arXiv subjects

Petros Voulgaris

Publications and source records attributed to Petros Voulgaris.

27 records · Page 2Linked to original sources

arXiv2021

Accelerated Almost-Sure Convergence Rates for Nonconvex Stochastic Gradient Descent using Stochastic Learning Rates

Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies almost-sure convergence rates of the Stochastic Gradient Descent method when instead of deterministic, its learning rate becomes stochastic. In particular, its learning rate is equipped with a multiplicative stochasticity, producing a stochastic learning rate scheme. Theoretical results show accelerated almost-sure convergence rates of Stochastic Gradient Descent in a nonconvex setting when using an appropriate stochastic learning rate, compared to a deterministic-learning-rate scheme. The theoretical results are verified empirically.

math.OC↗

arXiv2021

BFGS-ADMM for Large-Scale Distributed Optimization

We consider a class of distributed optimization problem where the objective function consists of a sum of strongly convex and smooth functions and a (possibly nonsmooth) convex regularizer. A multi-agent network is assumed, where each agent holds a private cost function and cooperates with its neighbors to compute the optimum of the aggregate objective. We propose a quasi-Newton Alternating Direction Method of Multipliers (ADMM) where the primal update is solved inexactly with approximated curvature information. By introducing an intermediate consensus variable, we achieve a block diagonal Hessian which eliminates the need for inner communication loops within the network when computing the update direction. We establish global linear convergence to the optimal primal-dual solution without the need for backtracking line search, under the assumption that component cost functions are strongly convex with Lipschitz continuous gradients. Numerical simulations on real datasets demonstrate the advantages of the proposed method over state of the art.

math.OC↗

arXiv2021

DN-ADMM: Distributed Newton ADMM for Multi-agent Optimization

In a multi-agent network, we consider the problem of minimizing an objective function that is expressed as the sum of private convex and smooth functions, and a (possibly) non-differentiable convex regularizer. We propose a novel distributed second-order method based on the framework of Alternating Direction Method of Multipliers (ADMM), by invoking approximate Newton iterations to the primal update corresponding to the differentiable part. In order to achieve a distributed implementation, the total Hessian matrix is split into a diagonal component (locally computable) and an off-diagonal component (that requires communication between neighboring agents). Subsequently, the Hessian inverse is approximated by a truncation of the Taylor expansion to $K$ terms: this amounts to fully distributed updates entailing $K$ distributed communication rounds. We establish global linear convergence to the primal-dual optimal solution under the assumption that the private functions are strongly convex and have Lipschitz continuous gradient. Numerical experiments demonstrate the merits of the approach comparatively with state-of-the-art methods.

math.OC↗

arXiv2021

Estimation and Planning of Exploration Over Grid Map Using A Spatiotemporal Model with Incomplete State Observations

Path planning over spatiotemporal models can be applied to a variety of applications such as UAVs searching for spreading wildfire in mountains or network of balloons in time-varying atmosphere deployed for inexpensive internet service. A notable aspect in such applications is the dynamically changing environment. However, path planning algorithms often assume static environments and only consider the vehicle's dynamics exploring the environment. We present a spatiotemporal model that uses a cross-correlation operator to consider spatiotemporal dependence. Also, we present an adaptive state estimator for path planning. Since the state estimation depends on the vehicle's path, the path planning needs to consider the trade-off between exploration and exploitation. We use a high-level decision-maker to choose an explorative path or an exploitative path. The overall proposed framework consists of an adaptive state estimator, a short-term path planner, and a high-level decision-maker. We tested the framework with a spatiotemporal model simulation where the state of each grid transits from normal, latent, and fire state. For the mission objective of visiting the grids with fire, the proposed framework outperformed the random walk (baseline) and the single-minded exploitation (or exploration) path.

cs.RO↗

arXiv2021

Learning Image Attacks toward Vision Guided Autonomous Vehicles

While adversarial neural networks have been shown successful for static image attacks, very few approaches have been developed for attacking online image streams while taking into account the underlying physical dynamics of autonomous vehicles, their mission, and environment. This paper presents an online adversarial machine learning framework that can effectively misguide autonomous vehicles' missions. In the existing image attack methods devised toward autonomous vehicles, optimization steps are repeated for every image frame. This framework removes the need for fully converged optimization at every frame to realize image attacks in real-time. Using reinforcement learning, a generative neural network is trained over a set of image frames to obtain an attack policy that is more robust to dynamic and uncertain environments. A state estimator is introduced for processing image streams to reduce the attack policy's sensitivity to physical variables such as unknown position and velocity. A simulation study is provided to validate the results.

cs.RO↗

arXiv2021

Backup Plan Constrained Model Predictive Control

This article proposes a new safety concept: backup plan safety. The backup plan safety is defined as the ability to complete one of the alternative missions in the case of primary mission abortion. To incorporate this new safety concept in control problems, we formulate a feasibility maximization problem that adopts additional (virtual) input horizons toward the alternative missions on top of the input horizon toward the primary mission. Cost functions for the primary and alternative missions construct multiple objectives, and multi-horizon inputs evaluate them. To address the feasibility maximization problem, we develop a multi-horizon multi-objective model predictive path integral control (3M) algorithm. Model predictive path integral control (MPPI) is a sampling-based scheme that can help the proposed algorithm deal with nonlinear dynamic systems and achieve computational efficiency by parallel computation. Simulations of the aerial vehicle and ground vehicle control problems demonstrate the new concept of backup plan safety and the performance of the proposed algorithm.

eess.SY↗

arXiv2021

Finite-Time Model Inference From A Single Noisy Trajectory

This paper proposes a novel model inference procedure to identify system matrix from a single noisy trajectory over a finite-time interval. The proposed inference procedure comprises an observation data processor, a redundant data processor and an ordinary least-square estimator, wherein the data processors mitigate the influence of observation noise on inference error. We first systematically investigate the comparisons with naive least-square-regression based model inference and uncover that 1) the same observation data has identical influence on the feasibility of the proposed and the naive model inferences, 2) the naive model inference uses all of the redundant data, while the proposed model inference optimally uses the basis and the redundant data. We then study the sample complexity of the proposed model inference in the presence of observation noise, which leads to the dependence of the processed bias in the observed system trajectory on time and coordinates. Particularly, we derive the sample-complexity upper bound (on the number of observations sufficient to infer a model with prescribed levels of accuracy and confidence) and the sample-complexity lower bound (high-probability lower bound on model error). Finally, the proposed model inference is numerically validated and analyzed.

eess.SY↗

arXiv2020

Robust Vehicle Lane Keeping Control with Networked Proactive Adaptation

Road condition is an important environmental factor for autonomous vehicle control. A dramatic change in the road condition from the nominal status is a source of uncertainty that can lead to a system failure. Once the vehicle encounters an uncertain environment, such as hitting an ice patch, it is too late to reduce the speed, and the vehicle can lose control. To cope with future uncertainties in advance, we study a proactive robust adaptive control architecture for autonomous vehicles' lane-keeping control problems. The data center generates a prior environmental uncertainty estimate by combining weather forecasts and measurements from anonymous vehicles through a spatio-temporal filter. The prior estimate contributes to designing a robust heading controller and nominal longitudinal velocity for proactive adaptation to each new abnormal condition. Then the control parameters are updated based on posterior information fusion with on-board measurements.

eess.SY↗

arXiv2019

Maya: Falsifying Power Sidechannels with Dynamic Control

The security of computers is at risk because of information leaking through physical outputs such as power, temperature, or electromagnetic (EM) emissions. Attackers can use advanced signal measurement and analysis to recover sensitive data from these sidechannels. To address this problem, this paper presents Maya, a simple and effective solution against power side-channels. The idea is to re-shape the power dissipated by an application in an application-transparent manner using control theory techniques - preventing attackers from learning any information. With control theory, a controller can reliably keep power close to a desired target value even when runtime conditions change unpredictably. Then, by changing these targets intelligently, power can be made to appear in any desired form, appearing to carry activity information which, in reality, is unrelated to the application. Maya can be implemented in privileged software or in simple hardware. In this paper, we implement Maya on two multiprocessor machines using Operating System (OS) threads, and show its effectiveness and ease of deployment.

cs.CR↗