Cognitive science suggests that the self-representation is critical for learning and problem-solving. However, there is a lack of computational methods that relate this claim to cognitively plausible robots and reinforcement learning. In this paper, we bridge this gap by developing a model that learns bidirectional action-effect associations to encode the representations of body schema and the peripersonal space from multisensory information, which is named multimodal BidAL. Through three different robotic experiments, we demonstrate that this approach significantly stabilizes the learning-based problem-solving under noisy conditions and that it improves transfer learning of robotic manipulation skills.