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In this work we propose the use of adaptive stochastic search as a building block for general, non-convex optimization operations within deep neural network architectures. Specifically, for an objective function located at some layer in the…
We have presented an optimal buffer sizing and buffer insertion methodology which uses stochastic models of the architecture and Continuous Time Markov Decision Processes CTMDPs. Such a methodology is useful in managing the scarce buffer…
Distributed Optimization is an increasingly important subject area with the rise of multi-agent control and optimization. We consider a decentralized stochastic optimization problem where the agents on a graph aim to asynchronously optimize…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
In this paper, we investigate the distributed convex optimization problem over a multi-agent system with Markovian switching communication networks. The objective function is the sum of each agent's local objective function, which cannot be…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as…
In this paper, we establish a general stochastic maximum principle for optimal control for systems described by a continuous-time Markov regime-switching stochastic recursive utilities model. The control domain is postulated not to be…
This paper investigates methods for estimating the optimal stochastic control policy for a Markov Decision Process with unknown transition dynamics and an unknown reward function. This form of model-free reinforcement learning comprises…
Motivated by a class of applied problems arising from physical layer based security in a digital communication system, in particular, by a secrecy sum-rate maximization problem, this paper studies a nonsmooth, difference-of-convex (dc)…
This paper applies computational techniques of convex stochastic optimization to optimal operation and valuation of electricity storages in the face of uncertain electricity prices. Our valuations are based on the indifference pricing…
The trend in the electric power system is to move towards increased amounts of distributed resources which suggests a transition from the current highly centralized to a more distributed control structure. In this paper, we propose a method…
In this paper, we discuss our approach and algorithmic framework for solving large-scale security constrained optimal power flow (SCOPF) problems. SCOPF is a mixed integer non-convex optimization problem that aims to obtain the minimum…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
This paper addresses the problem of voltage regulation in power distribution networks with deep-penetration of distributed energy resources, e.g., renewable-based generation, and storage-capable loads such as plug-in hybrid electric…
In this work, we propose a distributed algorithm for stochastic non-convex optimization. We consider a worker-server architecture where a set of $K$ worker nodes (WNs) in collaboration with a server node (SN) jointly aim to minimize a…
The optimal control problem of stochastic systems is commonly solved via robust or scenario-based optimization methods, which are both challenging to scale to long optimization horizons. We cast the optimal control problem of a stochastic…
We address distributed learning problems, both nonconvex and convex, over undirected networks. In particular, we design a novel algorithm based on the distributed Alternating Direction Method of Multipliers (ADMM) to address the challenges…