Solmaz S. Kia

Solmaz S. Kia, Bryan Van Scoy, Jorge Cortes et al.

This paper considers the problem of dynamic average consensus algorithm design for a group of communicating agents. This problem consists of designing a distributed algorithm that enables a group of agents with communication and computation capabilities to use local interactions to track the average of locally time-varying reference signals at each agent. The objective of this article is to provide an overview of the dynamic average consensus problem that serves as a comprehensive introduction to the problem definition, its applications, and the distributed methods available to solve them. Our primary intention, rather than providing a full account of all the available literature, is to introduce the reader, in a tutorial fashion, to the main ideas behind dynamic average consensus algorithms, the performance trade-offs considered in their design, and the requirements needed for their analysis and convergence guarantees.

Hossein Moradian, Solmaz S. Kia

This paper studies the robustness of a dynamic average consensus algorithm to communication delay over strongly connected and weight-balanced (SCWB) digraphs. Under delay-free communication, the algorithm of interest achieves a practical asymptotic tracking of the dynamic average of the time-varying agents' reference signals. For this algorithm, in both its continuous-time and discrete-time implementations, we characterize the admissible communication delay range and study the effect of the delay on the rate of convergence and the tracking error bound. Our study also includes establishing a relationship between the admissible delay bound and the maximum degree of the SCWB digraphs. We also show that for delays in the admissible bound, for static signals the algorithms achieve perfect tracking. Moreover, when the interaction topology is a connected undirected graph, we show that the discrete-time implementation is guaranteed to tolerate at least one step delay. Simulations demonstrate our results.

Navid Rezazadeh, Solmaz S. Kia

This paper considers the problem of privacy preservation against passive internal and external malicious agents in the continuous-time Laplacian average consensus algorithm over strongly connected and weight-balanced digraphs. For this problem, we evaluate the effectiveness of use of additive perturbation signals as a privacy preservation measure against malicious agents that know the graph topology. Our results include (a) identifying the necessary and sufficient conditions on admissible additive perturbation signals that do not perturb the convergence point of the algorithm from the average of initial values of the agents; (b) obtaining the necessary and sufficient condition on the knowledge set of a malicious agent that enables it to identify the initial value of another agent; (c) designing observers that internal and external malicious agents can use to identify the initial conditions of another agent when their knowledge set on that agent enables them to do so. We demonstrate our results through a numerical example.

Amir-Salar Esteki, Solmaz S. Kia

In this paper, we propose a novel solution for the distributed unconstrained optimization problem where the total cost is the summation of time-varying local cost functions of a group networked agents. The objective is to track the optimal trajectory that minimizes the total cost at each time instant. Our approach consists of a two-stage dynamics, where the first one samples the first and second derivatives of the local costs periodically to construct an estimate of the descent direction towards the optimal trajectory, and the second one uses this estimate and a consensus term to drive local states towards the time-varying solution while reaching consensus. The first part is carried out by the implementation of a weighted average consensus algorithm in the discrete-time framework and the second part is performed with a continuous-time dynamics. Using the Lyapunov stability analysis, an upper bound on the gradient of the total cost is obtained which is asymptotically reached. This bound is characterized by the properties of the local costs. To demonstrate the performance of the proposed method, a numerical example is conducted that studies tuning the algorithm's parameters and their effects on the convergence of local states to the optimal trajectory.

Mohammadreza Rostami, Shahriar Talebi, Solmaz S. Kia

We propose ScalarFedLQR, a communication-efficient federated algorithm for model-free learning of a common policy in linear quadratic regulator (LQR) control of heterogeneous agents. The method builds on a decomposed projected gradient mechanism, in which each agent communicates only a scalar projection of a local zeroth-order gradient estimate. The server aggregates these scalar messages to reconstruct a global descent direction, reducing per-agent uplink communication from O(d) to O(1), independent of the policy dimension. Crucially, the projection-induced approximation error diminishes as the number of participating agents increases, yielding a favorable scaling law: larger fleets enable more accurate gradient recovery, admit larger stepsizes, and achieve faster linear convergence despite high dimensionality. Under standard regularity conditions, all iterates remain stabilizing and the average LQR cost decreases linearly fast. Numerical results demonstrate performance comparable to full-gradient federated LQR with substantially reduced communication.

Mohammadreza Rostami, Solmaz S. Kia

Submodular maximization under matroid constraints is a fundamental problem in combinatorial optimization with applications in sensing, data summarization, active learning, and resource allocation. While the Sequential Greedy (SG) algorithm achieves only a $\frac{1}{2}$-approximation due to irrevocable selections, Continuous Greedy (CG) attains the optimal $\bigl(1-\frac{1}{e}\bigr)$-approximation via the multilinear relaxation, at the cost of a progressively dense decision vector that forces agents to exchange feature embeddings for nearly every ground-set element. We propose \textit{ATCG} (\underline{A}daptive \underline{T}hresholded \underline{C}ontinuous \underline{G}reedy), which gates gradient evaluations behind a per-partition progress ratio $η_i$, expanding each agent's active set only when current candidates fail to capture sufficient marginal gain, thereby directly bounding which feature embeddings are ever transmitted. Theoretical analysis establishes a curvature-aware approximation guarantee with effective factor $τ_{\mathrm{eff}}=\max\{τ,1-c\}$, interpolating between the threshold-based guarantee and the low-curvature regime where \textit{ATCG} recovers the performance of CG. Experiments on a class-balanced prototype selection problem over a subset of the CIFAR-10 animal dataset show that \textit{ATCG} achieves objective values comparable to those of the full CG method while substantially reducing communication overhead through adaptive active-set expansion.

Mohammadreza Rostami, Solmaz S. Kia

This paper introduces \texttt{FedMPDD} (\textbf{Fed}erated Learning via \textbf{M}ulti-\textbf{P}rojected \textbf{D}irectional \textbf{D}erivatives), a novel algorithm that simultaneously optimizes bandwidth utilization and enhances privacy in Federated Learning. The core idea of \texttt{FedMPDD} is to encode each client's high-dimensional gradient by computing its directional derivatives along multiple random vectors. This compresses the gradient into a much smaller message, significantly reducing uplink communication costs from $\mathcal{O}(d)$ to $\mathcal{O}(m)$, where $m \ll d$. The server then decodes the aggregated information by projecting it back onto the same random vectors. Our key insight is that averaging multiple projections overcomes the dimension-dependent convergence limitations of a single projection. We provide a rigorous theoretical analysis, establishing that \texttt{FedMPDD} converges at a rate of $\mathcal{O}(1/\sqrt{K})$, matching the performance of FedSGD. Furthermore, we demonstrate that our method provides some inherent privacy against gradient inversion attacks due to the geometric properties of low-rank projections, offering a tunable privacy-utility trade-off controlled by the number of projections. Extensive experiments on benchmark datasets validate our theory and demonstrates our results.

Navid Rezazadeh, Maxwell Kolarich, Solmaz S. Kia et al.

This paper proposes a data-driven method for learning convergent control policies from offline data using Contraction theory. Contraction theory enables constructing a policy that makes the closed-loop system trajectories inherently convergent towards a unique trajectory. At the technical level, identifying the contraction metric, which is the distance metric with respect to which a robot's trajectories exhibit contraction is often non-trivial. We propose to jointly learn the control policy and its corresponding contraction metric while enforcing contraction. To achieve this, we learn an implicit dynamics model of the robotic system from an offline data set consisting of the robot's state and input trajectories. Using this learned dynamics model, we propose a data augmentation algorithm for learning contraction policies. We randomly generate samples in the state-space and propagate them forward in time through the learned dynamics model to generate auxiliary sample trajectories. We then learn both the control policy and the contraction metric such that the distance between the trajectories from the offline data set and our generated auxiliary sample trajectories decreases over time. We evaluate the performance of our proposed framework on simulated robotic goal-reaching tasks and demonstrate that enforcing contraction results in faster convergence and greater robustness of the learned policy.

Jianan Zhu, Solmaz S. Kia

In cooperative localization, communicating mobile agents use inter-agent relative measurements to improve their dead-reckoning-based global localization. Measurement scheduling enables an agent to decide which subset of available inter-agent relative measurements it should process when its computational resources are limited. Optimal measurement scheduling is an NP-hard combinatorial optimization problem. The so-called sequential greedy (SG) algorithm is a popular suboptimal polynomial-time solution for this problem. However, the merit function evaluation for the SG algorithms requires access to the state estimate vector and error covariance matrix of all the landmark agents (teammates that an agent can take measurements from). This paper proposes a measurement scheduling for CL that follows the SG approach but reduces the communication and computation cost by using a neural network-based surrogate model as a proxy for the SG algorithm's merit function. The significance of this model is that it is driven by local information and only a scalar metadata from the landmark agents. This solution addresses the time and memory complexity issues of running the SG algorithm in three ways: (a) reducing the inter-agent communication message size, (b) decreasing the complexity of function evaluations by using a simpler surrogate (proxy) function, (c) reducing the required memory size.Simulations demonstrate our results.

Jianan Zhu, Solmaz S. Kia

This paper investigates an infra-structure free global localization of a group of communicating mobile agents (e.g., first responders or exploring robots) via an ultra-wideband (UWB) inter-agent ranging aided dead-reckoning. We propose a loosely coupled cooperative localization algorithm that acts as an augmentation atop the local dead-reckoning system of each mobile agent. This augmentation becomes active only when an agent wants to process a relative measurement it has taken. The main contribution of this paper is addressing the challenges in the proper processing of the UWB range measurements in the framework of a loosely coupled cooperative localization. Even though UWB offers a decimeter level accuracy in line-of-sight (LoS) ranging, its accuracy degrades significantly in non-line-of-sight (NLoS) due to the significant unknown positive bias in the measurements. Thus, the measurement models for the UWB LoS and NLoS ranging conditions are different, and proper processing of NLoS measurements requires a bias compensation measure. We also show that, in practice, the measurement modal discriminators determine the type of UWB range measurements should be probabilistic. To take into account the probabilistic nature of the NLoS identifiers when processing UWB inter-agent ranging feedback, we employ an interacting multiple model (IMM) estimator in our localization filter. We also propose a bias compensation method for NLoS UWB measurements. The effectiveness of our cooperative localization is demonstrated via an experiment for a group of pedestrians who use UWB relative range measurements among themselves to improve their shoe-mounted INS geolocation.

Navid Rezazadeh, Solmaz S. Kia

We study the problem of persistent monitoring of a finite number of inter-connected geographical nodes by a group of heterogeneous mobile agents. We assign to each geographical node a concave and increasing reward function that resets to zero after an agent's visit. Then, we design the optimal dispatch policy of which nodes to visit at what time and by what agent by finding a policy set that maximizes a utility that is defined as the total reward collected at visit times. We show that this optimization problem is NP-hard and its computational complexity increases exponentially with the number of the agents and the length of the mission horizon. By showing that the utility function is a monotone increasing and submodular set function of agents' policy, we proceed to propose a suboptimal dispatch policy design with a known optimality gap. To reduce the time complexity of constructing the feasible search set and also to induce robustness to changes in the operational factors, we perform our suboptimal policy design in a receding horizon fashion. Then, to compensate for the shortsightedness of the receding horizon approach for reward distribution beyond the feasible policies of the agents over the receding horizon, we add a new term to our utility, which provides a measure of nodal importance beyond the receding horizon's sight. This term gives the policy design an intuition to steer the agents towards the nodes with higher rewards on the patrolling graph. Finally, we discuss how our proposed algorithm can be implemented in a decentralized manner. A simulation study demonstrates our results.

Jianan Zhu, Solmaz S. Kia

We report two decentralized multi-agent cooperative localization algorithms in which, to reduce the communication cost, inter-agent state estimate correlations are not maintained but accounted for implicitly. In our first algorithm, to guarantee filter consistency, we account for unknown inter-agent correlations via an upper bound on the joint covariance matrix of the agents. In the second method, we use an optimization framework to estimate the unknown inter-agent cross-covariance matrix. In our algorithms, each agent localizes itself in a global coordinate frame using a local filter driven by local dead reckoning and occasional absolute measurement updates, and opportunistically corrects its pose estimate whenever it can obtain relative measurements with respect to other mobile agents. To process any relative measurement, only the agent taken the measurement and the agent the measurement is taken from need to communicate with each other. Consequently, our algorithms are decentralized algorithms that do not impose restrictive network-wide connectivity condition. Moreover, we make no assumptions about the type of agents or relative measurements. We demonstrate our algorithms in simulation and a robotic~experiment.

Reza Asadi, Solmaz S. Kia

When the underlying physical network layer in optimal network flow problems is a large graph, the associated optimization problem has a large set of decision variables. In this paper, we discuss how the cycle basis from graph theory can be used to reduce the size of this decision variable space. The idea is to eliminate the aggregated flow conservation constraint of these problems by explicitly characterizing its solutions in terms of the span of the columns of the transpose of a fundamental cycle basis matrix of the network plus a particular solution. We show that for any given input/output flow vector, a particular solution can be efficiently constructed from tracing any path that connects a source node to a sink node. We demonstrate our results over a minimum cost flow problem as well as an optimal power flow problem with storage and generation at the nodes. We also show that the new formulation of the minimum cost flow problem based on the cycle basis variables is amenable to a distributed solution. In this regard, we apply our method over a distributed alternating direction method of multipliers (ADMM) solution and demonstrate it over a numerical example.

Solmaz S. Kia, Jonathan Hechtbauer, David Gogokhiya et al.

This paper considers the problem of cooperative localization (CL) using inter-robot measurements for a group of networked robots with limited on-board resources. We propose a novel recursive algorithm in which each robot localizes itself in a global coordinate frame by local dead reckoning, and opportunistically corrects its pose estimate whenever it receives a relative measurement update message from a server. The computation and storage cost per robot in terms of the size of the team is of order O(1), and the robots are only required to transmit information when they are involved in a relative measurement. The server also only needs to compute and transmit update messages when it receives an inter-robot measurement. We show that under perfect communication, our algorithm is an alternative but exact implementation of a joint CL for the entire team via Extended Kalman Filter (EKF). The perfect communication however is not a hard requirement. In fact, we show that our algorithm is intrinsically robust with respect to communication failures, with formal guarantees that the updated estimates of the robots receiving the update message are of minimum variance in a first-order approximate sense at that given timestep. We demonstrate the performance of the algorithm in simulation and experiments.

Solmaz S. Kia, Stephen Rounds, Sonia Martinez

We consider cooperative localization technique for mobile agents with communication and computation capabilities. We start by provide and overview of different decentralization strategies in the literature, with special focus on how these algorithms maintain an account of intrinsic correlations between state estimate of team members. Then, we present a novel decentralized cooperative localization algorithm that is a decentralized implementation of a centralized Extended Kalman Filter for cooperative localization. In this algorithm, instead of propagating cross-covariance terms, each agent propagates new intermediate local variables that can be used in an update stage to create the required propagated cross-covariance terms. Whenever there is a relative measurement in the network, the algorithm declares the agent making this measurement as the interim master. By acquiring information from the interim landmark, the agent the relative measurement is taken from, the interim master can calculate and broadcast a set of intermediate variables which each robot can then use to update its estimates to match that of a centralized Extended Kalman Filter for cooperative localization. Once an update is done, no further communication is needed until the next relative measurement.