arXiv subjects

Shamak Dutta

Publications and source records attributed to Shamak Dutta.

9 recordsLinked to original sources

arXiv2026

Submodular Optimization with Applications to Decision and Control

Submodular set functions, characterized by the diminishing-returns property, provide a unifying combinatorial framework for many subset-selection problems in decision and control. Although exact maximization is NP-hard in general, the structural properties of submodular functions enable simple greedy algorithms that achieve constant-factor approximation guarantees for monotone objectives, with randomized greedy-based variants extending such guarantees to the non-monotone case. This survey reviews the theory, algorithms, and applications of submodular optimization with a focus on systems and control. We cover the structural properties of submodular functions, including curvature and the submodularity ratio, the constraint families that arise in practice (matroids, knapsack, and $p$-systems), and the main approximation algorithms for monotone and non-monotone submodular maximization, with up-to-date approximation ratios and hardness results. We then survey applications across sensor scheduling, multi-agent coordination, robust submodular optimization, leader-follower systems, distributed submodular optimization, game theory, system theory, resource allocation, social networks, and informative path planning. The survey emphasizes practically implementable greedy-based algorithms and instance-dependent refinements via curvature and the submodularity ratio. We close with observations on canonical control-theoretic objectives: certain functionals are submodular (the log-determinant and rank of the controllability Gramian, and the log-determinant of the Kalman filter information matrix), whereas closely related objectives fail to be sub- or supermodular (the steady-state Kalman filter error covariance, and the average control energy obtained from the inverse Gramian). We also highlight the cross-cutting open directions that follow.

math.OC↗

arXiv2026

Efficient Multi-Objective Planning with Weighted Maximization Using Large Neighbourhood Search

Autonomous navigation often requires the simultaneous optimization of multiple objectives. The most common approach scalarizes these into a single cost function using a weighted sum, but this method is unable to find all possible trade-offs and can therefore miss critical solutions. An alternative, the weighted maximum of objectives, can find all Pareto-optimal solutions, including those in non-convex regions of the trade-off space that weighted sum methods cannot find. However, the increased computational complexity of finding weighted maximum solutions in the discrete domain has limited its practical use. To address this challenge, we propose a novel search algorithm based on the Large Neighbourhood Search framework that efficiently solves the weighted maximum planning problem. Through extensive simulations, we demonstrate that our algorithm achieves comparable solution quality to existing weighted maximum planners with a runtime improvement of 1-2 orders of magnitude, making it a viable option for autonomous navigation.

cs.RO↗

arXiv2026

Hierarchical Informative Path Planning via Graph Guidance and Trajectory Optimization

We study informative path planning (IPP) with travel budgets in cluttered environments, where an agent collects measurements of a latent field modeled as a Gaussian process (GP) to reduce uncertainty at target locations. Graph-based solvers provide global guarantees but assume pre-selected measurement locations, while continuous trajectory optimization supports path-based sensing but is computationally intensive and sensitive to initialization in obstacle-dense settings. We propose a hierarchical framework with three stages: (i) graph-based global planning, (ii) segment-wise budget allocation using geometric and kernel bounds, and (iii) spline-based refinement of each segment with hard constraints and obstacle pruning. By combining global guidance with local refinement, our method achieves lower posterior uncertainty than graph-only and continuous baselines, while running faster than continuous-space solvers (up to 9x faster than gradient-based methods and 20x faster than black-box optimizers) across synthetic cluttered environments and Arctic datasets.

cs.RO↗

arXiv2023

A Unified Approach to Optimally Solving Sensor Scheduling and Sensor Selection Problems in Kalman Filtering

We consider a general form of the sensor scheduling problem for state estimation of linear dynamical systems, which involves selecting sensors that minimize the trace of the Kalman filter error covariance (weighted by a positive semidefinite matrix) subject to polyhedral constraints on the selected sensors. This general form captures several well-studied problems including sensor placement, sensor scheduling with budget constraints, and Linear Quadratic Gaussian (LQG) control and sensing co-design. We present a mixed integer optimization approach that is derived by exploiting the optimality of the Kalman filter. While existing work has focused on approximate methods to specific problem variants, our work provides a unified approach to computing optimal solutions to the general version of sensor scheduling. In simulation, we show this approach finds optimal solutions for systems with 30 to 50 states in seconds.

math.OC↗

arXiv2022

Approximation Algorithms for Robot Tours in Random Fields with Guaranteed Estimation Accuracy

We study the sample placement and shortest tour problem for robots tasked with mapping environmental phenomena modeled as stationary random fields. The objective is to minimize the resources used (samples or tour length) while guaranteeing estimation accuracy. We give approximation algorithms for both problems in convex environments. These improve previously known results, both in terms of theoretical guarantees and in simulations. In addition, we disprove an existing claim in the literature on a lower bound for a solution to the sample placement problem.

cs.RO↗

arXiv2022

Informative Path Planning in Random Fields via Mixed Integer Programming

We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum error over a finite set of prediction locations. The problem is known to be NP-hard. However, we strive to compute optimal solutions by leveraging advances in mixed integer optimization. Our approach is based on expanding the search space so we optimize not only over the collected measurement subset, but also over the class of all linear estimators. This allows us to formulate a mixed integer quadratic program that is convex in the continuous variables. The formulations are general and are not restricted to any covariance structure of the field. In simulations, we demonstrate the effectiveness of our approach over previous branch and bound algorithms.

eess.SY↗

arXiv2022

An Improved Greedy Algorithm for Subset Selection in Linear Estimation

In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements can be taken at any location in the continuous field, and the covariance between the field values at different points is given by the widely used squared exponential covariance function. One approach for observation selection is to perform a grid discretization of the space and obtain an approximate solution using the greedy algorithm. The solution quality improves with a finer grid resolution but at the cost of increased computation. We propose a method to reduce the computational complexity, or conversely to increase solution quality, of the greedy algorithm by considering a search space consisting only of prediction locations and centroids of cliques formed by the prediction locations. We demonstrate the effectiveness of our proposed approach in simulation, both in terms of solution quality and runtime.

math.OC↗

arXiv2018

Convolutional Neural Networks Regularized by Correlated Noise

Neurons in the visual cortex are correlated in their variability. The presence of correlation impacts cortical processing because noise cannot be averaged out over many neurons. In an effort to understand the functional purpose of correlated variability, we implement and evaluate correlated noise models in deep convolutional neural networks. Inspired by the cortex, correlation is defined as a function of the distance between neurons and their selectivity. We show how to sample from high-dimensional correlated distributions while keeping the procedure differentiable, so that back-propagation can proceed as usual. The impact of correlated variability is evaluated on the classification of occluded and non-occluded images with and without the presence of other regularization techniques, such as dropout. More work is needed to understand the effects of correlations in various conditions, however in 10/12 of the cases we studied, the best performance on occluded images was obtained from a model with correlated noise.

cs.LG↗

arXiv2016

Barcodes for Medical Image Retrieval Using Autoencoded Radon Transform

Using content-based binary codes to tag digital images has emerged as a promising retrieval technology. Recently, Radon barcodes (RBCs) have been introduced as a new binary descriptor for image search. RBCs are generated by binarization of Radon projections and by assembling them into a vector, namely the barcode. A simple local thresholding has been suggested for binarization. In this paper, we put forward the idea of "autoencoded Radon barcodes". Using images in a training dataset, we autoencode Radon projections to perform binarization on outputs of hidden layers. We employed the mini-batch stochastic gradient descent approach for the training. Each hidden layer of the autoencoder can produce a barcode using a threshold determined based on the range of the logistic function used. The compressing capability of autoencoders apparently reduces the redundancies inherent in Radon projections leading to more accurate retrieval results. The IRMA dataset with 14,410 x-ray images is used to validate the performance of the proposed method. The experimental results, containing comparison with RBCs, SURF and BRISK, show that autoencoded Radon barcode (ARBC) has the capacity to capture important information and to learn richer representations resulting in lower retrieval errors for image retrieval measured with the accuracy of the first hit only.

cs.CV↗