As unsupervised pretraining becomes increasingly ubiquitous in reinforcement learning, a more thorough theoretical understanding of these methods becomes of equal importance to their empirical success. We focus on the setting of unsupervised learning via interaction, where the forward-backward (FB) representation learning serves as a prototypical and popular example. In this paper, we shed light on FB by formally contextualizing the method within a broader class of recent methods that use regression to obtain a low-rank approximation of a successor measure ratio. Our analysis clarifies when FB representations can exist and how the low-rank approximation converges in practice. Building upon the theory, we propose a variant of FB that is both more amenable to theoretical understanding and simpler to optimize in practice. Experiments in didactic settings, as well as in 10 state-based and image-based continuous control domains, demonstrate that our method converges to desired representations with 105× smaller errors than FB, achieving +24% improved zero-shot performance on average. We also demonstrate that zero-shot policies inferred by our algorithm provide an efficient initialization if the user prefers further fine-tuning on downstream tasks. Our project website is available at https://chongyi-zheng.github.io/onestep-fb.
Hierarchical reinforcement learning can improve generalization by decomposing long-horizon decision-making into simpler subproblems. However, existing approaches often rely on restrictive design choices, such as fixed temporal abstractions or goal-conditioned objectives, which largely confine them to goal-reaching tasks and limit their applicability to general reward functions. In this paper, we introduce switching successor measures, an extension of successor measures that enables hierarchical control in zero-shot reinforcement learning without additional supervision, fixed horizons, or manually designed subgoals. We show that switching successor measures arise naturally from classical successor measures while preserving their underlying structure. Building on this result, we propose FB π-Switch, an algorithm that extracts both a high-level subgoal-selection policy and a low-level control policy directly from forward-backward (FB) representations, allowing hierarchical behavior to emerge from a single learned representation. Experiments on both goal-conditioned and general reward-based tasks show that FB π-Switch improves over non-hierarchical baselines and matches state-of-the-art hierarchical methods in goal-conditioned settings. These results demonstrate that structured successor representations provide a flexible foundation for hierarchical zero-shot reinforcement learning beyond goal-reaching tasks. Our project website is available at: https://stestokth.github.io/switching-successors/.
Preference-based reinforcement learning (PbRL) avoids explicit reward engineering by learning from pairwise human preference feedback. Existing offline PbRL methods typically follow a two-stage pipeline, first learning a reward or preference model from labeled preferences and then performing offline RL on unlabeled data. We revisit offline PbRL through the lens of reward-free representation learning (RFRL) from the zero-shot RL literature, and propose a new training framework that first learns latent successor-measure representations from reward-free offline data, followed by contrastive search and fine-tuning using preference data. Through extensive experiments and ablations, we show that our method achieves superior preference efficiency over offline PbRL baselines. This work is the first to connect RFRL with PbRL, highlighting its potential as a feedback-efficient solution. Our code is publicly available at https://github.com/rl-bandits-lab/FB-PbRL.
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.