assume the availability of given side information sequences at the nodes (see e.g., [@Ravi]-[@Chia]). In this paper, instead, we account for the cost of acquiring the side information by introducing side information VMs at an intermediate node and/ or at the final destination of a cascade model. As an example of the applications of interest, consider the computer network of Fig. \[fig:fig1\], where the intermediate and end nodes can obtain side information from remote data bases, but only at the cost of investing system resources such as time or bandwidth. Another example is a sensor network in which acquiring measurements entails an energy cost.

![A multi-hop computer network in which intermediate and end nodes can access side information by interrogating remote data bases via cost-constrained actions.[]{data-label="fig:fig1"}](db2_mod)

As shown in [@Permuter] for a point-to-point system, the optimal operation of a VM at the decoder requires taking actions that are guided by the message received from the encoder. This implies the exchange of an explicit control signal embedded in the message communicated to the decoder that instructs the latter on how to operate the VM. Generalizing to the cascade models under study, a key issue ** to be tackled in this work 