Factorized Spectral Representations for Reinforcement Learning

• URL: http://arxiv.org/abs/2607.13498v1
• Date: Wed, 15 Jul 2026 06:52:58 GMT
• Title: Factorized Spectral Representations for Reinforcement Learning
• Abstract summary: Spectral representation methods have become the leading paradigm for representation learning in continuous control.<n>We propose FaStR, which produces separate state, action, and next-state encoders that together form a single spectral representation.<n>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.
• Score: 4.503747347543387
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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