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Pragmatic Communication for Remote Control of Finite-State Markov Processes

Pietro Talli, Edoardo David Santi, Federico Chiariotti, Touraj Soleymani, Federico Mason, Andrea Zanella, Deniz Gündüz

TL;DR

The paper develops a general theory for pragmatic, goal-oriented remote control of finite-state Markov processes over costly zero-delay channels, introducing pull- and push-based architectures and three optimization algorithms. It proves that push-based policies strictly improve over pull-based ones and provides formal optimality guarantees and complexity results for each algorithm, including an exact POMDP-based Joint Policy Optimization with exponential cost and two polynomial-time, locally optimal alternatives. The framework captures implicit information from non-transmissions and yields scalable approaches that perform well in remote control tasks, with remote estimation posing greater computational challenges. The findings offer a principled path to design efficient, cooperative encoder–decoder strategies for cyber-physical systems under tight communication resources, with potential extensions to delays, losses, and multi-node settings.

Abstract

Pragmatic or goal-oriented communication can optimize communication decisions beyond the reliable transmission of data, instead aiming at directly affecting application performance with the minimum channel utilization. In this paper, we develop a general theoretical framework for the remote control of finite-state Markov processes, using pragmatic communication over a costly zero-delay communication channel. To that end, we model a cyber-physical system composed of an encoder, which observes and transmits the states of a process in real-time, and a decoder, which receives that information and controls the behavior of the process. The encoder and the decoder should cooperatively optimize the trade-off between the control performance (i.e., reward) and the communication cost (i.e., channel use). This scenario underscores a pragmatic (i.e., goal-oriented) communication problem, where the purpose is to convey only the data that is most valuable for the underlying task, taking into account the state of the decoder (hence, the pragmatic aspect). We investigate two different decision-making architectures: in pull-based remote control, the decoder is the only decision-maker, while in push-based remote control, the encoder and the decoder constitute two independent decision-makers, leading to a multi-agent scenario. We propose three algorithms to optimize our system (i.e., design the encoder and the decoder policies), discuss the optimality guarantees ofs the algorithms, and shed light on their computational complexity and fundamental limits.

Pragmatic Communication for Remote Control of Finite-State Markov Processes

TL;DR

The paper develops a general theory for pragmatic, goal-oriented remote control of finite-state Markov processes over costly zero-delay channels, introducing pull- and push-based architectures and three optimization algorithms. It proves that push-based policies strictly improve over pull-based ones and provides formal optimality guarantees and complexity results for each algorithm, including an exact POMDP-based Joint Policy Optimization with exponential cost and two polynomial-time, locally optimal alternatives. The framework captures implicit information from non-transmissions and yields scalable approaches that perform well in remote control tasks, with remote estimation posing greater computational challenges. The findings offer a principled path to design efficient, cooperative encoder–decoder strategies for cyber-physical systems under tight communication resources, with potential extensions to delays, losses, and multi-node settings.

Abstract

Pragmatic or goal-oriented communication can optimize communication decisions beyond the reliable transmission of data, instead aiming at directly affecting application performance with the minimum channel utilization. In this paper, we develop a general theoretical framework for the remote control of finite-state Markov processes, using pragmatic communication over a costly zero-delay communication channel. To that end, we model a cyber-physical system composed of an encoder, which observes and transmits the states of a process in real-time, and a decoder, which receives that information and controls the behavior of the process. The encoder and the decoder should cooperatively optimize the trade-off between the control performance (i.e., reward) and the communication cost (i.e., channel use). This scenario underscores a pragmatic (i.e., goal-oriented) communication problem, where the purpose is to convey only the data that is most valuable for the underlying task, taking into account the state of the decoder (hence, the pragmatic aspect). We investigate two different decision-making architectures: in pull-based remote control, the decoder is the only decision-maker, while in push-based remote control, the encoder and the decoder constitute two independent decision-makers, leading to a multi-agent scenario. We propose three algorithms to optimize our system (i.e., design the encoder and the decoder policies), discuss the optimality guarantees ofs the algorithms, and shed light on their computational complexity and fundamental limits.
Paper Structure (19 sections, 10 theorems, 26 equations, 9 figures, 3 algorithms)

This paper contains 19 sections, 10 theorems, 26 equations, 9 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation and Modeling
  4. Pull-Based Remote Control
  5. Push-Based Remote Control
  6. Special Case: Remote Estimation
  7. Proposed Algorithms
  8. Pull-Based Modified Policy Iteration Scheme
  9. Push-Based Alternating Policy Iteration Scheme
  10. Push-Based Joint Policy Optimization Scheme
  11. Theoretical Results and Computational Limits
  12. Optimality Analysis
  13. Computational and Performance Limitations
  14. The Remote Estimation Problem
  15. Numerical Results
  16. ...and 4 more sections

Key Result

Theorem 1

Without any loss of optimality, at each time $t$, the knowledge of the encoder can be described by $\langle s_t,\Delta_t,s_{t-\Delta_t}\rangle$, and that of the decoder by $\langle \Delta_t,s_{t-\Delta_t}\rangle$, where $\Delta_t$ is the time elapsed since the last transmission.

Figures (9)

  • Figure 1: A Markov model with $5$ states and $2$ actions in which the scheme may reach suboptimal solutions.
  • Figure 2: Results for the remote control task in an with $30$ states.
  • Figure 3: Results for the remote estimation task in an with $30$ states.
  • Figure 4: The trade-off curves between the average reward and the average channel use in the control task with 10 states. The density of the transition matrix is $d=0.9$.
  • Figure 5: The trade-off curves between the average correct estimation rate and the average channel use in the estimation task with 10 states. The density of the transition matrix is $d=0.19$ and the matrix was built ad hoc.
  • ...and 4 more figures

Theorems & Definitions (10)

  • Theorem 1
  • Lemma \inteval1+1.1
  • Theorem 2
  • Lemma \inteval2+1.1
  • Lemma \inteval2+1.2
  • Theorem 3
  • Lemma \inteval3+1.1
  • Theorem 4
  • Theorem 5
  • Corollary 5.1