15,507 research outputs found
Distributed Big-Data Optimization via Block-Iterative Convexification and Averaging
In this paper, we study distributed big-data nonconvex optimization in
multi-agent networks. We consider the (constrained) minimization of the sum of
a smooth (possibly) nonconvex function, i.e., the agents' sum-utility, plus a
convex (possibly) nonsmooth regularizer. Our interest is in big-data problems
wherein there is a large number of variables to optimize. If treated by means
of standard distributed optimization algorithms, these large-scale problems may
be intractable, due to the prohibitive local computation and communication
burden at each node. We propose a novel distributed solution method whereby at
each iteration agents optimize and then communicate (in an uncoordinated
fashion) only a subset of their decision variables. To deal with non-convexity
of the cost function, the novel scheme hinges on Successive Convex
Approximation (SCA) techniques coupled with i) a tracking mechanism
instrumental to locally estimate gradient averages; and ii) a novel block-wise
consensus-based protocol to perform local block-averaging operations and
gradient tacking. Asymptotic convergence to stationary solutions of the
nonconvex problem is established. Finally, numerical results show the
effectiveness of the proposed algorithm and highlight how the block dimension
impacts on the communication overhead and practical convergence speed
Collective Robot Reinforcement Learning with Distributed Asynchronous Guided Policy Search
In principle, reinforcement learning and policy search methods can enable
robots to learn highly complex and general skills that may allow them to
function amid the complexity and diversity of the real world. However, training
a policy that generalizes well across a wide range of real-world conditions
requires far greater quantity and diversity of experience than is practical to
collect with a single robot. Fortunately, it is possible for multiple robots to
share their experience with one another, and thereby, learn a policy
collectively. In this work, we explore distributed and asynchronous policy
learning as a means to achieve generalization and improved training times on
challenging, real-world manipulation tasks. We propose a distributed and
asynchronous version of Guided Policy Search and use it to demonstrate
collective policy learning on a vision-based door opening task using four
robots. We show that it achieves better generalization, utilization, and
training times than the single robot alternative.Comment: Submitted to the IEEE International Conference on Robotics and
Automation 201
Distributed Stochastic Optimization under Imperfect Information
We consider a stochastic convex optimization problem that requires minimizing
a sum of misspecified agentspecific expectation-valued convex functions over
the intersection of a collection of agent-specific convex sets. This
misspecification is manifested in a parametric sense and may be resolved
through solving a distinct stochastic convex learning problem. Our interest
lies in the development of distributed algorithms in which every agent makes
decisions based on the knowledge of its objective and feasibility set while
learning the decisions of other agents by communicating with its local
neighbors over a time-varying connectivity graph. While a significant body of
research currently exists in the context of such problems, we believe that the
misspecified generalization of this problem is both important and has seen
little study, if at all. Accordingly, our focus lies on the simultaneous
resolution of both problems through a joint set of schemes that combine three
distinct steps: (i) An alignment step in which every agent updates its current
belief by averaging over the beliefs of its neighbors; (ii) A projected
(stochastic) gradient step in which every agent further updates this averaged
estimate; and (iii) A learning step in which agents update their belief of the
misspecified parameter by utilizing a stochastic gradient step. Under an
assumption of mere convexity on agent objectives and strong convexity of the
learning problems, we show that the sequences generated by this collection of
update rules converge almost surely to the solution of the correctly specified
stochastic convex optimization problem and the stochastic learning problem,
respectively
A randomized primal distributed algorithm for partitioned and big-data non-convex optimization
In this paper we consider a distributed optimization scenario in which the
aggregate objective function to minimize is partitioned, big-data and possibly
non-convex. Specifically, we focus on a set-up in which the dimension of the
decision variable depends on the network size as well as the number of local
functions, but each local function handled by a node depends only on a (small)
portion of the entire optimization variable. This problem set-up has been shown
to appear in many interesting network application scenarios. As main paper
contribution, we develop a simple, primal distributed algorithm to solve the
optimization problem, based on a randomized descent approach, which works under
asynchronous gossip communication. We prove that the proposed asynchronous
algorithm is a proper, ad-hoc version of a coordinate descent method and thus
converges to a stationary point. To show the effectiveness of the proposed
algorithm, we also present numerical simulations on a non-convex quadratic
program, which confirm the theoretical results
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