arXiv subjects

Aneesh Raghavan

Publications and source records attributed to Aneesh Raghavan.

10 recordsLinked to original sources

arXiv2026

Finite-Sample Conformal Coverage Recovery via Fusion under Degraded Local Guarantees in Occupancy Map Estimation

Accurate and reliable environmental mapping is a fundamental requirement for multi-robot autonomy. While continuous mapping techniques like Gaussian Process Occupancy Mapping (GPOM) provide rich spatial correlation and uncertainty estimates, they lack formal, finite-sample guarantees on their predictive reliability. Conformal prediction can equip each robot's local map with a distribution-free coverage guarantee, but this local guarantee degrades in practice: temporal correlation along a robot's trajectory breaks the exchangeability on which conformal calibration relies, and each robot observes only a spatially limited, non-uniform portion of the environment. Taking these degraded per-agent guarantees as given, we develop a distributed fusion algorithm that recovers the desired coverage across the team. Robots exchange only lightweight scalar e-values with their neighbors, and a receiver fuses them using a per-neighborhood miscoverage budget and an uncertainty-attenuated fusion operator. We prove that the fused set-valued map recovers the target user-specified coverage level regardless of the communication graph topology or the underlying sensor noise distribution. However, a drawback is that wherever the fused evidence is insufficient, the map declines to commit and returns both labels (free and occupied), leaving a significant fraction of the domain unclassified rather than thresholded into a single decision. Simulated multi-agent mapping experiments demonstrate that the fused predictor reliably meets its theoretical coverage bounds, and illustrate that denser communication topologies significantly enhance map efficiency by shrinking this unclassified fraction.

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arXiv2026

Approximate Simulation-Based Verification of Compatibility of the Friedkin-Johnsen Model with Binary Observations

We consider a verification problem for opinion dynamics based on binary observations. The opinion dynamics is governed by a Friedkin-Johnsen (FJ) model, where only a sequence of binary outputs is available instead of the agents' continuous opinions. At every time-step we observe a binarized output for each agent depending on whether the opinion exceeds a fixed threshold. The objective is to verify whether an FJ model with a given set of stubbornness parameters and initial opinions can generate the observed binary outputs up to a small error. The FJ model is formulated as a transition system, and an approximate simulation relation of two transition systems is defined in terms of the proximity of their opinion trajectories and output sequences. We then construct a finite set of abstract FJ models by simplifying the influence matrix and discretizing the stubbornness parameters and the initial opinions. It is shown that the abstraction approximately simulates any concrete FJ model with continuous parameters and initial opinions, and is itself approximately simulated by some concrete FJ model. These results ensure that consistency verification can be performed over the finite abstraction. Specifically, by checking whether an abstract model satisfies the observation constraints, we can conclude whether the corresponding family of concrete FJ models is consistent with the binary observations. Finally, numerical experiments are presented to illustrate the proposed verification framework.

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arXiv2025

Sequential Binary Hypothesis Testing with Competing Agents under Information Asymmetry

This paper concerns sequential hypothesis testing in competitive multi-agent systems where agents exchange potentially manipulated information. Specifically, a two-agent scenario is studied where each agent aims to correctly infer the true state of nature while optimizing decision speed and accuracy. At each iteration, agents collect private observations, update their beliefs, and share (possibly corrupted) belief signals with their counterparts before deciding whether to stop and declare a state, or continue gathering more information. The analysis yields three main results: (1)~when agents share information strategically, the optimal signaling policy involves equal-probability randomization between truthful and inverted beliefs; (2)~agents maximize performance by relying solely on their own observations for belief updating while using received information only to anticipate their counterpart's stopping decision; and (3)~the agent reaching their confidence threshold first cause the other agent to achieve a higher conditional probability of error. Numerical simulations further demonstrate that agents with higher KL divergence in their conditional distributions gain competitive advantage. Furthermore, our results establish that information sharing -- despite strategic manipulation -- reduces overall system stopping time compared to non-interactive scenarios, which highlights the inherent value of communication even in this competitive setup.

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arXiv2024

An Active Parameter Learning Approach to The Identification of Safe Regions

We consider the problem of identification of safe regions in the environment of an autonomous system. The environment is divided into a finite collections of Voronoi cells, with each cell having a representative, the Voronoi center. The extent to which each region is considered to be safe by an oracle is captured through a trust distribution. The trust placed by the oracle conditioned on the region is modeled through a Bernoulli distribution whose the parameter depends on the region. The parameters are unknown to the system. However, if the agent were to visit a given region, it will receive a binary valued random response from the oracle on whether the oracle trusts the region or not. The objective is to design a path for the agent where, by traversing through the centers of the cells, the agent is eventually able to label each cell safe or unsafe. To this end, we formulate an active parameter learning problem with the objective of minimizing visits or stays in potentially unsafe regions. The active learning problem is formulated as a finite horizon stochastic control problem where the cost function is derived utilizing the large deviations principle (LDP). The challenges associated with a dynamic programming approach to solve the problem are analyzed. Subsequently, the optimization problem is relaxed to obtain single-step optimization problems for which closed form solution is obtained. Using the solution, we propose an algorithm for the active learning of the parameters. A relationship between the trust distributions and the label of a cell is defined and subsequently a classification algorithm is proposed to identify the safe regions. We prove that the algorithm identifies the safe regions with finite number of visits to unsafe regions. We demonstrate the algorithm through an example.

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arXiv2024

Collaborative Estimation of Real Valued Function by Two Agents and a Fusion Center with Knowledge Exchange

We consider a collaborative iterative algorithm with two agents and a fusion center for estimation of a real valued function (or ``model") on the set of real numbers. While the data collected by the agents is private, in every iteration of the algorithm, the models estimated by the agents are uploaded to the fusion center, fused, and, subsequently downloaded by the agents. We consider the estimation spaces at the agents and the fusion center to be Reproducing Kernel Hilbert Spaces (RKHS). Under suitable assumptions on these spaces, we prove that the algorithm is consistent, i.e., there exists a subsequence of the estimated models which converges to a model in the strong topology. To this end, we define estimation operators for the agents, fusion center, and, for every iteration of the algorithm constructively. We define valid input data sequences, study the asymptotic properties of the norm of the estimation operators, and, find sufficient conditions under which the estimation operator until any iteration is uniformly bounded. Using these results, we prove the existence of an estimation operator for the algorithm which implies the consistency of the considered estimation algorithm.

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arXiv2024

Motion Planning for Identification of Linear Classifiers

A given region in 2-D Euclidean space is divided by a unknown linear classifier in to two sets each carrying a label. The objective of an agent with known dynamics traversing the region is to identify the true classifier while paying a control cost across its trajectory. We consider two scenarios: (i) the agent is able to measure the true label perfectly; (ii) the observed label is the true label multiplied by noise. We present the following: (i) the classifier identification problem formulated as a control problem; (ii) geometric interpretation of the control problem resulting in one step modified control problems; (iii) control algorithms that result in data sets which are used to identify the true classifier with accuracy; (iv) convergence of estimated classifier to the true classifier when the observed label is not corrupted by noise; (iv) numerical example demonstrating the utility of the control algorithms.

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arXiv2024

Distributed Estimation by Two Agents with Different Feature Spaces

We consider the problem of estimation of a function by a system consisting of two agents and a fusion center. The two agents collect data comprising of samples of an independent variable and the corresponding value of a dependent variable. The objective of the system is to collaboratively estimate the function without any exchange of data among the members of the system. To this end, we propose the following framework. The agents are given a set of features using which they construct suitable function spaces to formulate and solve the estimation problems locally. The estimated functions are uploaded to a fusion space where an optimization problem is solved to fuse the estimates (also known as meta-learning) to obtain the system estimate of the mapping. The fused function is then downloaded by the agents to gather knowledge about the other agents estimate of the function. With respect to the framework, we present the following: a systematic construction of fusion space given the features of the agents; the derivation of an uploading operator for the agents to upload their estimated functions to a fusion space; the derivation of a downloading operator for the fused function to be downloaded. Through an example on least squares regression, we illustrate the distributed estimation architecture that has been developed.

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arXiv2024

Distributed Learning and Function Fusion in Reproducing Kernel Hilbert Space

We consider the problem of function estimation by a multi-agent system comprising of two agents and a fusion center. Each agent receives data comprising of samples of an independent variable (input) and the corresponding values of the dependent variable (output). The data remains local and is not shared with other members in the system. The objective of the system is to collaboratively estimate the function from the input to the output. To this end, we develop an iterative distributed algorithm for this function estimation problem. Each agent solves a local estimation problem in a Reproducing Kernel Hilbert Space (RKHS) and uploads the function to the fusion center. At the fusion center, the functions are fused by first estimating the data points that would have generated the uploaded functions and then subsequently solving a least squares estimation problem using the estimated data from both functions. The fused function is downloaded by the agents and is subsequently used for estimation at the next iteration along with incoming data. This procedure is executed sequentially and stopped when the difference between consecutively estimated functions becomes small enough. To analyze the algorithm, we define learning operators for the agents, fusion center and the system. We study the asymptotic properties of the norm of the learning operators and find sufficient conditions under which they converge to $1$. Given a sequence of data points, we define and prove the existence of the learning operator for the system. We prove that the porposed learning algorithm is consistent and demonstrate the same using an example. The paper has been submitted to L4DC 2024.

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arXiv2020

Order Effects of Measurements in Multi-Agent Hypothesis Testing

In multi-agent systems, agents observe data, and use them to make inferences and take actions. As a result sensing and control naturally interfere, more so from a real-time perspective. A natural consequence is that in multi-agent systems there are propositions based on the set of observed events that might not be simultaneously verifiable, which leads to the need for probability structures that allow such \textit{incompatible events}. We revisit the structure of events in a multi-agent system and we introduce the necessary new models that incorporate such incompatible events in the formalism. These models are essential for building non-commutative probability models, which are different than the classical models based on the Kolmogorov construction. From this perspective, we revisit the concepts of \textit{event-state-operation structure} and the needed \textit{relationship of incompatibility} from the literature and use them as a tool to study the needed new algebraic structure of the set of events. We present an example from multi-agent hypothesis testing where the set of events does not form a Boolean algebra, but forms an ortholattice. A possible construction of a `noncommutative probability space', accounting for \textit{incompatible events} is discussed. We formulate and solve the binary hypothesis testing problem in the noncommutative probability space. We illustrate the occurrence of `order effects' in the multi-agent hypothesis testing problem by computing the minimum probability of error that can be achieved with different orders of measurements.

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arXiv2020

Cooperative Hypothesis Testing by Two Observers with Asymmetric Information

We consider the binary hypothesis testing problem with two observers. There are two possible states of nature (or hypotheses). Observations collected by the two observers are statistically related to the true state of nature. The knowledge of joint distribution of the observations collected and the true state of nature is unknown to the observers. There are two problems to be solved by the observers: (i) true state of nature is known: find the distribution of the local information collected; (ii) true state of nature is unknown: collaboratively estimate the same using the distributions found by solving the first problem. We present four algorithms, each having two phases where the two problems are solved, with emphasis on the information exchange between the observers and resulting patterns. We prove different properties of the algorithms including the following: the probability spaces constructed as a consequence of solving the first problem are dependent on the information patterns at the observers; (ii) the rate of decay of probability of error of algorithms while solving the second problem is dependent on the information exchange between the observers. We present a numerical example demonstrating the four algorithms.

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