arXiv subjects

Alireza Aghasi

Publications and source records attributed to Alireza Aghasi.

At least 37 records · Page 2Linked to original sources

arXiv2022

Fast-Convergent Dynamics for Distributed Allocation of Resources Over Switching Sparse Networks with Quantized Communication Links

This paper proposes networked dynamics to solve resource allocation problems over time-varying multi-agent networks. The state of each agent represents the amount of used resources (or produced utilities) while the total amount of resources is fixed. The idea is to optimally allocate the resources among the group of agents by minimizing the overall cost function subject to fixed sum of resources. Each agents' information is restricted to its own state and cost function and those of its immediate in-neighbors. This is motivated by distributed applications such as mobile edge-computing, economic dispatch over smart grids, and multi-agent coverage control. This work provides a fast convergent solution (in comparison with linear dynamics) while considering relaxed network connectivity with quantized communication links. The proposed dynamics reaches optimal solution over switching (possibly disconnected) undirected networks as far as their union over some bounded non-overlapping time-intervals has a spanning-tree. We prove feasibility of the solution, uniqueness of the optimal state, and convergence to the optimal value under the proposed dynamics, where the analysis is applicable to similar 1st-order allocation dynamics with strongly sign-preserving nonlinearities, such as actuator saturation.

eess.SY↗

arXiv2022

Distributed Finite-Sum Constrained Optimization subject to Nonlinearity on the Node Dynamics

Motivated by recent development in networking and parallel data-processing, we consider a distributed and localized finite-sum (or fixed-sum) allocation technique to solve resource-constrained convex optimization problems over multi-agent networks (MANs). Such networks include (smart) agents representing an intelligent entity capable of communication, processing, and decision-making. In particular, we consider problems subject to practical nonlinear constraints on the dynamics of the agents in terms of their communications and actuation capabilities (referred to as the node dynamics), e.g., networks of mobile robots subject to actuator saturation and quantized communication. The considered distributed sum-preserving optimization solution further enables adding purposeful nonlinear constraints, for example, sign-based nonlinearities, to reach convergence in predefined-time or robust to impulsive noise and disturbances in faulty environments. Moreover, convergence can be achieved under minimal network connectivity requirements among the agents; thus, the solution is applicable over dynamic networks where the channels come and go due to the agent's mobility and limited range. This paper discusses how various nonlinearity constraints on the optimization problem (e.g., collaborative allocation of resources) can be addressed for different applications via a distributed setup (over a network).

eess.SY↗

arXiv2021

1st-Order Dynamics on Nonlinear Agents for Resource Allocation over Uniformly-Connected Networks

A general nonlinear $1$st-order consensus-based solution for distributed constrained convex optimization is proposed with network resource allocation applications. The solution is used to optimize continuously-differentiable strictly convex cost functions over weakly-connected undirected networks, while it is anytime feasible and models various nonlinearities to account for imperfections and constraints on the (physical model of) agents in terms of limited actuation capabilities, e.g., quantization and saturation. Due to such inherent nonlinearities, the existing linear solutions considering ideal agent models may not necessarily converge with guaranteed optimality and anytime feasibility. Some applications also impose specific nonlinearities, e.g., convergence in fixed/finite-time or sign-based robust disturbance-tolerant dynamics. Our proposed distributed protocol generalizes such nonlinear models. Putting convex set analysis together with nonsmooth Lyapunov analysis, we prove convergence, (i) regardless of the particular type of nonlinearity, and (ii) with weak network-connectivity requirements (uniform-connectivity).

eess.SY↗

arXiv2021

Inverse Constrained Reinforcement Learning

In real world settings, numerous constraints are present which are hard to specify mathematically. However, for the real world deployment of reinforcement learning (RL), it is critical that RL agents are aware of these constraints, so that they can act safely. In this work, we consider the problem of learning constraints from demonstrations of a constraint-abiding agent's behavior. We experimentally validate our approach and show that our framework can successfully learn the most likely constraints that the agent respects. We further show that these learned constraints are \textit{transferable} to new agents that may have different morphologies and/or reward functions. Previous works in this regard have either mainly been restricted to tabular (discrete) settings, specific types of constraints or assume the environment's transition dynamics. In contrast, our framework is able to learn arbitrary \textit{Markovian} constraints in high-dimensions in a completely model-free setting. The code can be found it: \url{https://github.com/shehryar-malik/icrl}.

cs.LG↗

arXiv2021

Distributed support-vector-machine over dynamic balanced directed networks

In this paper, we consider the binary classification problem via distributed Support-Vector-Machines (SVM), where the idea is to train a network of agents, with limited share of data, to cooperatively learn the SVM classifier for the global database. Agents only share processed information regarding the classifier parameters and the gradient of the local loss functions instead of their raw data. In contrast to the existing work, we propose a continuous-time algorithm that incorporates network topology changes in discrete jumps. This hybrid nature allows us to remove chattering that arises because of the discretization of the underlying CT process. We show that the proposed algorithm converges to the SVM classifier over time-varying weight balanced directed graphs by using arguments from the matrix perturbation theory.

eess.SY↗

arXiv2020

Optimal Allocation of Quantized Human Eye Depth Perception for Light Field Display Design

Creating immersive 3D stereoscopic, autostereoscopic, and lightfield experiences are becoming the center point of optical design of future head mounted displays and lightfield displays. However, despite the advancement in 3D and light field displays; there is no consensus on what are the necessary quantized depth levels for such emerging displays at stereoscopic or monocular modalities. Here we start from psychophysical theories and work toward defining and prioritizing quantized levels of depth that would saturate the human depth perception. We propose a general optimization framework, which locates the depth levels in a \emph{globally optimal} way for band limited displays. While the original problem is computationally intractable, we manage to find a tractable reformulation as maximally covering a region of interest with a selection of hypographs corresponding to the monocular depth of field profiles. The results show that on average 1731 stereoscopic and 8 monocular depth levels (distributed from 25 cm to infinity) would saturate the visual depth perception. Also the first 3 depth levels should be allocated at (148), then (83, 170), then (53, 90, 170) distances respectively from the face plane to minimize the monocular error in the entire population. The study further discusses the 3D spatial profile of the quantized stereoscopic and monocular depth levels. The study provides fundamental guidelines for designing optimal near eye displays, light-field monitors, and 3D screens.

eess.IV↗

arXiv2020

Learning To Solve Differential Equations Across Initial Conditions

Recently, there has been a lot of interest in using neural networks for solving partial differential equations. A number of neural network-based partial differential equation solvers have been formulated which provide performances equivalent, and in some cases even superior, to classical solvers. However, these neural solvers, in general, need to be retrained each time the initial conditions or the domain of the partial differential equation changes. In this work, we posit the problem of approximating the solution of a fixed partial differential equation for any arbitrary initial conditions as learning a conditional probability distribution. We demonstrate the utility of our method on Burger's Equation.

cs.LG↗

arXiv2019

Bilinear Compressed Sensing under known Signs via Convex Programming

We consider the bilinear inverse problem of recovering two vectors, $\boldsymbol{x} \in\mathbb{R}^L$ and $\boldsymbol{w} \in\mathbb{R}^L$, from their entrywise product. We consider the case where $\boldsymbol{x}$ and $\boldsymbol{w}$ have known signs and are sparse with respect to known dictionaries of size $K$ and $N$, respectively. Here, $K$ and $N$ may be larger than, smaller than, or equal to $L$. We introduce $\ell_1$-BranchHull, which is a convex program posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved. Under the assumptions that $\boldsymbol{x}$ and $\boldsymbol{w}$ satisfy a comparable-effective-sparsity condition and are $S_1$- and $S_2$-sparse with respect to a random dictionary, we present a recovery guarantee in a noisy case. We show that $\ell_1$-BranchHull is robust to small dense noise with high probability if the number of measurements satisfy $L\geqΩ\left((S_1+S_2)\log^{2}(K+N)\right)$. Numerical experiments show that the scaling constant in the theorem is not too large. We also introduce variants of $\ell_1$-BranchHull for the purposes of tolerating noise and outliers, and for the purpose of recovering piecewise constant signals. We provide an ADMM implementation of these variants and show they can extract piecewise constant behavior from real images.

math.OC↗

arXiv2019

Simultaneous Phase Retrieval and Blind Deconvolution via Convex Programming

We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a nontrivial convex relaxation of the bilinear measurements from convolution. We prove that if the two signals belong to known random subspaces of dimensions $k$ and $n$, then they can be recovered up to the inherent scaling ambiguity with $m \gg (k+n) \log^2 m$ phaseless measurements. Our method provides the first theoretical recovery guarantee for this problem by a computationally efficient algorithm and does not require a solution estimate to be computed for initialization. Our proof is based on Rademacher complexity estimates. Additionally, we provide an alternating direction method of multipliers (ADMM) implementation and provide numerical experiments that verify the theory.

cs.IT↗

arXiv2019

Fast Convex Pruning of Deep Neural Networks

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most $s$ terms that can re-create the layer outputs from the layer inputs, we can find these weights from $\mathcal{O}(s\log N/s)$ samples, where $N$ is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

cs.LG↗

arXiv2019

BranchHull: Convex bilinear inversion from the entrywise product of signals with known signs

We consider the bilinear inverse problem of recovering two vectors, $x$ and $w$, in $\mathbb{R}^L$ from their entrywise product. For the case where the vectors have known signs and belong to known subspaces, we introduce the convex program BranchHull, which is posed in the natural parameter space that does not require an approximate solution or initialization in order to be stated or solved. Under the structural assumptions that $x$ and $w$ are members of known $K$ and $N$ dimensional random subspaces, we present a recovery guarantee for the noiseless case and a noisy case. In the noiseless case, we prove that the BranchHull recovers $x$ and $w$ up to the inherent scaling ambiguity with high probability when $L\ \gg\ 2(K+N)$. The analysis provides a precise upper bound on the coefficient for the sample complexity. In a noisy case, we show that with high probability the BranchHull is robust to small dense noise when $L = Ω(K+N)$. BranchHull is motivated by the sweep distortion removal task in dielectric imaging, where one of the signals is a nonnegative reflectivity, and the other signal lives in a known wavelet subspace. Additional potential applications are blind deconvolution and self-calibration.

cs.IT↗

arXiv2018

A convex program for bilinear inversion of sparse vectors

We consider the bilinear inverse problem of recovering two vectors, $\boldsymbol{x}\in\mathbb{R}^L$ and $\boldsymbol{w}\in\mathbb{R}^L$, from their entrywise product. We consider the case where $\boldsymbol{x}$ and $\boldsymbol{w}$ have known signs and are sparse with respect to known dictionaries of size $K$ and $N$, respectively. Here, $K$ and $N$ may be larger than, smaller than, or equal to $L$. We introduce $\ell_1$-BranchHull, which is a convex program posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved. We study the case where $\boldsymbol{x}$ and $\boldsymbol{w}$ are $S_1$- and $S_2$-sparse with respect to a random dictionary and present a recovery guarantee that only depends on the number of measurements as $L\geqΩ(S_1+S_2)\log^{2}(K+N)$. Numerical experiments verify that the scaling constant in the theorem is not too large. One application of this problem is the sweep distortion removal task in dielectric imaging, where one of the signals is a nonnegative reflectivity, and the other signal lives in a known subspace, for example that given by dominant wavelet coefficients. We also introduce a variants of $\ell_1$-BranchHull for the purposes of tolerating noise and outliers, and for the purpose of recovering piecewise constant signals. We provide an ADMM implementation of these variants and show they can extract piecewise constant behavior from real images.

math.OC↗

arXiv2018

Blind Deconvolutional Phase Retrieval via Convex Programming

We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a nontrivial convex relaxation of the bilinear measurements from convolution. We prove that if the two signals belong to known random subspaces of dimensions $k$ and $n$, then they can be recovered up to the inherent scaling ambiguity with $m >> (k+n) \log^2 m$ phaseless measurements. Our method provides the first theoretical recovery guarantee for this problem by a computationally efficient algorithm and does not require a solution estimate to be computed for initialization. Our proof is based Rademacher complexity estimates. Additionally, we provide an ADMM implementation of the method and provide numerical experiments that verify the theory.

cs.IT↗

arXiv2017

Net-Trim: Convex Pruning of Deep Neural Networks with Performance Guarantee

We introduce and analyze a new technique for model reduction for deep neural networks. While large networks are theoretically capable of learning arbitrarily complex models, overfitting and model redundancy negatively affects the prediction accuracy and model variance. Our Net-Trim algorithm prunes (sparsifies) a trained network layer-wise, removing connections at each layer by solving a convex optimization program. This program seeks a sparse set of weights at each layer that keeps the layer inputs and outputs consistent with the originally trained model. The algorithms and associated analysis are applicable to neural networks operating with the rectified linear unit (ReLU) as the nonlinear activation. We present both parallel and cascade versions of the algorithm. While the latter can achieve slightly simpler models with the same generalization performance, the former can be computed in a distributed manner. In both cases, Net-Trim significantly reduces the number of connections in the network, while also providing enough regularization to slightly reduce the generalization error. We also provide a mathematical analysis of the consistency between the initial network and the retrained model. To analyze the model sample complexity, we derive the general sufficient conditions for the recovery of a sparse transform matrix. For a single layer taking independent Gaussian random vectors of length $N$ as inputs, we show that if the network response can be described using a maximum number of $s$ non-zero weights per node, these weights can be learned from $\mathcal{O}(s\log N)$ samples.

cs.LG↗

arXiv2016

Learning Shapes by Convex Composition

We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that overlap and occlude one another in such a way that they "match" a given scene as closely as possible. This paper derives general sufficient conditions under which this convex shape composition identifies a target composition. From a computational standpoint, we present two different methods for solving the associated optimization programs. The first method simply recasts the problem as a linear program, while the second uses the alternating direction method of multipliers with a series of easily computed proximal operators.

cs.CV↗

arXiv2016

Sweep Distortion Removal from THz Images via Blind Demodulation

Heavy sweep distortion induced by alignments and inter-reflections of layers of a sample is a major burden in recovering 2D and 3D information in time resolved spectral imaging. This problem cannot be addressed by conventional denoising and signal processing techniques as it heavily depends on the physics of the acquisition. Here we propose and implement an algorithmic framework based on low-rank matrix recovery and alternating minimization that exploits the forward model for THz acquisition. The method allows recovering the original signal in spite of the presence of temporal-spatial distortions. We address a blind-demodulation problem, where based on several observations of the sample texture modulated by an undesired sweep pattern, the two classes of signals are separated. The performance of the method is examined in both synthetic and experimental data, and the successful reconstructions are demonstrated. The proposed general scheme can be implemented to advance inspection and imaging applications in THz and other time-resolved sensing modalities.

cs.CV↗

arXiv2015

Convex Cardinal Shape Composition

We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them through basic set operations to characterize desired regions in an image. This is a combinatorial problem solving which requires an exhaustive search among a large number of possibilities. We propose a convex relaxation to the problem to make it computationally tractable. We take some major steps towards the analysis of the proposed convex program and characterizing its minimizers. Applications vary from shape-based characterization, object tracking, optical character recognition, and shape recovery in occlusion, to other disciplines such as the geometric packing problem.

math.OC↗

arXiv2013

A Geometric Approach to Joint Inversion with Applications to Contaminant Source Zone Characterization

This paper presents a new joint inversion approach to shape-based inverse problems. Given two sets of data from distinct physical models, the main objective is to obtain a unified characterization of inclusions within the spatial domain of the physical properties to be reconstructed. Although our proposed method generally applies to many types of inversion problems, the main motivation here is to characterize subsurface contaminant source-zones by processing down gradient hydrological data and cross-gradient electrical resistance tomography (ERT) observations. Inspired by Newton's method for multi-objective optimization, we present an iterative inversion scheme that suggests taking descent steps that can simultaneously reduce both data-model misfit terms. Such an approach, however, requires solving a non-smooth convex problem at every iteration, which is computationally expensive for a pixel-based inversion over the whole domain. Instead, we employ a parametric level set (PaLS) technique that substantially reduces the number of underlying parameters, making the inversion computationally tractable. The performance of the technique is examined and discussed through the reconstruction of source zone architectures that are representative of dense non-aqueous phase liquid (DNAPL) contaminant release in a statistically homogenous sandy aquifer. In these examples, the geometric configuration of the DNAPL mass is considered along with additional information about its spatial variability within the contaminated zone, such as the identification of low and high saturation regions. Comparison of the reconstructions with the true DNAPL architectures highlights the superior performance of the model-based technique and joint inversion scheme.

physics.geo-ph↗