arXiv subjects

Shreyas Sundaram

Publications and source records attributed to Shreyas Sundaram.

At least 19 recordsLinked to original sources

arXiv2026

A Unified Framework for Joint Sensor Placement and Scheduling for Intrusion Detection

We consider an intrusion detection task in which a defender must jointly optimize sensor placement locations and orientations to minimize the probability of missed detection of an intruder traversing a protected environment. We decompose this problem into a meta problem, termed SensorPlacement, and an embedded subproblem, termed OrientationScheduling. The OrientationScheduling subproblem, for a fixed sensor placement, is modeled as a 2-player zero-sum game between the defender and the intruder, where the defender seeks an orientation strategy for the deployed sensors to minimize the probability of missed detection, while the intruder seeks a path selection strategy to maximize it. Since the defender's strategy space grows combinatorially with the number of sensors and orientations, solving the game via standard linear programming becomes prohibitive. To this end, we develop an iterative and efficient equilibrium-seeking algorithm that exploits the structure of the game's payoff function and establishes theoretical guarantees for convergence to the Nash equilibrium (NE) of the game. This NE value is then used as a utility measure in the SensorPlacement meta problem. We show that this game-value-based utility function is weakly submodular over the set of sensor placements and propose a greedy placement algorithm with near-optimality guarantees. To our knowledge, this is the first unified framework to integrate game-theoretic utility design with (weak) submodular optimization, enabling principled joint optimization of sensor placement and orientation scheduling. Through extensive simulations, we demonstrate that the proposed approach achieves near-optimal detection performance while significantly reducing computation time compared to baselines.

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arXiv2026

HyParLyVe: Hyperplane Partitioning for Neural Lyapunov Verification

This work introduces HyParLyVe (Hyperplane Partitioned Lyapunov Verifier), a novel algorithm for sound and complete verification of neural Lyapunov candidates by interpreting shallow ReLU networks as hyperplane arrangements. This perspective reduces positive definiteness verification to a finite set of vertex evaluations, and the decrease condition to a bounded optimization problem over each region. We formally prove correctness of the proposed verification procedures and demonstrate that HyParLyVe achieves significant speedups over state-of-the-art methods.

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arXiv2026

Distributed Equilibrium-Seeking in Target Coverage Games via Self-Configurable Networks under Limited Communication

We study a target coverage problem in which a team of sensing agents, operating under limited communication, must collaboratively monitor targets that may be adaptively repositioned by an attacker. We model this interaction as a zero-sum game between the sensing team (known as the defender) and the attacker. However, computing an exact Nash equilibrium (NE) for this game is computationally prohibitive as the action space of the defender grows exponentially with the number of sensors and their possible orientations. Exploiting the submodularity property of the game's utility function, we propose a distributed framework that enables agents to self-configure their communication neighborhoods under bandwidth constraints and collaboratively maximize the target coverage. We establish theoretical guarantees showing that the resulting sensing strategies converge to an approximate NE of the game. To our knowledge, this is the first distributed, communication-aware approach that scales effectively for games with combinatorial action spaces while explicitly incorporating communication constraints. To this end, we leverage the distributed bandit-submodular optimization framework and the notion of Value of Coordination that were introduced in [1]. Through simulations, we show that our approach attains near-optimal game value and higher target coverage compared to baselines.

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arXiv2025

Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Data

The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system trajectory under i.i.d. random inputs, and assumes that the underlying dynamics is truly linear. In contrast, we consider the problem of identifying a linearized model when the true underlying dynamics is nonlinear, given that there is a certain constraint on the region where one can initialize the experiments. We provide a multiple trajectories-based deterministic data acquisition algorithm followed by a regularized least squares algorithm, and provide a finite sample error bound on the learned linearized dynamics. Our error bound shows that one can consistently learn the linearized dynamics, and demonstrates a trade-off between the error due to nonlinearity and the error due to noise. We validate our results through numerical experiments, where we also show the potential insufficiency of linear system identification using a single trajectory with i.i.d. random inputs, when nonlinearity does exist.

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arXiv2025

Sensor Scheduling in Intrusion Detection Games with Uncertain Payoffs

We study the problem of sensor scheduling for an intrusion detection task. We model this as a two-player zero-sum game over a graph, where the defender (Player 1) seeks to identify the optimal strategy for scheduling sensor orientations to minimize the probability of missed detection at minimal cost, while the intruder (Player 2) aims to identify the optimal path selection strategy to maximize missed detection probability at minimal cost. The defender's strategy space grows exponentially with the number of sensors, making direct computation of the Nash Equilibrium (NE) strategies computationally expensive. To tackle this, we propose a distributed variant of the Weighted Majority algorithm that exploits the structure of the game's payoff matrix, enabling efficient computation of the NE strategies with provable convergence guarantees. Next, we consider a more challenging scenario where the defender lacks knowledge of the true sensor models and, consequently, the game's payoff matrix. For this setting, we develop online learning algorithms that leverage bandit feedback from sensors to estimate the NE strategies. By building on existing results from perturbation theory and online learning in matrix games, we derive high-probability order-optimal regret bounds for our algorithms. Finally, through simulations, we demonstrate the empirical performance of our proposed algorithms in both known and unknown payoff scenarios.

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arXiv2025

A Primal-Dual Gradient Descent Approach to the Connectivity Constrained Sensor Coverage Problem

Sensor networks play a critical role in many situational awareness applications. In this paper, we study the problem of determining sensor placements to balance coverage and connectivity objectives over a target region. Leveraging algebraic graph theory, we formulate a novel optimization problem to maximize sensor coverage over a spatial probability density of event likelihoods while adhering to connectivity constraints. To handle the resulting non-convexity under constraints, we develop an augmented Lagrangian-based gradient descent algorithm inspired by recent approaches to efficiently identify points satisfying the Karush-Kuhn-Tucker (KKT) conditions. We establish convergence guarantees by showing necessary assumptions are satisfied in our setup, including employing Mangasarian-Fromowitz constraint qualification to prove the existence of a KKT point. Numerical simulations under different probability densities demonstrate that the optimized sensor networks effectively cover high-priority regions while satisfying desired connectivity constraints.

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arXiv2025

Robust Information Selection for Hypothesis Testing with Misclassification Penalties

We study the problem of robust information selection for a Bayesian hypothesis testing / classification task, where the goal is to identify the true state of the world from a finite set of hypotheses based on observations from the selected information sources. We introduce a novel misclassification penalty framework, which enables non-uniform treatment of different misclassification events. Extending the classical subset selection framework, we study the problem of selecting a subset of sources that minimize the maximum penalty of misclassification under a limited budget, despite deletions or failures of a subset of the selected sources. We characterize the curvature properties of the objective function and propose an efficient greedy algorithm with performance guarantees. Next, we highlight certain limitations of optimizing for the maximum penalty metric and propose a submodular surrogate metric to guide the selection of the information set. We propose a greedy algorithm with near-optimality guarantees for optimizing the surrogate metric. Finally, we empirically demonstrate the performance of our proposed algorithms in several instances of the information set selection problem.

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arXiv2025

Learning Dynamical Systems by Leveraging Data from Similar Systems

We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide finite sample error bounds of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems, such as upper bounds on noise levels and model difference, is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.

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arXiv2024

On the Geometric Convergence of Byzantine-Resilient Distributed Optimization Algorithms

The problem of designing distributed optimization algorithms that are resilient to Byzantine adversaries has received significant attention. For the Byzantine-resilient distributed optimization problem, the goal is to (approximately) minimize the average of the local cost functions held by the regular (non adversarial) agents in the network. In this paper, we provide a general algorithmic framework for Byzantine-resilient distributed optimization which includes some state-of-the-art algorithms as special cases. We analyze the convergence of algorithms within the framework, and derive a geometric rate of convergence of all regular agents to a ball around the optimal solution (whose size we characterize). Furthermore, we show that approximate consensus can be achieved geometrically fast under some minimal conditions. Our analysis provides insights into the relationship among the convergence region, distance between regular agents' values, step-size, and properties of the agents' functions for Byzantine-resilient distributed optimization.

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arXiv2024

Classification with a Network of Partially Informative Agents: Enabling Wise Crowds from Individually Myopic Classifiers

We consider the problem of classification with a (peer-to-peer) network of heterogeneous and partially informative agents, each receiving local data generated by an underlying true class, and equipped with a classifier that can only distinguish between a subset of the entire set of classes. We propose an iterative algorithm that uses the posterior probabilities of the local classifier and recursively updates each agent's local belief on all the possible classes, based on its local signals and belief information from its neighbors. We then adopt a novel distributed min-rule to update each agent's global belief and enable learning of the true class for all agents. We show that under certain assumptions, the beliefs on the true class converge to one asymptotically almost surely. We provide the asymptotic convergence rate, and demonstrate the performance of our algorithm through simulation with image data and experimented with random forest classifiers and MobileNet.

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arXiv2024

The Minimizer of the Sum of Two Strongly Convex Functions

The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the functions is not available, limiting information to individual minimizers and convexity parameters -- either due to privacy concerns or the nature of solution analysis -- necessitates an exploration of the region encompassing potential minimizers based solely on these known quantities. The characterization of this region becomes notably intricate when dealing with multivariate strongly convex functions compared to the univariate case. This paper contributes outer and inner approximations for the region harboring the minimizer of the sum of two strongly convex functions, given a constraint on the norm of the gradient at the minimizer of the sum. Notably, we explicitly delineate the boundaries and interiors of both the outer and inner approximations. Intriguingly, the boundaries as well as the interiors turn out to be identical. Furthermore, we establish that the boundary of the region containing potential minimizers aligns with that of the outer and inner approximations.

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arXiv2024

Control of SIR Epidemics: Sacrificing Optimality for Feasibility

We study the impact of parameter estimation and state measurement errors on a control framework for optimally mitigating the spread of epidemics. We capture the epidemic spreading process using a susceptible-infected-removed (SIR) epidemic model and consider isolation as the control strategy. We use a control strategy to remove (isolate) a portion of the infected population. Our goal is to maintain the daily infected population below a certain level, while minimizing the resource captured by the isolation rate. Distinct from existing works on leveraging control strategies in epidemic spreading, we propose a parameter estimation strategy and further characterize the parameter estimation error bound. In order to deal with uncertainties, we propose a robust control strategy by overestimating the seriousness of the epidemic and study the feasibility of the system. Compared to the optimal control strategy, we establish that the proposed strategy under parameter estimation and measurement errors will sacrifice optimality to flatten the curve.

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arXiv2024

Optimal Sensor and Actuator Selection for Factored Markov Decision Processes: Complexity, Approximability and Algorithms

Factored Markov Decision Processes (fMDPs) are a class of Markov Decision Processes (MDPs) in which the states (and actions) can be factored into a set of state (and action) variables and can be encoded compactly using a factored representation. In this paper, we consider a setting where the state of the fMDP is not directly observable, and the agent relies on a set of potential sensors to gather information. We formulate the problem of selecting a set of sensors for fMDPs (under a limited budget) to maximize the infinite-horizon discounted return provided by the optimal policy. We show the fundamental result that it is NP-hard to approximate this problem to within a factor of $n^{1-c}$ for any $c > 1$, where $n$ is the number of state variables. Our inapproximability results for sensor selection also extend to a general class of Partially Observable MDPs (POMDPs). We also consider the dual problem of budgeted actuator selection (at design-time) to maximize the expected return under the optimal policy, for which we establish similar inapproximability results. Finally, we consider a simple greedy algorithm and empirically show that, despite the lack of formal theoretical guarantees, it performs effectively in practice, achieving on average over $70\%$ of the optimal solution value across a variety of real-world and randomly generated problem instances.

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arXiv2024

Submodular Information Selection for Hypothesis Testing with Misclassification Penalties

We consider the problem of selecting an optimal subset of information sources for a hypothesis testing/classification task where the goal is to identify the true state of the world from a finite set of hypotheses, based on finite observation samples from the sources. In order to characterize the learning performance, we propose a misclassification penalty framework, which enables nonuniform treatment of different misclassification errors. In a centralized Bayesian learning setting, we study two variants of the subset selection problem: (i) selecting a minimum cost information set to ensure that the maximum penalty of misclassifying the true hypothesis is below a desired bound and (ii) selecting an optimal information set under a limited budget to minimize the maximum penalty of misclassifying the true hypothesis. Under certain assumptions, we prove that the objective (or constraints) of these combinatorial optimization problems are weak (or approximate) submodular, and establish high-probability performance guarantees for greedy algorithms. Further, we propose an alternate metric for information set selection which is based on the total penalty of misclassification. We prove that this metric is submodular and establish near-optimal guarantees for the greedy algorithms for both the information set selection problems. Finally, we present numerical simulations to validate our theoretical results over several randomly generated instances.

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arXiv2024

C3D: Cascade Control with Change Point Detection and Deep Koopman Learning for Autonomous Surface Vehicles

In this paper, we discuss the development and deployment of a robust autonomous system capable of performing various tasks in the maritime domain under unknown dynamic conditions. We investigate a data-driven approach based on modular design for ease of transfer of autonomy across different maritime surface vessel platforms. The data-driven approach alleviates issues related to a priori identification of system models that may become deficient under evolving system behaviors or shifting, unanticipated, environmental influences. Our proposed learning-based platform comprises a deep Koopman system model and a change point detector that provides guidance on domain shifts prompting relearning under severe exogenous and endogenous perturbations. Motion control of the autonomous system is achieved via an optimal controller design. The Koopman linearized model naturally lends itself to a linear-quadratic regulator (LQR) control design. We propose the C3D control architecture Cascade Control with Change Point Detection and Deep Koopman Learning. The framework is verified in station keeping task on an ASV in both simulation and real experiments. The approach achieved at least 13.9 percent improvement in mean distance error in all test cases compared to the methods that do not consider system changes.

cs.RO↗

arXiv2024

Scalable Distributed Optimization of Multi-Dimensional Functions Despite Byzantine Adversaries

The problem of distributed optimization requires a group of networked agents to compute a parameter that minimizes the average of their local cost functions. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to "Byzantine" agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or assume certain statistical properties of the functions at the agents. In this paper, we provide two resilient, scalable, distributed optimization algorithms for multi-dimensional functions. Our schemes involve two filters, (1) a distance-based filter and (2) a min-max filter, which each remove neighborhood states that are extreme (defined precisely in our algorithms) at each iteration. We show that these algorithms can mitigate the impact of up to $F$ (unknown) Byzantine agents in the neighborhood of each regular agent. In particular, we show that if the network topology satisfies certain conditions, all of the regular agents' states are guaranteed to converge to a bounded region that contains the minimizer of the average of the regular agents' functions.

cs.MA↗

arXiv2024

Byzantine-Resilient Distributed Optimization of Multi-Dimensional Functions

The problem of distributed optimization requires a group of agents to reach agreement on a parameter that minimizes the average of their local cost functions using information received from their neighbors. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to malicious (or ``Byzantine'') agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or provide analysis under certain assumptions on the statistical properties of the functions at the agents. In this paper, we propose a resilient distributed optimization algorithm for multi-dimensional convex functions. Our scheme involves two filtering steps at each iteration of the algorithm: (1) distance-based and (2) component-wise removal of extreme states. We show that this algorithm can mitigate the impact of up to $F$ Byzantine agents in the neighborhood of each regular node, without knowing the identities of the Byzantine agents in advance. In particular, we show that if the network topology satisfies certain conditions, all of the regular states are guaranteed to asymptotically converge to a bounded region that contains the global minimizer.

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arXiv2023

Resilience for Distributed Consensus with Constraints

This paper proposes a new approach that enables multi-agent systems to achieve resilient \textit{constrained} consensus in the presence of Byzantine attacks, in contrast to existing literature that is only applicable to \textit{unconstrained} resilient consensus problems. The key enabler for our approach is a new device called a \textit{$(γ_i,α_i)$-resilient convex combination}, which allows normal agents in the network to utilize their locally available information to automatically isolate the impact of the Byzantine agents. Such a resilient convex combination is computable through linear programming, whose complexity scales well with the size of the overall system. By applying this new device to multi-agent systems, we introduce network and constraint redundancy conditions under which resilient constrained consensus can be achieved with an exponential convergence rate. We also provide insights on the design of a network such that the redundancy conditions are satisfied. Finally, numerical simulations and an example of safe multi-agent learning are provided to demonstrate the effectiveness of the proposed results.

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