Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2507.13181

Spectral Bellman Method: Unifying Representation and Exploration in RL

Ofir Nabati·Bo Dai·Shie Mannor·Guy Tennenholtz
View original source ↗Read source document ↗Export metadata ↓

Abstract

Representation learning is critical to the empirical and theoretical success of reinforcement learning. However, many existing methods are induced from model-learning aspects, misaligning them with the RL task in hand. This work introduces the Spectral Bellman Method, a novel framework derived from the Inherent Bellman Error (IBE) condition. It aligns representation learning with the fundamental structure of Bellman updates across a \textit{space} of possible value functions, making it directly suited for value-based RL. Our key insight is a fundamental spectral relationship: under the zero-IBE condition, the transformation of a \textit{distribution} of value functions by the Bellman operator is intrinsically linked to the feature covariance structure. This connection yields a new, theoretically-grounded objective for learning state-action features that capture this Bellman-aligned covariance, requiring only a simple modification to existing algorithms. We demonstrate that our learned representations enable structured exploration by aligning feature covariance with Bellman dynamics, improving performance in hard-exploration and long-horizon tasks. Our framework naturally extends to multi-step Bellman operators, offering a principled path toward learning more powerful and structurally sound representations for value-based RL.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ofir Nabati, Bo Dai, Shie Mannor, Guy Tennenholtz. 2026-02-01. Spectral Bellman Method: Unifying Representation and Exploration in RL. https://arxiv.org/abs/2507.13181

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Rollout Total Correlation for Deep Reinforcement Learning

Learning task-relevant representations is crucial for reinforcement learning. Recent approaches aim to learn such representations by improving the temporal consistency in the observed transitions. However, they only consider individual transitions and can fail to achieve long-term consistency. Instead, we argue that capturing aspects of the state that correlate with other states and actions of the trajectory---even more distant in the future---could further help in extracting task-relevant information. Hence, in this paper we investigate how to learn representations by maximizing the rollout total correlation, the correlation among all learned representations and actions within the trajectories produced by the agent. For improving rollout total correlation, we propose to combine two complementary lower bounds based on a generative and a discriminative model, combined with a simple and effective technique of chunk-wise mini-batching. Furthermore, we propose an intrinsic reward based on the learned representation for better exploration. Experimental evaluations on a set of challenging image-based simulated control tasks show that our method achieves better sample efficiency, and robustness to both white noise and natural video backgrounds compared to leading baselines.

cs.LG↗
arXiv2026

Reward Shaping to Mitigate Reward Hacking in RLHF

Reinforcement learning from human feedback (RLHF) is widely used to align large language models (LLMs) with human preferences. However, RLHF remains vulnerable to \emph{reward hacking}, whereby a policy exploits imperfections in the reward function instead of learning the intended behavior, thereby undermining alignment. Although reward shaping can stabilize RLHF training and partially mitigate reward hacking, shaping methods and their underlying design principles have not been systematically investigated. To address this gap, we conduct a comprehensive study of prevalent reward-shaping techniques. Our analysis identifies two key design principles: (1) the reinforcement-learning reward should be bounded, and (2) it should grow rapidly at first and then gradually saturate. Motivated by these principles, we propose Preference as Reward (PAR), a novel method that uses the latent preferences encoded in the reward model as the reinforcement-learning signal. We further show that PAR possesses two variance-reduction properties that stabilize RLHF training and substantially widen the practical window for early stopping. Our evaluation consists of two parts. First, we compare PAR with several other reward-shaping strategies using Proximal Policy Optimization (PPO) as the reinforcement-learning algorithm and Gemma2-2B as the base model. Second, we compare PAR with the vanilla baseline (i.e., unshaped reward) across four base models and four reinforcement-learning algorithms. In the first set of experiments, PAR consistently outperforms other reward-shaping methods and also reflects high data efficiency and robustness. The second set of experiments shows that PAR is particularly effective for actor-critic RL algorithms when value estimates become unstable and demonstrates its effectiveness across different base models. The code is available at https://github.com/PorUna-byte/PAR.

cs.LG↗
arXiv2026

Trajectory Entropy Reinforcement Learning for Robust Robot Motor Skill Learning

Simplicity is a critical inductive bias for designing data-driven controllers, especially when robustness is important. Despite the impressive results of deep reinforcement learning in complex control tasks, it is prone to capturing intricate and spurious correlations between observations and actions, leading to failure under slight perturbations to the environment. To tackle this problem, in this work we introduce a novel inductive bias towards simple policies in reinforcement learning. The simplicity inductive bias is introduced by minimizing the entropy of entire action trajectories, corresponding to the number of bits required to describe information in action trajectories after the agent observes state trajectories. Our reinforcement learning agent, Trajectory Entropy Reinforcement Learning, is optimized to minimize the trajectory entropy while maximizing rewards. We show that the trajectory entropy can be effectively estimated by learning a variational parameterized action prediction model, and use the prediction model to construct an information-regularized reward function. Furthermore, we construct a practical algorithm that enables the joint optimization of models, including the policy and the prediction model. Experimental evaluations on several high-dimensional locomotion tasks show that our learned policies produce more cyclical and consistent action trajectories, and achieve superior performance, and robustness to noise and dynamic changes than the state-of-the-art.

cs.LG↗