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Researcher profile

Linda Bushnell

Linda Bushnell contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
eess.SYSystems and ControlMachine LearningArtificial IntelligenceCryptography and Securitymath.OCComputational ComplexityLogic in Computer Science

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Published work

7 published item(s)

preprint2026arXiv

Polyhedral Instability Governs Regret in Online Learning

Many online decision problems over combinatorial actions are addressed via convex relaxations, leading to online convex optimization with piecewise linear objectives and induced polyhedral structure. We show that regret in such problems is governed by \emph{polyhedral instability}: the number of changes of the active region. Under full information feedback and fixed partition assumptions, if $\mathrm{RS}_T$ denotes the number of region switches and $V_{\max}$ the maximum number of vertices per region, we prove $\Regret_T= Θ(\sqrt{(1+\mathrm{RS}_T)\,T\,\log V_{\max}})$ interpolating between experts-like and dimension-dependent OCO rates. For online submodular--concave games under Lovász convexification, this reduces to the permutation-switch count $\mathrm{SC}_T$, yielding the matching rate $\Regret_T= Θ(\sqrt{(1+\mathrm{SC}_T)\,T\,\log n})$. Experiments on synthetic and real combinatorial problems (shortest path, influence maximization) validate the predicted scaling and indicate that low-instability regimes can arise in practice without explicit enumeration of actions.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

The WidthWall: A Strict Expressivity Hierarchy for Hypergraph Neural Networks

Hypergraphs provide a natural framework to model higher-order interactions in scientific, social, and biological systems. Hypergraph neural networks (HGNNs) aim to learn from such data, yet it remains unclear which higher-order structures these models can represent. We show that hypergraph expressivity is governed by which small patterns an architecture can detect and count. We formalize this via homomorphism densities, which measure how often a structural motif appears in a hypergraph. Combining classical homomorphism-count completeness with invariant approximation, we show that homomorphism densities generate all continuous hypergraph invariants and organize them into a strict hierarchy indexed by hypertree width. This yields a Width Wall: a fundamental architectural limit beyond which no hidden dimension, training procedure or fixed-depth HGNN can represent invariants requiring wider patterns. Our framework provides a unified characterization of 15 HGNN architectures, precisely identifies information lost by clique expansion, and motivates density-aware models that extend expressivity beyond bounded-width message passing. We experimentally validate this finding on an APPLICATION NODE CLASSIFICATION SUITE of real-world hypergraphs, where the Width Wall predicts when graph-reduction baselines fail and when density features help.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Control Synthesis for Cyber-Physical Systems to Satisfy Metric Interval Temporal Logic Objectives under Timing and Actuator Attacks

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex tasks that are time-sensitive, in the presence of an adversary. The task is specified as a formula in metric interval temporal logic (MITL). The adversary is assumed to have the ability to tamper with the control input to the CPS and also manipulate timing information perceived by the CPS. In order to model the interaction between the CPS and the adversary, and also the effect of these two classes of attacks, we define an entity called a durational stochastic game (DSG). DSGs probabilistically capture transitions between states in the environment, and also the time taken for these transitions. With the policy of the defender represented as a finite state controller (FSC), we present a value-iteration based algorithm that computes an FSC that maximizes the probability of satisfying the MITL specification under the two classes of attacks. A numerical case-study on a signalized traffic network is presented to illustrate our results.

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preprint2020arXiv

FRESH: Interactive Reward Shaping in High-Dimensional State Spaces using Human Feedback

Reinforcement learning has been successful in training autonomous agents to accomplish goals in complex environments. Although this has been adapted to multiple settings, including robotics and computer games, human players often find it easier to obtain higher rewards in some environments than reinforcement learning algorithms. This is especially true of high-dimensional state spaces where the reward obtained by the agent is sparse or extremely delayed. In this paper, we seek to effectively integrate feedback signals supplied by a human operator with deep reinforcement learning algorithms in high-dimensional state spaces. We call this FRESH (Feedback-based REward SHaping). During training, a human operator is presented with trajectories from a replay buffer and then provides feedback on states and actions in the trajectory. In order to generalize feedback signals provided by the human operator to previously unseen states and actions at test-time, we use a feedback neural network. We use an ensemble of neural networks with a shared network architecture to represent model uncertainty and the confidence of the neural network in its output. The output of the feedback neural network is converted to a shaping reward that is augmented to the reward provided by the environment. We evaluate our approach on the Bowling and Skiing Atari games in the arcade learning environment. Although human experts have been able to achieve high scores in these environments, state-of-the-art deep learning algorithms perform poorly. We observe that FRESH is able to achieve much higher scores than state-of-the-art deep learning algorithms in both environments. FRESH also achieves a 21.4% higher score than a human expert in Bowling and does as well as a human expert in Skiing.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Privacy-Preserving Resilience of Cyber-Physical Systems to Adversaries

A cyber-physical system (CPS) is expected to be resilient to more than one type of adversary. In this paper, we consider a CPS that has to satisfy a linear temporal logic (LTL) objective in the presence of two kinds of adversaries. The first adversary has the ability to tamper with inputs to the CPS to influence satisfaction of the LTL objective. The interaction of the CPS with this adversary is modeled as a stochastic game. We synthesize a controller for the CPS to maximize the probability of satisfying the LTL objective under any policy of this adversary. The second adversary is an eavesdropper who can observe labeled trajectories of the CPS generated from the previous step. It could then use this information to launch other kinds of attacks. A labeled trajectory is a sequence of labels, where a label is associated to a state and is linked to the satisfaction of the LTL objective at that state. We use differential privacy to quantify the indistinguishability between states that are related to each other when the eavesdropper sees a labeled trajectory. Two trajectories of equal length will be differentially private if they are differentially private at each state along the respective trajectories. We use a skewed Kantorovich metric to compute distances between probability distributions over states resulting from actions chosen according to policies from related states in order to quantify differential privacy. Moreover, we do this in a manner that does not affect the satisfaction probability of the LTL objective. We validate our approach on a simulation of a UAV that has to satisfy an LTL objective in an adversarial environment.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Safety-Critical Online Control with Adversarial Disturbances

This paper studies the control of safety-critical dynamical systems in the presence of adversarial disturbances. We seek to synthesize state-feedback controllers to minimize a cost incurred due to the disturbance, while respecting a safety constraint. The safety constraint is given by a bound on an H-inf norm, while the cost is specified as an upper bound on the H-2 norm of the system. We consider an online setting where costs at each time are revealed only after the controller at that time is chosen. We propose an iterative approach to the synthesis of the controller by solving a modified discrete-time Riccati equation. Solutions of this equation enforce the safety constraint. We compare the cost of this controller with that of the optimal controller when one has complete knowledge of disturbances and costs in hindsight. We show that the regret function, which is defined as the difference between these costs, varies logarithmically with the time horizon. We validate our approach on a process control setup that is subject to two kinds of adversarial attacks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Submodular Input Selection for Synchronization in Kuramoto Networks

Synchronization is an essential property of engineered and natural networked dynamical systems. The Kuramoto model of nonlinear synchronization has been widely studied in applications including entrainment of clock cells in brain networks and power system stability. Synchronization of Kuramoto networks has been found to be challenging in the presence of signed couplings between oscillators and when the network includes oscillators with heterogeneous natural frequencies. In this paper, we study the problem of minimum-set control input selection for synchronizing signed Kuramoto networks. We first derive sufficient conditions for synchronization in homogeneous as well as heterogeneous Kuramoto networks using a passivity-based framework. We then develop a submodular algorithm for selecting a minimum set of control inputs for a given Kuramoto network. We evaluate our approach through a numerical study on multiple classes of graphs, including undirected, directed, and cycle graphs.

0 citations0 reviewsNo code linkedOpen access