Measurement Dependent Noisy Search with Stochastic Coefficients

Consider the problem of recovering an unknown sparse unit vector via a sequence of linear observations with stochastic magnitude and additive noise. An agent sequentially selects measurement vectors and collects observations subject to noise affected by the measurement vector. We propose two algorithms of varying computational complexity for sequentially and adaptively designing measurement vectors. The proposed algorithms aim to augment the learning of the unit common support vector with an estimate of the stochastic coefficient. Numerically, we study the probability of error in estimating the support achieved by our proposed algorithms and demonstrate improvements over random-coding based strategies utilized in prior works.