# Deception in Supervisory Control

## TL;DR

This paper explores how to design optimal deceptive and reference policies in adversarial supervisory control settings modeled by Markov decision processes, balancing deception and task achievement.

## Contribution

It introduces a formal framework for synthesizing optimal deceptive and reference policies, highlighting the convexity and NP-hardness of the respective optimization problems.

## Key findings

- Deceptive policy synthesis reduces to a convex optimization problem.
- Reference policy synthesis is NP-hard and involves nonconvex optimization.
- The framework enables strategic decision-making in adversarial environments.

## Abstract

The use of deceptive strategies is important for an agent that attempts not to reveal his intentions in an adversarial environment. We consider a setting in which a supervisor provides a reference policy and expects an agent to follow the reference policy and perform a task. The agent may instead follow a different, deceptive policy to achieve a different task. We model the environment and the behavior of the agent with a Markov decision process, represent the tasks of the agent and the supervisor with reachability specifications, and study the synthesis of optimal deceptive policies for such agents. We also study the synthesis of optimal reference policies that prevent deceptive strategies of the agent and achieve the supervisor's task with high probability. We show that the synthesis of optimal deceptive policies has a convex optimization problem formulation, while the synthesis of optimal reference policies requires solving a nonconvex optimization problem. We also show that the synthesis of optimal reference policies is NP-hard.