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We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying Markov random processes parameterized by the underlying optimization variable. These time-varying samples make gradient directions in our update biased and dependent, which can potentially lead to the divergence of the iterates. In our two-time-scale approach, one scale is to estimate the true gradient from these samples, which is then used to update the estimate of the optimal solution. While these two iterates are implemented simultaneously, the former is updated "faster" (using bigger step sizes) than the latter (using smaller step sizes). Our first contribution is to characterize the finite-time complexity of the proposed two-time-scale stochastic gradient method. In particular, we provide explicit formulas for the convergence rates of this method under different structural assumptions, namely, strong convexity, convexity, the Polyak-Lojasiewicz condition, and general non-convexity. We apply our framework to two problems in control and reinforcement learning. First, we look at the standard online actor-critic algorithm over finite state and action spaces and derive a convergence rate of O(k^(-2/5)), which recovers the best known rate derived specifically for this problem. Second, we study an online actor-critic algorithm for the linear-quadratic regulator and show that a convergence rate of O(k^(-2/3)) is achieved. This is the first time such a result is known in the literature. Finally, we support our theoretical analysis with numerical simulations where the convergence rates are visualized.

Current challenges of the manufacturing industry require modular and changeable manufacturing systems that can be adapted to variable conditions with little effort. At the same time, production recipes typically represent important company know-how that should not be directly tied to changing plant configurations. Thus, there is a need to model general production recipes independent of specific plant layouts. For execution of such a recipe however, a binding to then available production resources needs to be made. In this contribution, select a suitable modeling language to model and execute such recipes. Furthermore, we present an approach to solve the issue of recipe modeling and execution in modular plants using semantically modeled capabilities and skills as well as BPMN. We make use of BPMN to model \emph{capability processes}, i.e. production processes referencing abstract descriptions of resource functions. These capability processes are not bound to a certain plant layout, as there can be multiple resources fulfilling the same capability. For execution, every capability in a capability process is replaced by a skill realizing it, effectively creating a \emph{skill process} consisting of various skill invocations. The presented solution is capable of orchestrating and executing complex processes that integrate production steps with typical IT functionalities such as error handling, user interactions and notifications. Benefits of the approach are demonstrated using a flexible manufacturing system.

We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we consider PDEs where the function is constrained to be positive and integrate to unity, as is the case with Fokker-Planck equations. Our approach involves reparameterizing the solution as the exponential of a neural network appropriately normalized to ensure both requirements are satisfied. This then gives rise to nonlinear a partial integro-differential equation (PIDE) where the integral appearing in the equation is handled by a novel application of importance sampling. Secondly, we tackle a number of Hamilton-Jacobi-Bellman (HJB) equations that appear in stochastic optimal control problems. The key contribution is that these equations are approached in their unsimplified primal form which includes an optimization problem as part of the equation. We extend the DGM algorithm to solve for the value function and the optimal control \simultaneously by characterizing both as deep neural networks. Training the networks is performed by taking alternating stochastic gradient descent steps for the two functions, a technique inspired by the policy improvement algorithms (PIA).

Fog computing is introduced by shifting cloud resources towards the users' proximity to mitigate the limitations possessed by cloud computing. Fog environment made its limited resource available to a large number of users to deploy their serverless applications, composed of several serverless functions. One of the primary intentions behind introducing the fog environment is to fulfil the demand of latency and location-sensitive serverless applications through its limited resources. The recent research mainly focuses on assigning maximum resources to such applications from the fog node and not taking full advantage of the cloud environment. This introduces a negative impact in providing the resources to a maximum number of connected users. To address this issue, in this paper, we investigated the optimum percentage of a user's request that should be fulfilled by fog and cloud. As a result, we proposed DeF-DReL, a Systematic Deployment of Serverless Functions in Fog and Cloud environments using Deep Reinforcement Learning, using several real-life parameters, such as distance and latency of the users from nearby fog node, user's priority, the priority of the serverless applications and their resource demand, etc. The performance of the DeF-DReL algorithm is further compared with recent related algorithms. From the simulation and comparison results, its superiority over other algorithms and its applicability to the real-life scenario can be clearly observed.

We provide a decision theoretic analysis of bandit experiments. The setting corresponds to a dynamic programming problem, but solving this directly is typically infeasible. Working within the framework of diffusion asymptotics, we define suitable notions of asymptotic Bayes and minimax risk for bandit experiments. For normally distributed rewards, the minimal Bayes risk can be characterized as the solution to a nonlinear second-order partial differential equation (PDE). Using a limit of experiments approach, we show that this PDE characterization also holds asymptotically under both parametric and non-parametric distribution of the rewards. The approach further describes the state variables it is asymptotically sufficient to restrict attention to, and therefore suggests a practical strategy for dimension reduction. The upshot is that we can approximate the dynamic programming problem defining the bandit experiment with a PDE which can be efficiently solved using sparse matrix routines. We derive the optimal Bayes and minimax policies from the numerical solutions to these equations. The proposed policies substantially dominate existing methods such as Thompson sampling. The framework also allows for substantial generalizations to the bandit problem such as time discounting and pure exploration motives.

We consider M-estimation problems, where the target value is determined using a minimizer of an expected functional of a Levy process. With discrete observations from the Levy process, we can produce a "quasi-path" by shuffling increments of the Levy process, we call it a quasi-process. Under a suitable sampling scheme, a quasi-process can converge weakly to the true process according to the properties of the stationary and independent increments. Using this resampling technique, we can estimate objective functionals similar to those estimated using the Monte Carlo simulations, and it is available as a contrast function. The M-estimator based on these quasi-processes can be consistent and asymptotically normal.

Frame-online speech enhancement systems in the short-time Fourier transform (STFT) domain usually have an algorithmic latency equal to the window size due to the use of the overlap-add algorithm in the inverse STFT (iSTFT). This algorithmic latency allows the enhancement models to leverage future contextual information up to a length equal to the window size. However, current frame-online systems only partially leverage this future information. To fully exploit this information, this study proposes an overlapped-frame prediction technique for deep learning based frame-online speech enhancement, where at each frame our deep neural network (DNN) predicts the current and several past frames that are necessary for overlap-add, instead of only predicting the current frame. In addition, we propose a novel loss function to account for the scale difference between predicted and oracle target signals. Evaluations results on a noisy-reverberant speech enhancement task show the effectiveness of the proposed algorithms.

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional Bayesian inverse problems. With Bayesian imaging applications in mind, in this work we present the proximal nested sampling methodology to objectively compare alternative Bayesian imaging models for applications that use images to inform decisions under uncertainty. The methodology is based on nested sampling, a Monte Carlo approach specialised for model comparison, and exploits proximal Markov chain Monte Carlo techniques to scale efficiently to large problems and to tackle models that are log-concave and not necessarily smooth (e.g., involving l_1 or total-variation priors). The proposed approach can be applied computationally to problems of dimension O(10^6) and beyond, making it suitable for high-dimensional inverse imaging problems. It is validated on large Gaussian models, for which the likelihood is available analytically, and subsequently illustrated on a range of imaging problems where it is used to analyse different choices of dictionary and measurement model.

We present a pipelined multiplier with reduced activities and minimized interconnect based on online digit-serial arithmetic. The working precision has been truncated such that $p<n$ bits are used to compute $n$ bits product, resulting in significant savings in area and power. The digit slices follow variable precision according to input, increasing upto $p$ and then decreases according to the error profile. Pipelining has been done to achieve high throughput and low latency which is desirable for compute intensive inner products. Synthesis results of the proposed designs have been presented and compared with the non-pipelined online multiplier, pipelined online multiplier with full working precision and conventional serial-parallel and array multipliers. For $8, 16, 24$ and $32$ bit precision, the proposed low power pipelined design show upto $38\%$ and $44\%$ reduction in power and area respectively compared to the pipelined online multiplier without working precision truncation.

Multi-view networks are ubiquitous in real-world applications. In order to extract knowledge or business value, it is of interest to transform such networks into representations that are easily machine-actionable. Meanwhile, network embedding has emerged as an effective approach to generate distributed network representations. Therefore, we are motivated to study the problem of multi-view network embedding, with a focus on the characteristics that are specific and important in embedding this type of networks. In our practice of embedding real-world multi-view networks, we identify two such characteristics, which we refer to as preservation and collaboration. We then explore the feasibility of achieving better embedding quality by simultaneously modeling preservation and collaboration, and propose the mvn2vec algorithms. With experiments on a series of synthetic datasets, an internal Snapchat dataset, and two public datasets, we further confirm the presence and importance of preservation and collaboration. These experiments also demonstrate that better embedding can be obtained by simultaneously modeling the two characteristics, while not over-complicating the model or requiring additional supervision.