Convergence Results for the EM Approach to Mixtures of Experts Architectures

The Expectation-Maximization (EM) algorithm is an iterative approach to maximum likelihood parameter estimation. Jordan and Jacobs (1993) recently proposed an EM algorithm for the mixture of experts architecture of Jacobs, Jordan, Nowlan and Hinton (1991) and the hierarchical mixture of experts architecture of Jordan and Jacobs (1992). They showed empirically that the EM algorithm for these architectures yields significantly faster convergence than gradient ascent. In the current paper we provide a theoretical analysis of this algorithm. We show that the algorithm can be regarded as a variable metric algorithm with its searching direction having a positive projection on the gradient of the log likelihood. We also analyze the convergence of the algorithm and provide an explicit expression for the convergence rate. In addition, we describe an acceleration technique that yields a significant speedup in simulation experiments.

Mobilized ad-hoc networks: A reinforcement learning approach

Research in mobile ad-hoc networks has focused on situations in which nodes have no control over their movements. We investigate an important but overlooked domain in which nodes do have control over their movements. Reinforcement learning methods can be used to control both packet routing decisions and node mobility, dramatically improving the connectivity of the network. We first motivate the problem by presenting theoretical bounds for the connectivity improvement of partially mobile networks and then present superior empirical results under a variety of different scenarios in which the mobile nodes in our ad-hoc network are embedded with adaptive routing policies and learned movement policies.