14 research outputs found
Distributed Stochastic Nonconvex Optimization and Learning based on Successive Convex Approximation
We study distributed stochastic nonconvex optimization in multi-agent
networks. We introduce a novel algorithmic framework for the distributed
minimization of the sum of the expected value of a smooth (possibly nonconvex)
function (the agents' sum-utility) plus a convex (possibly nonsmooth)
regularizer. The proposed method hinges on successive convex approximation
(SCA) techniques, leveraging dynamic consensus as a mechanism to track the
average gradient among the agents, and recursive averaging to recover the
expected gradient of the sum-utility function. Almost sure convergence to
(stationary) solutions of the nonconvex problem is established. Finally, the
method is applied to distributed stochastic training of neural networks.
Numerical results confirm the theoretical claims, and illustrate the advantages
of the proposed method with respect to other methods available in the
literature.Comment: Proceedings of 2019 Asilomar Conference on Signals, Systems, and
Computer
Energy efficiency optimization in MIMO interference channels: A successive pseudoconvex approximation approach
In this paper, we consider the (global and sum) energy efficiency
optimization problem in downlink multi-input multi-output multi-cell systems,
where all users suffer from multi-user interference. This is a challenging
problem due to several reasons: 1) it is a nonconvex fractional programming
problem, 2) the transmission rate functions are characterized by
(complex-valued) transmit covariance matrices, and 3) the processing-related
power consumption may depend on the transmission rate. We tackle this problem
by the successive pseudoconvex approximation approach, and we argue that
pseudoconvex optimization plays a fundamental role in designing novel iterative
algorithms, not only because every locally optimal point of a pseudoconvex
optimization problem is also globally optimal, but also because a descent
direction is easily obtained from every optimal point of a pseudoconvex
optimization problem. The proposed algorithms have the following advantages: 1)
fast convergence as the structure of the original optimization problem is
preserved as much as possible in the approximate problem solved in each
iteration, 2) easy implementation as each approximate problem is suitable for
parallel computation and its solution has a closed-form expression, and 3)
guaranteed convergence to a stationary point or a Karush-Kuhn-Tucker point. The
advantages of the proposed algorithm are also illustrated numerically.Comment: submitted to IEEE Transactions on Signal Processin