneck of the FB architecture, making accurate low-rank representation learning difficult. In this work, we analyze temporal abstraction as a mechanism to mitigate this mismatch. By characterizing the spectral properties of the transition operator, we show that temporal abstraction acts analogously to a low-pass filter that suppresses high-frequency spectral components. This suppression reduces the effective rank of the induced SR while preserving a formal bound on the resulting value function error. Empirically, we show that this alignment is a key factor for stable FB learning, particularly at high discount factors where bootstrapping becomes error-prone. Our results identify temporal abstraction as a principled mechanism for shaping the spectral structure of the underlying MDP and enabling effective long-horizon representations in continuous control.

A central challenge in image-based Model-Based Reinforcement Learning (MBRL) is to learn representations that distill essential information from irrelevant visual details. While promising, reconstruction-based methods often waste capacity on large task-irrelevant regions. Decoder-free methods instead learn robust representations by leveraging Data Augmentation (DA), but reliance on such external regularizers limits versatility. We propose R2-Dreamer, a decoder-free MBRL framework with a self-supervised objective that serves as an internal regularizer, preventing representation collapse without resorting to DA. The core of our method is a redundancy-reduction objective inspired by Barlow Twins, which can be easily integrated into existing frameworks. On DeepMind Control Suite and Meta-World, R2-Dreamer is competitive with strong baselines such as DreamerV3 and TD-MPC2 while training 1.59x faster than DreamerV3, and yields substantial gains on DMC-Subtle with tiny task-relevant objects. These results suggest that an effective internal regularizer can enable versatile, high-performance decoder-free MBRL. Code is available at https://github.com/NM512/r2dreamer.

Rapid adaptation in complex control systems remains a central challenge in reinforcement learning. We introduce a framework in which policy and value functions share a low-dimensional coefficient vector - a goal embedding - that captures task identity and enables immediate adaptation to novel tasks without retraining representations. During pretraining, we jointly learn structured value bases and compatible policy bases through a bilinear actor-critic decomposition. The critic factorizes as Q = sum_k G_k(g) y_k(s,a), where G_k(g) is a goal-conditioned coefficient vector and y_k(s,a) are learned value basis functions. This multiplicative gating - where a context signal scales a set of state-dependent bases - is reminiscent of gain modulation observed in Layer 5 pyramidal neurons, where top-down inputs modulate the gain of sensory-driven responses without altering their tuning. Building on Successor Features, we extend the decomposition to the actor, which composes a set of primitive policies weighted by the same coefficients G_k(g). At test time the bases are frozen and G_k(g) is estimated zero-shot via a single forward pass, enabling immediate adaptation to novel tasks without any gradient update. We train a Soft Actor-Critic agent on the MuJoCo Ant environment under a multi-directional locomotion objective, requiring the agent to walk in eight directions specified as continuous goal vectors. The bilinear structure allows each policy head to specialize to a subset of directions, while the shared coefficient layer generalizes across them, accommodating novel directions by interpolating in goal embedding space. Our results suggest that shared low-dimensional goal embeddings offer a general mechanism for rapid, structured adaptation in high-dimensional control, and highlight a potentially biologically plausible principle for efficient transfer in complex reinforcement learning systems.

Whether uniquely quantum resources confer advantages in fully classical, competitive environments remains an open question. Competitive zero-sum reinforcement learning is particularly challenging, as success requires modelling dynamic interactions between opposing agents rather than static state-action mappings. Here, we conduct a controlled study isolating the role of quantum entanglement in a quantum-classical hybrid agent trained on Pong, a competitive Markov game. An 8-qubit parameterised quantum circuit serves as a feature extractor within a proximal policy optimisation framework, allowing direct comparison between separable circuits and architectures incorporating fixed (CZ) or trainable (IsingZZ) entangling gates. Entangled circuits consistently outperform separable counterparts with comparable parameter counts and, in low-capacity regimes, match or exceed classical multilayer perceptron baselines. Representation similarity analysis further shows that entangled circuits learn structurally distinct features, consistent with improved modelling of interacting state variables. These findings establish entanglement as a function resource for representation learning in competitive reinforcement learning.

Learning compact state representations in Markov Decision Processes (MDPs) has proven crucial for addressing the curse of dimensionality in large-scale reinforcement learning (RL) problems. Existing principled approaches leverage structural priors on the MDP by constructing state representations as linear combinations of the state-graph Laplacian eigenvectors. When the transition graph is unknown or the state space is prohibitively large, the graph spectral features can be estimated directly via sample trajectories. In this work, we prove an upper bound on the approximation error of linear value function approximation under the learned spectral features. We show how this error scales with the algebraic connectivity of the state-graph, grounding the approximation quality in the topological structure of the MDP. We further bound the error introduced by the eigenvector estimation itself, leading to an end-to-end error decomposition across the representation learning pipeline. Additionally, our expression of the Laplacian operator for the RL setting, although equivalent to existing ones, prevents some common misunderstandings, of which we show some examples from the literature. Our results hold for general (non-uniform) policies without any assumptions on the symmetry of the induced transition kernel. We validate our theoretical findings with numerical simulations on gridworld environments.

Meta-Reinforcement Learning addresses the critical limitations of conventional Reinforcement Learning in multi-task and non-stationary environments by enabling fast policy adaptation and improved generalization. We introduce a novel Meta-RL framework that integrates a bi-level optimization scheme with a hybrid actor-critic architecture specially designed to enhance sample efficiency and inter-task adaptability. To improve knowledge transfer, we meta-learn a shared state feature extractor jointly optimized across actor and critic networks, providing efficient representation learning and limiting overfitting to individual tasks or dominant profiles. Additionally, we propose a parameter-sharing mechanism between the outer- and inner-loop actor networks, to reduce redundant learning and accelerate adaptation during task revisitation. The approach is validated on a real-world Building Energy Management Systems dataset covering nearly a decade of temporal and structural variability, for which we propose a task preparation method to promote generalization. Experiments demonstrate effective task adaptation and better performance compared to conventional RL and Meta-RL methods.

Learned world models excel at interpolative generalization but fail at extrapolative generalization to novel physical properties. This limitation arises because they learn statistical correlations rather than the environment's underlying generative rules, such as physical invariances and conservation laws. We argue that learning these invariances is key to robust extrapolation. To achieve this, we first introduce Symmetry Exploration, an unsupervised exploration strategy where an agent is intrinsically motivated by a Hamiltonian-based curiosity bonus to actively probe and challenge its understanding of conservation laws, thereby collecting physically informative data. Second, we design a Hamiltonian-based world model that learns from the collected data, using a novel self-supervised contrastive objective to identify the invariant physical state from raw, view-dependent pixel observations. Our framework, DreamSAC, trained on this actively curated data, significantly outperforms state-of-the-art baselines in 3D physics simulations on tasks requiring extrapolation.

Offline meta-reinforcement learning seeks to learn a policy that generalizes to new related tasks online. Context-based methods infer a task representation from transition histories, yet learning an effective task representation without supervision remains challenging. Existing methods relying on contrastive learning learn discriminative task representations, but fail to identify task-specific dynamics, while relying on reconstruction can be insufficient to model long-horizon dependencies, limiting generalization to new tasks. We investigate the impact of temporal consistency in latent space on task representation learning, showing that enforcing multi-step predictions in latent space encourages task representations that are able to capture task-dependent dynamics while preventing representation collapse. We provide theoretical analysis characterizing sources of error in value estimation and show through extensive experiments on MuJoCo, Contextual DeepMind Control, and MetaWorld benchmarks that temporal consistency significantly improves both zero-shot and few-shot generalization.