Multilinear compressive learning (MCL) is an efficient signal acquisition and learning paradigm for multidimensional signals. The level of signal compression affects the detection or classification performance of an MCL model, with higher compression rates often associated with lower inference accuracy. However, higher compression rates are more amenable to a wider range of applications, especially those that require low operating bandwidth and minimal energy consumption such as Internet of Things (IoT) applications. Many communication protocols provide support for adaptive data transmission to maximize the throughput and minimize energy consumption. By developing compressive sensing and learning models that can operate with an adaptive compression rate, we can maximize the informational content throughput of the whole application. In this article, we propose a novel optimization scheme that enables such a feature for MCL models. Our proposal enables the practical implementation of adaptive compressive signal acquisition and inference systems. Experimental results demonstrated that the proposed approach can significantly reduce the amount of computations required during the training phase of remote learning systems but also improve the informational content throughput via adaptive-rate sensing.