  ML-augmented algorithms utilize predictions to achieve performance beyond
their worst-case bounds. Producing these predictions might be a costly
operation -- this motivated Im et al. '22 to introduce the study of algorithms
which use predictions parsimoniously. We design parsimonious algorithms for
caching and MTS with action predictions, proposed by Antoniadis et al. '20,
focusing on the parameters of consistency (performance with perfect
predictions) and smoothness (dependence of their performance on the prediction
error). Our algorithm for caching is 1-consistent, robust, and its smoothness
deteriorates with the decreasing number of available predictions. We propose an
algorithm for general MTS whose consistency and smoothness both scale linearly
with the decreasing number of predictions. Without the restriction on the
number of available predictions, both algorithms match the earlier guarantees
achieved by Antoniadis et al. '20.
