Low dynamic range (LDR) cameras cannot deal with wide dynamic range inputs, frequently leading to local overexposure issues. We present a learning-based system to reduce these artifacts without resorting to complex acquisition mechanisms like alternating exposures or costly processing that are typical of high dynamic range (HDR) imaging. We propose a transformer-based deep neural network (DNN) to infer the missing HDR details. In an ablation study, we show the importance of using a multiscale DNN and train it with the proper cost function to achieve stateof-the-art quality. To aid the reconstruction of the overexposed areas, our DNN takes a reference frame from the past as an additional input. This leverages the commonly occurring temporal instabilities of autoexposure to our advantage: since well-exposed details in the current frame may be overexposed in the future, we use reinforcement learning to train a reference frame selection DNN that decides whether to adopt the current frame as a future reference. Without resorting to alternating exposures, we obtain therefore a causal, HDR hallucination algorithm with potential application in common video acquisition settings.