Task-Induced Representational Invariances Depend on Learning Objective in Deep RL
Authors: Manu Srinath Halvagal, Sebastian Lee, SueYeon Chung
Organizations: Department of Physics, Harvard University · 2Kempner Institute, Harvard University · Center for Computational Neuroscience, Flatiron Institute
Abstract
Reinforcement Learning (RL) has long served as a model for goal-directed animal behavior in neuroscience. Modern deep RL has shown remarkable success across many domains, further strengthening this connection. The ability to learn abstract representations of high-dimensional state spaces underlies much of this success. However, theoretical understanding of these learned representations remains limited, hindering direct comparisons between models and animal learning. We address this gap by analyzing deep RL representations through the lens of MDP reduction theory. Investigating canonical RL algorithms in a navigation task, we find that even when performance is comparable, the value-based method (DQN) learns representations that are invariant to MDP homomorphism symmetries, while the policy-gradient method (PPO) learns representations invariant to action symmetries. These differences emerge consistently across domains, have downstream consequences for transfer learning, and appear in LLMs in a prompt-dependent manner. Our findings provide a principled approach to comparing learned representations across RL algorithms, with demonstrated practical implications and possible insights for neural coding in the brain.
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.
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 \emph{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.
Deep reinforcement learning (RL) algorithms often suffer from low run-to-run robustness, manifesting as significant performance variation across independent runs of identically configured agents. Although this issue poses a spectrum of challenges across research and practice, relatively few studies develop methods to evaluate it; RL research instead often reports uncertainty in the estimated mean performance. In this paper, we outline the limitations of conventional uncertainty and variation estimates, particularly their misalignment with purpose and the risk of underreporting. We then propose an alternative percentile-based statistic and visualization method, min-max IPR and run-wise percentile highlighting, respectively. These percentile-based tools are easy to interpret and rely on standard properties of sample percentiles, providing rich information about run-to-run performance variation. We demonstrate this through three case studies. First, we show that LayerNorm and penultimate-layer normalizations narrow performance variation in PPO, whereas the variation is mostly unchanged in SAC. Second, we compare PPO, SAC, TD-MPC, and TD-MPC2, and show TD-MPC exhibits the least variation while being the most data efficient among the four. Finally, in a comparison of DQN and Rainbow on five Atari environments, we show that both algorithms exhibit similar levels of performance variation.