| The advent of distributed and agile sensing systems that collect data, in multiple locations and through a variety of sensing modalities, has brought about new and exciting challenges to the field of signal processing. Motivated by problems that arise in the development of these systems, the thesis makes contributions in three domains: (1) distributed optimization for inference in sensor networks, (2) statistical tests for optimality that mitigate the problem of sensitivity to local maxima, and (3) development and analysis of reinforcement learning solutions to stochastic decision problems for resource allocation in agile sensing.; A novel incremental gradient method, called incremental aggregated gradient (IAG), that can be used by wireless sensor networks to perform inference in a distributed manner, is proposed and analyzed. A gradient aggregation concept relaxes the common requirement of incremental methods for a diminishing step size for convergence, and a fast convergence rate is established.; The convergence of IAG is established under a certain unimodality assumption. For non-convex problems however, for example when IAG is applied to find the maximum likelihood estimator, the method might stagnate at a local maximum. To mitigate this weakness, the following question is addressed: Given the location of a relative maximum of the log-likelihood function, how to assess whether it is the global maximum? We analyze and improve an existing statistical tool, called A Test for Global Maximum, that answers this question by posing it as a hypothesis testing problem. Tests that are insensitive to model mismatch are proposed, thereby overcoming a fundamental weakness of this tool.; Finding optimal policies for controlling an agile sensing system is formulated as a reinforcement learning problem and solved via a novel approximate dynamic programming algorithm that approximates the solution of the associated multi-stage non-convex optimization problem by solving a sequence of single-stage convex problems. Via this approximation a plethora of off-the-shelf classification methods can be applied to approximate the solution of the more complicated reinforcement learning problem. The consequences of the approximation are investigated by deriving finite sample upper bounds on the performance of the estimated policy relative to the performance of the optimal one. |
