M. Amin Rahimian

Yuxin Liu, M. Amin Rahimian

Information sharing among competing suppliers can improve decision-making under uncertainty, yet strategic concerns regarding rival exploitation often deter voluntary disclosure. We study information-sharing mechanisms in a Cournot oligopoly with uncertain demand, where a platform aggregates suppliers' signals through privacy-preserving channels and may also possess an exogenous external signal. The central challenge is to balance strategic safety with informational utility: privacy noise reduces the exposure of individual signals, but also lowers the value of the shared information pool. We first characterize a baseline setting in which access to aggregated information is contingent on participation. In a two-firm market without an external signal, firms refuse to share regardless of the privacy level. In an \(n\)-firm market, sharing may arise even without privacy safeguards because non-participating firms lose access to the aggregated signal. Building on this baseline, we show that privacy protection alone is insufficient to incentivize disclosure; it must be combined with a sufficiently informative external signal. We further show that firms with more accurate private signals require stronger privacy protection. Overall, our results characterize the sharing-feasible region and highlight the complementarity between privacy design and the external information environment.

Peilin He, Liou Tang, M. Amin Rahimian et al.

Differential Privacy (DP) is being increasingly adopted for non-Euclidean data that lie on complex, high-dimensional manifolds. Existing DP mechanisms for manifold data consider geometric properties when calibrating privacy perturbations, but they largely fail to capture variations in data density within datasets, leading to biased perturbations and suboptimal privacy-utility trade-offs due to heterogeneous data distributions. In this paper, we propose a novel density-aware differential privacy mechanism on Riemannian manifolds, referred to as Conformal-DP, that leverages conformal transformations to calibrate perturbations based on local densities and to induce a density-balanced geometry. We prove that our mechanism satisfies $ε$-differential privacy on any complete Riemannian manifold under mild regularity assumptions. In addition, we derive a closed-form expected geodesic error bound that depends only on the underlying data density ratio and is independent of global curvature. Our empirical results on synthetic and real-world datasets demonstrate that the proposed Conformal-DP mechanism substantially improves the privacy-utility trade-off in heterogeneous data distribution settings, with worst-case performance comparable to state-of-the-art manifold DP mechanisms that assume uniformly distributed data.

Marios Papachristou, M. Amin Rahimian, Arash Azadegan

Modern production systems are increasingly defined by dense networks of multi-tier sourcing dependencies, where localized upstream disruptions can cascade into system-wide collapses. While supply chain resilience has garnered significant managerial attention, we still lack theoretically-grounded, reliable, analytical metrics that can distinguish inherently resilient architectures from fragile ones. This paper addresses this gap by developing a structural resilience framework and a novel metric, defined as the maximum supplier failure rate that a network can sustain while maintaining an aggregate production level. Using node percolation theory and branching processes, we identify four critical structural determinants of resilience: the number of raw materials, the number of finished goods, sourcing requirements, and sourcing influence. Our analysis reveals two distinct regimes: "top hat" architectures, which are characterized by excessive raw materials and high centralization, making them inherently fragile; and "rolling pin" structures, which maintain controlled input/output widths and sparsity, allowing them to absorb non-trivial shocks. To operationalize these insights, we formulate resilience computation as a scalable linear program that approximates cascading failure sizes in large-scale networks with cycles, heterogeneous suppliers, and structural decoupling. Furthermore, we extend our framework to account for exogenous failure correlations, such as those arising from geographic or geopolitical factors that can undermine traditional supplier and input diversification strategies. We validate our theoretical results using multi-echelon supply chain data. These tools can inform network design, supplier diversification, and inventory planning to proactively reduce systemic risk.

Abdulrahman A. Ahmed, M. Amin Rahimian, Qiushi Chen et al.

The opioid epidemic remains a major public health challenge in the United States, requiring a multi-pronged intervention approach to mitigate harms to communities. Given the heterogeneity of the epidemic across the country, it is crucial for policymakers to understand localized treatment effects of different intervention components and utilize limited resources efficiently. While locally calibrated simulation models offer a useful computational tool to project the epidemic outcomes for any given intervention policy, collecting simulation results for all intervention combinations to estimate localized treatment effects for each community is impractical because the number of possible intervention combinations grows exponentially with the number of interventions and levels at which they are applied. To tackle this, we develop a bi-level metamodel framework with a two-stage sequential design for efficient sampling. The metamodel consists of a response function linking health outcomes to each intervention component's treatment effect, and a Gaussian process regression to learn spatial and socio-economic structures of the treatment effects based on locally-contextualized covariates. With two-stage sequential sampling, we leverage spatial correlations and posterior uncertainty to sequentially sample the most informative counties and treatment conditions. We apply this framework to estimate treatment effects of buprenorphine dispensing and naloxone distribution on overdose mortality rates using a calibrated agent-based opioid epidemic model in PA counties. Our approach achieves approximately 5% average relative error using one-tenth the number of runs required for an exhaustive simulation. Our bi-level framework provides a computationally efficient approach to support policymakers, in evaluating resource-allocation strategies to mitigate the opioid epidemic in local communities.

Marios Papachristou, M. Amin Rahimian

We study distributed estimation and learning problems in a networked environment where agents exchange information to estimate unknown statistical properties of random variables from their privately observed samples. The agents can collectively estimate the unknown quantities by exchanging information about their private observations, but they also face privacy risks. Our novel algorithms extend the existing distributed estimation literature and enable the participating agents to estimate a complete sufficient statistic from private signals acquired offline or online over time and to preserve the privacy of their signals and network neighborhoods. This is achieved through linear aggregation schemes with adjusted randomization schemes that add noise to the exchanged estimates subject to differential privacy (DP) constraints, both in an offline and online manner. We provide convergence rate analysis and tight finite-time convergence bounds. We show that the noise that minimizes the convergence time to the best estimates is the Laplace noise, with parameters corresponding to each agent's sensitivity to their signal and network characteristics. Our algorithms are amenable to dynamic topologies and balancing privacy and accuracy trade-offs. Finally, to supplement and validate our theoretical results, we run experiments on real-world data from the US Power Grid Network and electric consumption data from German Households to estimate the average power consumption of power stations and households under all privacy regimes and show that our method outperforms existing first-order, privacy-aware, distributed optimization methods.

Tom A. Rutter, Yuxin Liu, M. Amin Rahimian

Researchers increasingly use data on social and economic networks to study a range of social science questions, but releasing statistics derived from networks can raise significant privacy concerns. We show how to release network connectedness indices that quantify assortative mixing across node attributes under edge-adjacent differential privacy. Standard privacy techniques perform poorly in this setting both because connectedness indices have high global sensitivity and because a single node's attribute can potentially be an input to connectedness in thousands of cells, leading to poor composition. Our method, which is straightforward to apply, first adds noise to node attributes, then analytically debiases downstream statistics, and finally applies a second layer of noise to protect the presence or absence of individual edges. We prove consistency and asymptotic normality of our estimators for both discrete and continuous labels and show our method works well in simulations and on real networks with as few as 200 nodes collected by social scientists.

Marios Papachristou, M. Amin Rahimian

How can agents exchange information to learn while protecting privacy? Healthcare centers collaborating on clinical trials must balance knowledge sharing with safeguarding sensitive patient data. We address this challenge by using differential privacy (DP) to control information leakage. Agents update belief statistics via log-linear rules, and DP noise provides plausible deniability and rigorous performance guarantees. We study two settings: distributed maximum likelihood estimation (MLE) with a finite set of private signals and online learning from an intermittent signal stream. Noisy aggregation introduces trade-offs between rejecting low-quality states and accepting high-quality ones. The MLE setting naturally applies to hypothesis testing with formal statistical guarantees. Through simulations, we demonstrate differentially private, distributed survival analysis on real-world clinical trial data, evaluating treatment efficacy and the impact of biomedical indices on patient survival. Our methods enable privacy-preserving inference with greater efficiency and lower error rates than homomorphic encryption and first-order DP optimization approaches.

Jan Hązła, Ali Jadbabaie, Elchanan Mossel et al.

We study the computations that Bayesian agents undertake when exchanging opinions over a network. The agents act repeatedly on their private information and take myopic actions that maximize their expected utility according to a fully rational posterior belief. We show that such computations are NP-hard for two natural utility functions: one with binary actions, and another where agents reveal their posterior beliefs. In fact, we show that distinguishing between posteriors that are concentrated on different states of the world is NP-hard. Therefore, even approximating the Bayesian posterior beliefs is hard. We also describe a natural search algorithm to compute agents' actions, which we call elimination of impossible signals, and show that if the network is transitive, the algorithm can be modified to run in polynomial time.

M. Amin Rahimian, Amir G. Aghdam

In this paper, structural controllability of a leader-follower multi-agent system with multiple leaders is studied from a graph-theoretic point of view. The problem of preservation of structural controllability under simultaneous failures in both the communication links and the agents is investigated. The effects of the loss of agents and communication links on the controllability of an information flow graph are previously studied. In this work, the corresponding results are exploited to introduce some useful indices and importance measures that help characterize and quantify the role of individual links and agents in the controllability of the overall network. Existing results are then extended by considering the effects of losses in both links and agents at the same time. To this end, the concepts of joint (r,s)-controllability and joint t-controllability are introduced as quantitative measures of reliability for a multi-agent system, and their important properties are investigated. Lastly, the class of jointly critical digraphs is introduced and it is stated that if a digraph is jointly critical, then joint t-controllability is a necessary and sufficient condition for remaining controllable following the failure of any set of links and agents, with cardinality less than t. Various examples are exploited throughout the paper to elaborate on the analytical findings.

M. Amin Rahimian, Amir Ajorlou, Amir G. Aghdam

In this work, the ability to distinguish digraphs from the output response of some observing agents in a multi-agent network under the agreement protocol has been studied. Given a fixed observation point, it is desired to find sufficient graphical conditions under which the failure of a set of edges in the network information flow digraph is distinguishable from another set. When the latter is empty, this corresponds to the detectability of the former link set given the response of the observing agent. In developing the results, a powerful extension of the all-minors matrix tree theorem in algebraic graph theory is proved which relates the minors of the transformed Laplacian of a directed graph to the number and length of the shortest paths between its vertices. The results reveal an intricate relationship between the ability to distinguish the responses of a healthy and a faulty multi-agent network and the inter-nodal paths in their information flow digraphs. The results have direct implications for the operation and design of multi-agent systems subject to multiple link losses. Simulations and examples are presented to illustrate the analytic findings.

M. Amin Rahimian, Ali Jadbabaie

This work investigates the case of a network of agents that attempt to learn some unknown state of the world amongst the finitely many possibilities. At each time step, agents all receive random, independently distributed private signals whose distributions are dependent on the unknown state of the world. However, it may be the case that some or any of the agents cannot distinguish between two or more of the possible states based only on their private observations, as when several states result in the same distribution of the private signals. In our model, the agents form some initial belief (probability distribution) about the unknown state and then refine their beliefs in accordance with their private observations, as well as the beliefs of their neighbors. An agent learns the unknown state when her belief converges to a point mass that is concentrated at the true state. A rational agent would use the Bayes' rule to incorporate her neighbors' beliefs and own private signals over time. While such repeated applications of the Bayes' rule in networks can become computationally intractable, in this paper, we show that in the canonical cases of directed star, circle or path networks and their combinations, one can derive a class of memoryless update rules that replicate that of a single Bayesian agent but replace the self beliefs with the beliefs of the neighbors. This way, one can realize an exponentially fast rate of learning similar to the case of Bayesian (fully rational) agents. The proposed rules are a special case of the Learning without Recall.

M. Amin Rahimian, Ali Jadbabaie

We consider several estimation and learning problems that networked agents face when making decisions given their uncertainty about an unknown variable. Our methods are designed to efficiently deal with heterogeneity in both size and quality of the observed data, as well as heterogeneity over time (intermittence). The goal of the studied aggregation schemes is to efficiently combine the observed data that is spread over time and across several network nodes, accounting for all the network heterogeneities. Moreover, we require no form of coordination beyond the local neighborhood of every network agent or sensor node. The three problems that we consider are (i) maximum likelihood estimation of the unknown given initial data sets, (ii) learning the true model parameter from streams of data that the agents receive intermittently over time, and (iii) minimum variance estimation of a complete sufficient statistic from several data points that the networked agents collect over time. In each case we rely on an aggregation scheme to combine the observations of all agents; moreover, when the agents receive streams of data over time, we modify the update rules to accommodate the most recent observations. In every case, we demonstrate the efficiency of our algorithms by proving convergence to the globally efficient estimators given the observations of all agents. We supplement these results by investigating the rate of convergence and providing finite-time performance guarantees.