901 research outputs found
Computational Approaches for Stochastic Shortest Path on Succinct MDPs
We consider the stochastic shortest path (SSP) problem for succinct Markov
decision processes (MDPs), where the MDP consists of a set of variables, and a
set of nondeterministic rules that update the variables. First, we show that
several examples from the AI literature can be modeled as succinct MDPs. Then
we present computational approaches for upper and lower bounds for the SSP
problem: (a)~for computing upper bounds, our method is polynomial-time in the
implicit description of the MDP; (b)~for lower bounds, we present a
polynomial-time (in the size of the implicit description) reduction to
quadratic programming. Our approach is applicable even to infinite-state MDPs.
Finally, we present experimental results to demonstrate the effectiveness of
our approach on several classical examples from the AI literature
Asynchronous Optimization Methods for Efficient Training of Deep Neural Networks with Guarantees
Asynchronous distributed algorithms are a popular way to reduce
synchronization costs in large-scale optimization, and in particular for neural
network training. However, for nonsmooth and nonconvex objectives, few
convergence guarantees exist beyond cases where closed-form proximal operator
solutions are available. As most popular contemporary deep neural networks lead
to nonsmooth and nonconvex objectives, there is now a pressing need for such
convergence guarantees. In this paper, we analyze for the first time the
convergence of stochastic asynchronous optimization for this general class of
objectives. In particular, we focus on stochastic subgradient methods allowing
for block variable partitioning, where the shared-memory-based model is
asynchronously updated by concurrent processes. To this end, we first introduce
a probabilistic model which captures key features of real asynchronous
scheduling between concurrent processes; under this model, we establish
convergence with probability one to an invariant set for stochastic subgradient
methods with momentum.
From the practical perspective, one issue with the family of methods we
consider is that it is not efficiently supported by machine learning
frameworks, as they mostly focus on distributed data-parallel strategies. To
address this, we propose a new implementation strategy for shared-memory based
training of deep neural networks, whereby concurrent parameter servers are
utilized to train a partitioned but shared model in single- and multi-GPU
settings. Based on this implementation, we achieve on average 1.2x speed-up in
comparison to state-of-the-art training methods for popular image
classification tasks without compromising accuracy
Sequential Decision Algorithms for Measurement-Based Impromptu Deployment of a Wireless Relay Network along a Line
We are motivated by the need, in some applications, for impromptu or
as-you-go deployment of wireless sensor networks. A person walks along a line,
starting from a sink node (e.g., a base-station), and proceeds towards a source
node (e.g., a sensor) which is at an a priori unknown location. At equally
spaced locations, he makes link quality measurements to the previous relay, and
deploys relays at some of these locations, with the aim to connect the source
to the sink by a multihop wireless path. In this paper, we consider two
approaches for impromptu deployment: (i) the deployment agent can only move
forward (which we call a pure as-you-go approach), and (ii) the deployment
agent can make measurements over several consecutive steps before selecting a
placement location among them (which we call an explore-forward approach). We
consider a light traffic regime, and formulate the problem as a Markov decision
process, where the trade-off is among the power used by the nodes, the outage
probabilities in the links, and the number of relays placed per unit distance.
We obtain the structures of the optimal policies for the pure as-you-go
approach as well as for the explore-forward approach. We also consider natural
heuristic algorithms, for comparison. Numerical examples show that the
explore-forward approach significantly outperforms the pure as-you-go approach.
Next, we propose two learning algorithms for the explore-forward approach,
based on Stochastic Approximation, which asymptotically converge to the set of
optimal policies, without using any knowledge of the radio propagation model.
We demonstrate numerically that the learning algorithms can converge (as
deployment progresses) to the set of optimal policies reasonably fast and,
hence, can be practical, model-free algorithms for deployment over large
regions.Comment: 29 pages. arXiv admin note: text overlap with arXiv:1308.068
Reduced Complexity Filtering with Stochastic Dominance Bounds: A Convex Optimization Approach
This paper uses stochastic dominance principles to construct upper and lower
sample path bounds for Hidden Markov Model (HMM) filters. Given a HMM, by using
convex optimization methods for nuclear norm minimization with copositive
constraints, we construct low rank stochastic marices so that the optimal
filters using these matrices provably lower and upper bound (with respect to a
partially ordered set) the true filtered distribution at each time instant.
Since these matrices are low rank (say R), the computational cost of evaluating
the filtering bounds is O(XR) instead of O(X2). A Monte-Carlo importance
sampling filter is presented that exploits these upper and lower bounds to
estimate the optimal posterior. Finally, using the Dobrushin coefficient,
explicit bounds are given on the variational norm between the true posterior
and the upper and lower bounds
Distributing Multipartite Entanglement over Noisy Quantum Networks
A quantum internet aims at harnessing networked quantum technologies, namely
by distributing bipartite entanglement between distant nodes. However,
multipartite entanglement between the nodes may empower the quantum internet
for additional or better applications for communications, sensing, and
computation. In this work, we present an algorithm for generating multipartite
entanglement between different nodes of a quantum network with noisy quantum
repeaters and imperfect quantum memories, where the links are entangled pairs.
Our algorithm is optimal for GHZ states with 3 qubits, maximising
simultaneously the final state fidelity and the rate of entanglement
distribution. Furthermore, we determine the conditions yielding this
simultaneous optimality for GHZ states with a higher number of qubits, and for
other types of multipartite entanglement. Our algorithm is general also in the
sense that it can optimise simultaneously arbitrary parameters. This work opens
the way to optimally generate multipartite quantum correlations over noisy
quantum networks, an important resource for distributed quantum technologies.Comment: More detailed calculations of the metrics and minor changes.
Keywords: Quantum Internet, QLANs, Multipartite Entanglement, Entanglement
Distribution, Multi-objective Routing, Quantum Network
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