Smoother Entropy for Active State Trajectory Estimation and Obfuscation in POMDPs

In this article, we study the problem of controlling a partially observed Markov decision process (POMDP) to either aid or hinder the estimation of its state trajectory. We encode the estimation objectives via the
smoother entropy
, which is the conditional entropy of the state trajectory given measurements and controls. Consideration of the smoother entropy contrasts with previous approaches that instead resort to marginal (or instantaneous) state entropies due to tractability concerns. By establishing novel expressions for the smoother entropy in terms of the POMDP belief state, we show that both the problems of minimizing and maximizing the smoother entropy in POMDPs can surprisingly be reformulated as belief-state Markov decision processes with concave cost and value functions. The significance of these reformulations is that they render the smoother entropy a tractable optimization objective, with structural properties amenable to the use of standard POMDP solution techniques for
both
active estimation and obfuscation. Simulations illustrate that optimization of the smoother entropy leads to superior trajectory estimation and obfuscation compared to alternative approaches.