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Despite the growing interest in unsupervised learning, extracting meaningful knowledge from unlabelled audio remains an open challenge. To take a step in this direction, we recently proposed a problem-agnostic speech encoder (PASE), that combines a convolutional encoder followed by multiple neural networks, called workers, tasked to solve self-supervised problems (i.e., ones that do not require manual annotations as ground truth). PASE was shown to capture relevant speech information, including speaker voice-print and phonemes. This paper proposes PASE+, an improved version of PASE for robust speech recognition in noisy and reverberant environments. To this end, we employ an online speech distortion module, that contaminates the input signals with a variety of random disturbances. We then propose a revised encoder that better learns short- and long-term speech dynamics with an efficient combination of recurrent and convolutional networks. Finally, we refine the set of workers used in self-supervision to encourage better cooperation. Results on TIMIT, DIRHA and CHiME-5 show that PASE+ significantly outperforms both the previous version of PASE as well as common acoustic features. Interestingly, PASE+ learns transferable representations suitable for highly mismatched acoustic conditions.