Getting the Best Out of Both Worlds: Algorithms for Hierarchical Inference at the Edge

We consider a resource-constrained Edge Device (ED), such as an IoT sensor or a microcontroller unit, embedded with a small-size ML model (S-ML) for a generic classification application and an Edge Server (ES) that hosts a large-size ML model (L-ML). Since the inference accuracy of S-ML is lower than that of the L-ML, offloading all the data samples to the ES results in high inference accuracy, but it defeats the purpose of embedding S-ML on the ED and deprives the benefits of reduced latency, bandwidth savings, and energy efficiency of doing local inference. In order to get the best out of both worlds, i.e., the benefits of doing inference on the ED and the benefits of doing inference on ES, we explore the idea of Hierarchical Inference (HI), wherein S-ML inference is only accepted when it is correct, otherwise the data sample is offloaded for L-ML inference. However, the ideal implementation of HI is infeasible as the correctness of the S-ML inference is not known to the ED. We thus propose an online meta-learning framework that the ED can use to predict the correctness of the S-ML inference. In particular, we propose to use the probability corresponding to the maximum probability class output by S-ML for a data sample and decide whether to offload it or not. The resulting online learning problem turns out to be a Prediction with Expert Advice (PEA) problem with continuous expert space. For a full feedback scenario, where the ED receives feedback on the correctness of the S-ML once it accepts the inference, we propose the HIL-F algorithm and prove a sublinear regret bound
$\sqrt {n\ln (1/\lambda _{\text {min}})/2}$
without any assumption on the smoothness of the loss function, where
$n$
is the number of data samples and
$\lambda _{\text {min}}$
is the minimum difference between any two distinct maximum probability values across the data samples. For a no-local feedback scenario, where the ED does not receive the ground truth for the classification, we propose the HIL-N algorithm and prove that it has
$O\left ({n^{2/{3}}\ln ^{1/{3}}(1/\lambda _{\text {min}})}\right)$
regret bound. We evaluate and benchmark the performance of the proposed algorithms for image classification application using four datasets, namely, Imagenette and Imagewoof, MNIST, and CIFAR-10.