Symmetry-aware robot policy learning requires coupled observation-action transformations. For pixel observations, even simple physical symmetries can induce complex, viewpoint-dependent image transformations that are difficult to specify by hand. Existing symmetry-aware methods often rely on representations with predefined transformations, requiring preprocessing tailored to the sensing setup and task. We introduce MIRROR, a framework that learns how a known symmetry group operates jointly on observations and actions in partially observable Markov decision processes (POMDPs) from offline interaction data. MIRROR couples these transformations through adversarial tuple matching over one-step transition tuples, while explicit group-consistency regularization penalizes violations of the group-operation axioms. On four Robosuite tabletop manipulation tasks, MIRROR achieves the lowest aggregate error on three of four symmetry-quality metrics, including a 61% reduction in compatibility error (which measures consistency under transformation composition) relative to an adapted LaLiGAN baseline. Using the learned transformations in frame-averaged behavior cloning (BC) yields higher mean success rates than vanilla BC on all four tasks, increasing average success from 80.48% to 85.12%, with per-task gains up to 9.66 percentage points. We also repeat symmetry discovery and policy training in simulation with heightmap and segmentation-mask observations, then deploy the resulting policy zero-shot on a real Kinova GEN3 arm. Project page: https://pomdp-mirror.github.io.

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