Hidden Markov Models:Inverse Filtering,Belief Estimation and Privacy Protection

A hidden Markov model(HMM)comprises a state with Markovian dynamics that can only be observed via noisy sensors.This paper considers three problems connected to HMMs,namely,inverse filtering,belief estimation from actions,and privacy enforcement in such a context.First,the authors discuss how HMM parameters and sensor measurements can be reconstructed from posterior distributions of an HMM filter.Next,the authors consider a rational decision-maker that forms a private belief(posterior distribution)on the state of the world by filtering private information.The authors show how to estimate such posterior distributions from observed optimal actions taken by the agent.In the setting of adversarial systems,the authors finally show how the decision-maker can protect its private belief by confusing the adversary using slightly sub-optimal actions.Applications range from financial portfolio investments to life science decision systems.

Identifiability and Solvability in Inverse Linear Quadratic Optimal Control Problems

In this paper, the inverse linear quadratic(LQ) problem over finite time-horizon is studied.Given the output observations of a dynamic process, the goal is to recover the corresponding LQ cost function. Firstly, by considering the inverse problem as an identification problem, its model structure is shown to be strictly globally identifiable under the assumption of system invertibility. Next, in the noiseless case a necessary and sufficient condition is proposed for the solvability of a positive semidefinite weighting matrix and its unique solution is obtained with two proposed algorithms under the condition of persistent excitation. Furthermore, a residual optimization problem is also formulated to solve a best-fit approximate cost function from sub-optimal observations. Finally, numerical simulations are used to demonstrate the effectiveness of the proposed methods.