  Various applications for inter-machine communications are on the rise.
Whether it is for autonomous driving vehicles or the internet of everything,
machines are more connected than ever to improve their performance in
fulfilling a given task. While in traditional communications the goal has often
been to reconstruct the underlying message, under the emerging task-oriented
paradigm, the goal of communication is to enable the receiving end to make more
informed decisions or more precise estimates/computations. Motivated by these
recent developments, in this paper, we perform an indirect design of the
communications in a multi-agent system (MAS) in which agents cooperate to
maximize the averaged sum of discounted one-stage rewards of a collaborative
task. Due to the bit-budgeted communications between the agents, each agent
should efficiently represent its local observation and communicate an
abstracted version of the observations to improve the collaborative task
performance. We first show that this problem can be approximated as a form of
data-quantization problem which we call task-oriented data compression (TODC).
We then introduce the state-aggregation for information compression algorithm
(SAIC) to solve the formulated TODC problem. It is shown that SAIC is able to
achieve near-optimal performance in terms of the achieved sum of discounted
rewards. The proposed algorithm is applied to a geometric consensus problem and
its performance is compared with several benchmarks. Numerical experiments
confirm the promise of this indirect design approach for task-oriented
multi-agent communications.
