Belief-State Control for Sequential Multibiometric Identification: Structural Results and Explicit Finite-Grid Bounds

Source abstract

Sequential multibiometric identification requires choosing which source to query, when to stop, and which identity to declare. We formulate this task as a discounted belief-state Markov decision process with heterogeneous observation models and source-dependent costs. Contraction yields a unique value function and an optimal stationary policy. Concavity gives convex identity-specific stopping regions and, in the binary case, a two-threshold rule. Comparative statics describe acquisition-cost effects, while Blackwell dominance removes less informative, no-cheaper sources. Using the affine dependence of a fixed history rule’s cost on the initial prior, together with a stopping-specific pathwise bound, we derive explicit global Lipschitz constants without imposing Lipschitz continuity of the belief kernel. These estimates give uniform worst-case bounds for finite-grid value approximation and nearest-neighbor grid-policy loss on the original belief process. A contraction-based perturbation bound separates belief quantization, numerical-integration perturbation, and value-iteration error. Under source-wise pairwise identifiability, every stationary Bellman-minimizing selector stops almost surely. For Gaussian scores, a mean–variance condition makes source dominance directly verifiable. A reproducible synthetic study illustrates the structural and numerical results.