Stochastic optimization methods for the simultaneous control of parameter-dependent systems

We address the application of stochastic optimization methods for the simultaneous control of parameter-dependent systems. In particular, we focus on the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro, and on the recently developed Continuous Stochastic Gradient (CSG) algorithm. We consider the problem of computing simultaneous controls through the minimization of a cost functional defined as the superposition of individual costs for each realization of the system. We compare the performances of these stochastic approaches, in terms of their computational complexity, with those of the more classical Gradient Descent (GD) and Conjugate Gradient (CG) algorithms, and we discuss the advantages and disadvantages of each methodology. In agreement with well-established results in the machine learning context, we show how the SGD and CSG algorithms can significantly reduce the computational burden when treating control problems depending on a large amount of parameters. This is corroborated by numerical experiments

Learning and Management for Internet-of-Things: Accounting for Adaptivity and Scalability

Internet-of-Things (IoT) envisions an intelligent infrastructure of networked smart devices offering task-specific monitoring and control services. The unique features of IoT include extreme heterogeneity, massive number of devices, and unpredictable dynamics partially due to human interaction. These call for foundational innovations in network design and management. Ideally, it should allow efficient adaptation to changing environments, and low-cost implementation scalable to massive number of devices, subject to stringent latency constraints. To this end, the overarching goal of this paper is to outline a unified framework for online learning and management policies in IoT through joint advances in communication, networking, learning, and optimization. From the network architecture vantage point, the unified framework leverages a promising fog architecture that enables smart devices to have proximity access to cloud functionalities at the network edge, along the cloud-to-things continuum. From the algorithmic perspective, key innovations target online approaches adaptive to different degrees of nonstationarity in IoT dynamics, and their scalable model-free implementation under limited feedback that motivates blind or bandit approaches. The proposed framework aspires to offer a stepping stone that leads to systematic designs and analysis of task-specific learning and management schemes for IoT, along with a host of new research directions to build on.Comment: Submitted on June 15 to Proceeding of IEEE Special Issue on Adaptive and Scalable Communication Network

Adaptively parametrized surface wave tomography: methodology and a new model of the European upper mantle

In this study, we aim to close the gap between regional and global traveltime tomography in the context of surface wave tomography of the upper mantle implementing the principle of adaptive parametrization. Observations of seismic surface waves are a very powerful tool to constrain the 3-D structure of the Earth's upper mantle, including its anisotropy, because they sample this volume efficiently due to their sensitivity over a wide depth range along the ray path. On a global scale, surface wave tomography models are often parametrized uniformly, without accounting for inhomogeneities in data coverage and, as a result, in resolution, that are caused by effective under- or overparametrization in many areas. If the local resolving power of seismic data is not taken into account when parametrizing the model, features will be smeared and distorted in tomographic maps, with subsequent misinterpretation. Parametrization density has to change locally, for models to be robustly constrained without losing any accurate information available in the best sampled regions. We have implemented a new algorithm for upper mantle surface wave tomography, based on adaptive-voxel parametrization, with voxel size defined by both the ‘hit count' (number of observations sampling the voxel) and ‘azimuthal coverage' (how well different azimuths with respect to the voxel are covered by the source-station distribution). High image resolution is achieved in regions with dense data coverage, while lower image resolution is kept in regions where data coverage is poorer. This way, parametrization is everywhere tuned to optimal resolution, minimizing both the computational costs, and the non-uniqueness of the solution. The spacing of our global grid is locally as small as ∼50 km. We apply our method to identify a new global model of vertically and horizontally polarized shear velocity, with resolution particularly enhanced in the European lithosphere and upper mantle. We find our new model to resolve lithospheric thickness and radial anisotropy better than earlier results based on the same data. Robust features of our model include, for example, the Trans-European Suture Zone, the Panonnian Basin, thinned lithosphere in the Aegean and Western Mediterranean, possible small-scale mantle upwellings under Iberia and Massif Central, subduction under the Aegean arc and a very deep cratonic root underneath southern Finlan

SHADHO: Massively Scalable Hardware-Aware Distributed Hyperparameter Optimization

Computer vision is experiencing an AI renaissance, in which machine learning models are expediting important breakthroughs in academic research and commercial applications. Effectively training these models, however, is not trivial due in part to hyperparameters: user-configured values that control a model's ability to learn from data. Existing hyperparameter optimization methods are highly parallel but make no effort to balance the search across heterogeneous hardware or to prioritize searching high-impact spaces. In this paper, we introduce a framework for massively Scalable Hardware-Aware Distributed Hyperparameter Optimization (SHADHO). Our framework calculates the relative complexity of each search space and monitors performance on the learning task over all trials. These metrics are then used as heuristics to assign hyperparameters to distributed workers based on their hardware. We first demonstrate that our framework achieves double the throughput of a standard distributed hyperparameter optimization framework by optimizing SVM for MNIST using 150 distributed workers. We then conduct model search with SHADHO over the course of one week using 74 GPUs across two compute clusters to optimize U-Net for a cell segmentation task, discovering 515 models that achieve a lower validation loss than standard U-Net.Comment: 10 pages, 6 figure