How to Protect Your Privacy? A Framework for Counter-Adversarial Decision Making
Inês Lourenço, Robert Mattila, Cristian R. Rojas, Bo Wahlberg · 2020
We consider a counter-adversarial sequential decision-making problem where an agent computes its private belief (posterior distribution) of the current state of the world, by filtering private information. According to its private be-lief, the agent performs an action, which is observed by an adversarial agent. We have recently shown how the adversarial agent can reconstruct the private belief of the decision-making agent via inverse optimization. The main contribution of this paper is a method to obfuscate the private belief of the agent from the adversary, by performing a suboptimal action. The proposed method optimizes the trade-off between obfuscating the private belief and limiting the increase in cost accrued due to taking a suboptimal action. We propose a probabilistic relaxation to obtain a linear optimization problem for solving the trade-off. In numerical examples, we show that the proposed methods enable the agent to obfuscate its private belief without compromising its cost budget.