  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
belief, 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.
