Decision rules are among the most expressive data mining models. We propose the first distributed streaming algorithm to learn decision rules for regression tasks. The algorithm is available in SAMOA (SCALABLE ADVANCED MASSIVE ONLINE ANALYSIS), an open-source platform for mining big data streams. It uses a hybrid of vertical and horizontal parallelism to distribute Adaptive Model Rules (AMRules) on a cluster. The decision rules built by AMRules are comprehensible models, where the antecedent of a rule is a conjunction of conditions on the attribute values, and the consequent is a linear combination of the attributes. Our evaluation shows that this implementation is scalable in relation to CPU and memory consumption. On a small commodity Samza cluster of 9 nodes, it can handle a rate of more than 30000 instances per second, and achieve a speedup of up to 4.7x over the sequential version.