Dynamic interaction of neurons in lateral orbitofrontal cortex with the sensory cortex implements value-prediction computations that are history dependent and error based, providing plasticity essential for flexible decision-making. Adaptive behaviour crucially depends on flexible decision-making, which in mammals relies on the frontal cortex, specifically the orbitofrontal cortex (OFC)(1-9). How OFC encodes decision variables and instructs sensory areas to guide adaptive behaviour are key open questions. Here we developed a reversal learning task for head-fixed mice, monitored the activity of neurons of the lateral OFC using two-photon calcium imaging and investigated how OFC dynamically interacts with primary somatosensory cortex (S1). Mice learned to discriminate 'go' from 'no-go' tactile stimuli(10,11)and adapt their behaviour upon reversal of stimulus-reward contingency ('rule switch'). Imaging individual neurons longitudinally across all behavioural phases revealed a distinct engagement of S1 and lateral OFC, with S1 neural activity reflecting initial task learning, whereas lateral OFC neurons responded saliently and transiently to the rule switch. We identified direct long-range projections from lateral OFC to S1 that can feed this activity back to S1 as value prediction error. This top-down signal updated sensory representations in S1 by functionally remapping responses in a subpopulation of neurons that was sensitive to reward history. Functional remapping crucially depended on top-down feedback as chemogenetic silencing of lateral OFC neurons disrupted reversal learning, as well as plasticity in S1. The dynamic interaction of lateral OFC with sensory cortex thus implements computations critical for value prediction that are history dependent and error based, providing plasticity essential for flexible decision-making.