arXiv subjects

Iman Shames

Publications and source records attributed to Iman Shames.

At least 37 records · Page 2Linked to original sources

arXiv2025

Joint State and Noise Covariance Estimation

This paper tackles the problem of jointly estimating the noise covariance matrix alongside states (parameters such as poses and points) from measurements corrupted by Gaussian noise and, if available, prior information. In such settings, the noise covariance matrix determines the weights assigned to individual measurements in the least squares problem. We show that the joint problem exhibits a convex structure and provide a full characterization of the optimal noise covariance estimate (with analytical solutions) within joint maximum a posteriori and likelihood frameworks and several variants. Leveraging this theoretical result, we propose two novel algorithms that jointly estimate the primary parameters and the noise covariance matrix. Our BCD algorithm can be easily integrated into existing nonlinear least squares solvers, with negligible per-iteration computational overhead. To validate our approach, we conduct extensive experiments across diverse scenarios and offer practical insights into their application in robotics and computer vision estimation problems with a particular focus on SLAM.

cs.RO↗

arXiv2025

Two-Player Dynamic Potential LQ Games with Sequentially Revealed Costs

We investigate a novel finite-horizon linear-quadratic (LQ) feedback dynamic potential game with a priori unknown cost matrices played between two players. The cost matrices are revealed to the players sequentially, with the potential for future values to be previewed over a short time window. We propose an algorithm that enables the players to predict and track a feedback Nash equilibrium trajectory, and we measure the quality of their resulting decisions by introducing the concept of \emph{price of uncertainty}. We show that under the proposed algorithm, the price of uncertainty is bounded by horizon-invariant constants. The constants are the sum of three terms; the first and second terms decay exponentially as the preview window grows, and another depends on the magnitude of the differences between the cost matrices for each player. Through simulations, we illustrate that the resulting price of uncertainty initially decays at an exponential rate as the preview window lengthens, then remains constant for large time horizons.

math.OC↗

arXiv2025

An Asynchronous Decentralised Optimisation Algorithm for Nonconvex Problems

In this paper, we consider nonconvex decentralised optimisation and learning over a network of distributed agents. We develop an ADMM algorithm based on the Randomised Block Coordinate Douglas-Rachford splitting method which enables agents in the network to distributedly and asynchronously compute a set of first-order stationary solutions of the problem. To the best of our knowledge, this is the first decentralised and asynchronous algorithm for solving nonconvex optimisation problems with convergence proof. The numerical examples demonstrate the efficiency of the proposed algorithm for distributed Phase Retrieval and sparse Principal Component Analysis problems.

math.OC↗

arXiv2025

ZORMS-LfD: Learning from Demonstrations with Zeroth-Order Random Matrix Search

We propose Zeroth-Order Random Matrix Search for Learning from Demonstrations (ZORMS-LfD). ZORMS-LfD enables the costs, constraints, and dynamics of constrained optimal control problems, in both continuous and discrete time, to be learned from expert demonstrations without requiring smoothness of the learning-loss landscape. In contrast, existing state-of-the-art first-order methods require the existence and computation of gradients of the costs, constraints, dynamics, and learning loss with respect to states, controls and/or parameters. Most existing methods are also tailored to discrete time, with constrained problems in continuous time receiving only cursory attention. We demonstrate that ZORMS-LfD matches or surpasses the performance of state-of-the-art methods in terms of both learning loss and compute time across a variety of benchmark problems. On unconstrained continuous-time benchmark problems, ZORMS-LfD achieves similar loss performance to state-of-the-art first-order methods with an over $80$\% reduction in compute time. On constrained continuous-time benchmark problems where there is no specialized state-of-the-art method, ZORMS-LfD is shown to outperform the commonly used gradient-free Nelder-Mead optimization method.

cs.LG↗

arXiv2025

Adversarial Attacks and Detection in Visual Place Recognition for Safer Robot Navigation

Stand-alone Visual Place Recognition (VPR) systems have little defence against a well-designed adversarial attack, which can lead to disastrous consequences when deployed for robot navigation. This paper extensively analyzes the effect of four adversarial attacks common in other perception tasks and four novel VPR-specific attacks on VPR localization performance. We then propose how to close the loop between VPR, an Adversarial Attack Detector (AAD), and active navigation decisions by demonstrating the performance benefit of simulated AADs in a novel experiment paradigm -- which we detail for the robotics community to use as a system framework. In the proposed experiment paradigm, we see the addition of AADs across a range of detection accuracies can improve performance over baseline; demonstrating a significant improvement -- such as a ~50% reduction in the mean along-track localization error -- can be achieved with True Positive and False Positive detection rates of only 75% and up to 25% respectively. We examine a variety of metrics including: Along-Track Error, Percentage of Time Attacked, Percentage of Time in an `Unsafe' State, and Longest Continuous Time Under Attack. Expanding further on these results, we provide the first investigation into the efficacy of the Fast Gradient Sign Method (FGSM) adversarial attack for VPR. The analysis in this work highlights the need for AADs in real-world systems for trustworthy navigation, and informs quantitative requirements for system design.

cs.CV↗

arXiv2025

Properties of Fixed Points of Generalised Extra Gradient Methods Applied to Min-Max Problems

This paper studies properties of fixed points of generalised Extra-gradient (GEG) algorithms applied to min-max problems. We discuss connections between saddle points of the objective function of the min-max problem and GEG fixed points. We show that, under appropriate step-size selections, the set of saddle points (Nash equilibria) is a subset of stable fixed points of GEG. Convergence properties of the GEG algorithm are obtained through a stability analysis of a discrete-time dynamical system. The results and benefits when compared to existing methods are illustrated through numerical examples.

math.OC↗

arXiv2025

Modular Decomposition of Hierarchical Finite State Machines

Hierarchical Finite State Machines (HFSMs) are a standard software-modelling concept which extends the classical Finite State Machine (FSM) notion with the useful abstraction of hierarchical nesting. That is, an HFSM is an FSM whose states can be other FSMs. The hierarchy in HFSMs is provided at design time, and can be removed by expanding nested states, allowing HFSMs to inherit the semantics of FSMs. However, because hierarchy is a useful representation of the structure of an FSM, we would like to be able to invert this operation: given an FSM, can we compute equivalent HFSMs? This is the topic of this paper. By adapting the analogous theory of `modular decomposition' from graph theory into automata theory, we are able to compute an efficient representation of the space of equivalent HFSMs to a given one. Specifically, we first define a module of an FSM, which is a collection of nodes which can be treated as a nested FSM. Unlike modules in graphs, some modules in FSMs are lacking in algebraic structure. We identify a simple and natural restriction of the modules, called thin modules, which regain many of the critical properties from modules in graphs. We then construct a linear-space directed graph which uniquely represents every thin module, and hence every equivalent (thin) HFSM. We call this graph the modular decomposition. The modular decomposition makes clear the significant common structure underlying equivalent thin HFSMs. We provide an $O(n^2k)$ algorithm for constructing the modular decomposition of an $n$-state $k$-symbol FSM. We demonstrate the applicability of this theory on the following `bottleneck' problem: given an HFSM, find an equivalent one where the size of the largest component FSM is minimised. The modular decomposition gives a simple greedy algorithm for the bottleneck problem on thin HFSMs, which we demonstrate on a wristwatch HFSM example from Harel (1987).

cs.FL↗

arXiv2025

Electric Grid Topology and Admittance Estimation: Quantifying Phasor-based Measurement Requirements

In this paper, we quantify voltage and current phasor-based measurement requirements for the unique estimation of the electric grid topology and admittance parameters. Our approach is underpinned by the concept of a rigidity matrix that has been extensively studied in graph rigidity theory. Specifically, we show that the rank of the rigidity matrix is the same as that of a voltage coefficient matrix in a corresponding electric power system. Accordingly, we show that there is a minimum number of measurements required to uniquely estimate the admittance matrix and corresponding grid topology. By means of a numerical example on the IEEE 4-node radial network, we demonstrate that our approach is suitable for applications in electric power grids.

eess.SY↗

arXiv2025

Preference graphs: a combinatorial tool for game theory

The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation indicates the preferred choice for that player. We show that the preference graph is a surprisingly fundamental tool for studying normal-form games, which arises from natural axioms and which underlies many key game-theoretic concepts, including dominated strategies and strict Nash equilibria, as well as classes of games like potential games, supermodular games and weakly acyclic games. The preference graph is especially related to game dynamics, playing a significant role in the behaviour of fictitious play and the replicator dynamic. Overall, we aim to equip game theorists with the tools and understanding to apply the preference graph to new problems in game theory.

cs.GT↗

arXiv2024

Prying Pedestrian Surveillance-Evasion: Minimum-Time Evasion from an Agile Pursuer

A new surveillance-evasion differential game is posed and solved in which an agile pursuer (the prying pedestrian) seeks to remain within a given surveillance range of a less agile evader that aims to escape. In contrast to previous surveillance-evasion games, the pursuer is agile in the sense of being able to instantaneously change the direction of its velocity vector, whilst the evader is constrained to have a finite maximum turn rate. Both the game of kind concerned with conditions under which the evader can escape, and the game of degree concerned with the evader seeking to minimize the escape time whilst the pursuer seeks to maximize it, are considered. The game-of-degree solution is surprisingly complex compared to solutions to analogous pursuit-evasion games with an agile pursuer since it exhibits dependence on the ratio of the pursuer's speed to the evader's speed. It is, however, surprisingly simple compared to solutions to classic surveillance-evasion games with a turn-limited pursuer.

eess.SY↗

arXiv2024

A Behavior Tree-inspired programming language for autonomous agents

We propose a design for a functional programming language for autonomous agents, built off the ideas and motivations of Behavior Trees (BTs). BTs are a popular model for designing agents behavior in robotics and AI. However, as their growth has increased dramatically, the simple model of BTs has come to be limiting. There is a growing push to increase the functionality of BTs, with the end goal of BTs evolving into a programming language in their own right, centred around the defining BT properties of modularity and reactiveness. In this paper, we examine how the BT model must be extended in order to grow into such a language. We identify some fundamental problems which must be solved: implementing `reactive' selection, 'monitoring' safety-critical conditions, and passing data between actions. We provide a variety of small examples which demonstrate that these problems are complex, and that current BT approaches do not handle them in a manner consistent with modularity. We instead provide a simple set of modular programming primitives for handling these use cases, and show how they can be combined to build complex programs. We present a full specification for our BT-inspired language, and give an implementation in the functional programming language Haskell. Finally, we demonstrate our language by translating a large and complex BT into a simple, unambiguous program.

cs.PL↗

arXiv2024

Improving Visual Place Recognition Based Robot Navigation By Verifying Localization Estimates

Visual Place Recognition (VPR) systems often have imperfect performance, affecting the `integrity' of position estimates and subsequent robot navigation decisions. Previously, SVM classifiers have been used to monitor VPR integrity. This research introduces a novel Multi-Layer Perceptron (MLP) integrity monitor which demonstrates improved performance and generalizability, removing per-environment training and reducing manual tuning requirements. We test our proposed system in extensive real-world experiments, presenting two real-time integrity-based VPR verification methods: a single-query rejection method for robot navigation to a goal zone (Experiment 1); and a history-of-queries method that takes a best, verified, match from its recent trajectory and uses an odometer to extrapolate a current position estimate (Experiment 2). Noteworthy results for Experiment 1 include a decrease in aggregate mean along-track goal error from ~9.8m to ~3.1m, and an increase in the aggregate rate of successful mission completion from ~41% to ~55%. Experiment 2 showed a decrease in aggregate mean along-track localization error from ~2.0m to ~0.5m, and an increase in the aggregate localization precision from ~97% to ~99%. Overall, our results demonstrate the practical usefulness of a VPR integrity monitor in real-world robotics to improve VPR localization and consequent navigation performance.

cs.CV↗

arXiv2024

An online optimization algorithm for tracking a linearly varying optimal point with zero steady-state error

In this paper, we develop an online optimization algorithm for solving a class of nonconvex optimization problems with a linearly varying optimal point. The global convergence of the algorithm is guaranteed using the circle criterion for the class of functions whose gradient is bounded within a sector. Also, we show that the corresponding Luré-type nonlinear system involves a double integrator, which demonstrates its ability to track a linearly varying optimal point with zero steady-state error. The algorithm is applied to solving a time-of-arrival based localization problem with constant velocity and the results show that the algorithm is able to estimate the source location with zero steady-state error.

math.OC↗

arXiv2024

Online Non-Stationary Stochastic Quasar-Convex Optimization

Recent research has shown that quasar-convexity can be found in applications such as identification of linear dynamical systems and generalized linear models. Such observations have in turn spurred exciting developments in design and analysis algorithms that exploit quasar-convexity. In this work, we study the online stochastic quasar-convex optimization problems in a dynamic environment. We establish regret bounds of online gradient descent in terms of cumulative path variation and cumulative gradient variance for losses satisfying quasar-convexity and strong quasar-convexity. We then apply the results to generalized linear models (GLM) when the underlying parameter is time-varying. We establish regret bounds of online gradient descent when applying to GLMs with leaky ReLU activation function, logistic activation function, and ReLU activation function. Numerical results are presented to corroborate our findings.

math.OC↗

arXiv2024

Online Interior-point Methods for Time-varying Equality-constrained Optimization

An important challenge in the online convex optimization (OCO) setting is to incorporate generalized inequalities and time-varying constraints. The inclusion of constraints in OCO widens the applicability of such algorithms to dynamic and safety-critical settings such as the online optimal power flow (OPF) problem. In this work, we propose the first projection-free OCO algorithm admitting time-varying linear constraints and convex generalized inequalities: the online interior-point method for time-varying equality constraints (OIPM-TEC). We derive simultaneous sublinear dynamic regret and constraint violation bounds for OIPM-TEC under standard assumptions. For applications where a given tolerance around optima is accepted, we employ an alternative OCO performance metric -- the epsilon-regret -- and a more computationally efficient algorithm, the epsilon-OIPM-TEC, that possesses sublinear bounds under this metric. Finally, we showcase the performance of these two algorithms on an online OPF problem and compare them to another OCO algorithm from the literature.

math.OC↗

arXiv2024

Minimisation of Polyak-Łojasewicz Functions Using Random Zeroth-Order Oracles

The application of a zeroth-order scheme for minimising Polyak-Łojasewicz (PL) functions is considered. The framework is based on exploiting a random oracle to estimate the function gradient. The convergence of the algorithm to a global minimum in the unconstrained case and to a neighbourhood of the global minimum in the constrained case along with their corresponding complexity bounds are presented. The theoretical results are demonstrated via numerical examples.

math.OC↗

arXiv2024

Online Convex Optimization Using Coordinate Descent Algorithms

This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number of iterations of the algorithm. Instead of solving the problem exactly at each time step, we only apply a finite number of iterations at each time step. Commonly used notions of regret are used to measure the performance of the online algorithm. Moreover, coordinate descent algorithms with different updating rules are considered, including both deterministic and stochastic rules that are developed in the literature of classical offline optimization. A thorough regret analysis is given for each case. Finally, numerical simulations are provided to illustrate the theoretical results.

math.OC↗

arXiv2024

The Attractor of the Replicator Dynamic in Zero-Sum Games

In this paper we characterise the long-run behaviour of the replicator dynamic in zero-sum games (symmetric or non-symmetric). Specifically, we prove that every zero-sum game possesses a unique global replicator attractor, which we then characterise. Most surprisingly, this attractor depends only on each player's preference order over their own strategies and not on the cardinal payoff values, defined by a finite directed graph we call the game's preference graph. When the game is symmetric, this graph is a tournament whose nodes are strategies; when the game is not symmetric, this graph is the game's response graph. We discuss the consequences of our results on chain recurrence and Nash equilibria.

cs.GT↗