  It is common to address the curse of dimensionality in Markov decision
processes (MDPs) by exploiting low-rank representations. This motivates much of
the recent theoretical study on linear MDPs. However, most approaches require a
given representation under unrealistic assumptions about the normalization of
the decomposition or introduce unresolved computational challenges in practice.
Instead, we consider an alternative definition of linear MDPs that
automatically ensures normalization while allowing efficient representation
learning via contrastive estimation. The framework also admits
confidence-adjusted index algorithms, enabling an efficient and principled
approach to incorporating optimism or pessimism in the face of uncertainty. To
the best of our knowledge, this provides the first practical representation
learning method for linear MDPs that achieves both strong theoretical
guarantees and empirical performance. Theoretically, we prove that the proposed
algorithm is sample efficient in both the online and offline settings.
Empirically, we demonstrate superior performance over existing state-of-the-art
model-based and model-free algorithms on several benchmarks.
