# Deception in Optimal Control

arXiv: https://arxiv.org/abs/1805.03090 · HTML: https://mlsanity.com/paper/1805.03090/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2018.

## Built on by (most cited first, 10 of 10)

- [Deceptive Reinforcement Learning for Privacy-Preserving Planning](https://mlsanity.com/paper/2102.03022/) (2021)
- [Satisficing Paths and Independent Multi-Agent Reinforcement Learning in Stochastic Games](https://mlsanity.com/paper/2110.04638/) (2021)
- [Deceptive Decision-Making Under Uncertainty](https://mlsanity.com/paper/2109.06740/) (2021)
- [Deceptive Reinforcement Learning in Model-Free Domains](https://mlsanity.com/paper/2303.10838/) (2023)
- [Deceptive Planning for Resource Allocation](https://mlsanity.com/paper/2206.01306/) (2022)
- [Planning for Attacker Entrapment in Adversarial Settings](https://mlsanity.com/paper/2303.00822/) (2023)
- [Deceptive Path Planning via Reinforcement Learning with Graph Neural Networks](https://mlsanity.com/paper/2402.06552/) (2024)
- [Preserving the Privacy of Reward Functions in MDPs through Deception](https://mlsanity.com/paper/2407.09809/) (2024)
- [Value of Information-based Deceptive Path Planning Under Adversarial Interventions](https://mlsanity.com/paper/2503.24284/) (2025)
- [Repeated Deceptive Path Planning against Learnable Observer](https://mlsanity.com/paper/2605.07174/) (2026)

## Abstract (arXiv)

In this paper, we consider an adversarial scenario where one agent seeks to achieve an objective and its adversary seeks to learn the agent's intentions and prevent the agent from achieving its objective. The agent has an incentive to try to deceive the adversary about its intentions, while at the same time working to achieve its objective. The primary contribution of this paper is to introduce a mathematically rigorous framework for the notion of deception within the context of optimal control. The central notion introduced in the paper is that of a belief-induced reward: a reward dependent not only on the agent's state and action, but also adversary's beliefs. Design of an optimal deceptive strategy then becomes a question of optimal control design on the product of the agent's state space and the adversary's belief space. The proposed framework allows for deception to be defined in an arbitrary control system endowed with a reward function, as well as with additional specifications limiting the agent's control policy. In addition to defining deception, we discuss design of optimally deceptive strategies under uncertainties in agent's knowledge about the adversary's learning process. In the latter part of the paper, we focus on a setting where the agent's behavior is governed by a Markov decision process, and show that the design of optimally deceptive strategies under lack of knowledge about the adversary naturally reduces to previously discussed problems in control design on partially observable or uncertain Markov decision processes. Finally, we present two examples of deceptive strategies: a "cops and robbers" scenario and an example where an agent may use camouflage while moving. We show that optimally deceptive strategies in such examples follow the intuitive idea of how to deceive an adversary in the above settings.