arXiv subjects

Linda Bushnell

Publications and source records attributed to Linda Bushnell.

At least 19 recordsLinked to original sources

arXiv2026

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.

cs.LG↗

arXiv2026

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 $\Regret_T= \Theta(\sqrt{(1+\mathrm{RS}_T)\,T\,\log V_{\max}})$ interpolating between experts-like and dimension-dependent OCO rates. For online submodular--concave games under Lov\'{a}sz convexification, this reduces to the permutation-switch count $\mathrm{SC}_T$, yielding the matching rate $\Regret_T= \Theta(\sqrt{(1+\mathrm{SC}_T)\,T\,\log n})$. 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.

cs.LG↗

arXiv2024

A Method for Fast Autonomy Transfer in Reinforcement Learning

This paper introduces a novel reinforcement learning (RL) strategy designed to facilitate rapid autonomy transfer by utilizing pre-trained critic value functions from multiple environments. Unlike traditional methods that require extensive retraining or fine-tuning, our approach integrates existing knowledge, enabling an RL agent to adapt swiftly to new settings without requiring extensive computational resources. Our contributions include development of the Multi-Critic Actor-Critic (MCAC) algorithm, establishing its convergence, and empirical evidence demonstrating its efficacy. Our experimental results show that MCAC significantly outperforms the baseline actor-critic algorithm, achieving up to 22.76x faster autonomy transfer and higher reward accumulation. This advancement underscores the potential of leveraging accumulated knowledge for efficient adaptation in RL applications.

cs.LG↗

arXiv2021

A Reinforcement Learning Approach for Dynamic Information Flow Tracking Games for Detecting Advanced Persistent Threats

Advanced Persistent Threats (APTs) are stealthy attacks that threaten the security and privacy of sensitive information. Interactions of APTs with victim system introduce information flows that are recorded in the system logs. Dynamic Information Flow Tracking (DIFT) is a promising detection mechanism for detecting APTs. DIFT taints information flows originating at system entities that are susceptible to an attack, tracks the propagation of the tainted flows, and authenticates the tainted flows at certain system components according to a pre-defined security policy. Deployment of DIFT to defend against APTs in cyber systems is limited by the heavy resource and performance overhead associated with DIFT. In this paper, we propose a resource-efficient model for DIFT by incorporating the security costs, false-positives, and false-negatives associated with DIFT. Specifically, we develop a game-theoretic framework and provide an analytical model of DIFT that enables the study of trade-off between resource efficiency and the effectiveness of detection. Our game model is a nonzero-sum, infinite-horizon, average reward stochastic game. Our model incorporates the information asymmetry between players that arises from DIFT's inability to distinguish malicious flows from benign flows and APT's inability to know the locations where DIFT performs a security analysis. Additionally, the game has incomplete information as the transition probabilities (false-positive and false-negative rates) are unknown. We propose a multiple-time scale stochastic approximation algorithm to learn an equilibrium solution of the game. We prove that our algorithm converges to an average reward Nash equilibrium. We evaluate our proposed model and algorithm on a real-world ransomware dataset and validate the effectiveness of the proposed approach.

math.OC↗

arXiv2021

Stochastic Dynamic Information Flow Tracking Game using Supervised Learning for Detecting Advanced Persistent Threats

Advanced persistent threats (APTs) are organized prolonged cyberattacks by sophisticated attackers. Although APT activities are stealthy, they interact with the system components and these interactions lead to information flows. Dynamic Information Flow Tracking (DIFT) has been proposed as one of the effective ways to detect APTs using the information flows. However, wide range security analysis using DIFT results in a significant increase in performance overhead and high rates of false-positives and false-negatives generated by DIFT. In this paper, we model the strategic interaction between APT and DIFT as a non-cooperative stochastic game. The game unfolds on a state space constructed from an information flow graph (IFG) that is extracted from the system log. The objective of the APT in the game is to choose transitions in the IFG to find an optimal path in the IFG from an entry point of the attack to an attack target. On the other hand, the objective of DIFT is to dynamically select nodes in the IFG to perform security analysis for detecting APT. Our game model has imperfect information as the players do not have information about the actions of the opponent. We consider two scenarios of the game (i) when the false-positive and false-negative rates are known to both players and (ii) when the false-positive and false-negative rates are unknown to both players. Case (i) translates to a game model with complete information and we propose a value iteration-based algorithm and prove the convergence. Case (ii) translates to a game with unknown transition probabilities. In this case, we propose Hierarchical Supervised Learning (HSL) algorithm that integrates a neural network, to predict the value vector of the game, with a policy iteration algorithm to compute an approximate equilibrium. We implemented our algorithms on real attack datasets and validated the performance of our approach.

cs.GT↗

arXiv2021

Dynamic Information Flow Tracking for Detection of Advanced Persistent Threats: A Stochastic Game Approach

Advanced Persistent Threats (APTs) are stealthy customized attacks by intelligent adversaries. This paper deals with the detection of APTs that infiltrate cyber systems and compromise specifically targeted data and/or infrastructures. Dynamic information flow tracking is an information trace-based detection mechanism against APTs that taints suspicious information flows in the system and generates security analysis for unauthorized use of tainted data. In this paper, we develop an analytical model for resource-efficient detection of APTs using an information flow tracking game. The game is a nonzero-sum, turn-based, stochastic game with asymmetric information as the defender cannot distinguish whether an incoming flow is malicious or benign and hence has only partial state observation. We analyze equilibrium of the game and prove that a Nash equilibrium is given by a solution to the minimum capacity cut set problem on a flow-network derived from the system, where the edge capacities are obtained from the cost of performing security analysis. Finally, we implement our algorithm on the real-world dataset for a data exfiltration attack augmented with false-negative and false-positive rates and compute an optimal defender strategy.

cs.GT↗

arXiv2020

Secure Control in Partially Observable Environments to Satisfy LTL Specifications

This paper studies the synthesis of control policies for an agent that has to satisfy a temporal logic specification in a partially observable environment, in the presence of an adversary. The interaction of the agent (defender) with the adversary is modeled as a partially observable stochastic game. The goal is to generate a defender policy to maximize satisfaction of a given temporal logic specification under any adversary policy. The search for policies is limited to the space of finite state controllers, which leads to a tractable approach to determine policies. We relate the satisfaction of the specification to reaching (a subset of) recurrent states of a Markov chain. We present an algorithm to determine a set of defender and adversary finite state controllers of fixed sizes that will satisfy the temporal logic specification, and prove that it is sound. We then propose a value-iteration algorithm to maximize the probability of satisfying the temporal logic specification under finite state controllers of fixed sizes. Lastly, we extend this setting to the scenario where the size of the finite state controller of the defender can be increased to improve the satisfaction probability. We illustrate our approach with an example.

eess.SY↗

arXiv2020

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.

eess.SY↗

arXiv2020

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.

eess.SY↗

arXiv2020

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.

eess.SY↗

arXiv2020

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.

eess.SY↗

arXiv2020

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.

cs.AI↗

arXiv2019

Covert Channel-Based Transmitter Authentication in Controller Area Networks

In recent years, the security of automotive Cyber-Physical Systems (CPSs) is facing urgent threats due to the widespread use of legacy in-vehicle communication systems. As a representative legacy bus system, the Controller Area Network (CAN) hosts Electronic Control Units (ECUs) that are crucial vehicle functioning. In this scenario, malicious actors can exploit CAN vulnerabilities, such as the lack of built-in authentication and encryption schemes, to launch CAN bus attacks with life-threatening consequences (e.g., disabling brakes). In this paper, we present TACAN (Transmitter Authentication in CAN), which provides secure authentication of ECUs on the legacy CAN bus by exploiting the covert channels, without introducing CAN protocol modifications or traffic overheads. TACAN turns upside-down the originally malicious concept of covert channels and exploits it to build an effective defensive technique that facilitates transmitter authentication via a centralized, trusted Monitor Node. TACAN consists of three different covert channels for ECU authentication: 1) the Inter-Arrival Time (IAT)-based; 2) the Least Significant Bit (LSB)-based; and 3) a hybrid covert channel, exploiting the combination of the first two. In order to validate TACAN, we implement the covert channels on the University of Washington (UW) EcoCAR (Chevrolet Camaro 2016) testbed. We further evaluate the bit error, throughput, and detection performance of TACAN through extensive experiments using the EcoCAR testbed and a publicly available dataset collected from Toyota Camry 2010. We demonstrate the feasibility of TACAN and the effectiveness of detecting CAN bus attacks, highlighting no traffic overheads and attesting the regular functionality of ECUs.

cs.CR↗

arXiv2019

Linear Temporal Logic Satisfaction in Adversarial Environments using Secure Control Barrier Certificates

This paper studies the satisfaction of a class of temporal properties for cyber-physical systems (CPSs) over a finite-time horizon in the presence of an adversary, in an environment described by discrete-time dynamics. The temporal logic specification is given in safe-LTL_F, a fragment of linear temporal logic over traces of finite length. The interaction of the CPS with the adversary is modeled as a two-player zero-sum discrete-time dynamic stochastic game with the CPS as defender. We formulate a dynamic programming based approach to determine a stationary defender policy that maximized the probability of satisfaction of a safe-LTL_F formula over a finite time-horizon under any stationary adversary policy. We introduce secure control barrier certificates (S-CBCs), a generalization of barrier certificates and control barrier certificates that accounts for the presence of an adversary, and use S-CBCs to provide a lower bound on the above satisfaction probability. When the dynamics of the evolution of the system state has a specific underlying structure, we present a way to determine an S-CBC as a polynomial in the state variables using sum-of-squares optimization. An illustrative example demonstrates our approach.

eess.SY↗

arXiv2019

Mitigating Vulnerabilities of Voltage-based Intrusion Detection Systems in Controller Area Networks

Data for controlling a vehicle is exchanged among Electronic Control Units (ECUs) via in-vehicle network protocols such as the Controller Area Network (CAN) protocol. Since these protocols are designed for an isolated network, the protocols do not encrypt data nor authenticate messages. Intrusion Detection Systems (IDSs) are developed to secure the CAN protocol by detecting abnormal deviations in physical properties. For instance, a voltage-based IDS (VIDS) exploits voltage characteristics of each ECU to detect an intrusion. An ECU with VIDS must be connected to the CAN bus using extra wires to measure voltages of the CAN bus lines. These extra wires, however, may introduce new attack surfaces to the CAN bus if the ECU with VIDS is compromised. We investigate new vulnerabilities of VIDS and demonstrate that an adversary may damage an ECU with VIDS, block message transmission, and force an ECU to retransmit messages. In order to defend the CAN bus against these attacks, we propose two hardware-based Intrusion Response Systems (IRSs) that disconnect the compromised ECU from the CAN bus once these attacks are detected. We develop four voltage-based attacks by exploiting vulnerabilities of VIDS and evaluate the effectiveness of the proposed IRSs using a CAN bus testbed.

cs.CR↗

arXiv2019

Potential-Based Advice for Stochastic Policy Learning

This paper augments the reward received by a reinforcement learning agent with potential functions in order to help the agent learn (possibly stochastic) optimal policies. We show that a potential-based reward shaping scheme is able to preserve optimality of stochastic policies, and demonstrate that the ability of an agent to learn an optimal policy is not affected when this scheme is augmented to soft Q-learning. We propose a method to impart potential based advice schemes to policy gradient algorithms. An algorithm that considers an advantage actor-critic architecture augmented with this scheme is proposed, and we give guarantees on its convergence. Finally, we evaluate our approach on a puddle-jump grid world with indistinguishable states, and the continuous state and action mountain car environment from classical control. Our results indicate that these schemes allow the agent to learn a stochastic optimal policy faster and obtain a higher average reward.

cs.LG↗

arXiv2019

Detecting ADS-B Spoofing Attacks using Deep Neural Networks

The Automatic Dependent Surveillance-Broadcast (ADS-B) system is a key component of the Next Generation Air Transportation System (NextGen) that manages the increasingly congested airspace. It provides accurate aircraft localization and efficient air traffic management and also improves the safety of billions of current and future passengers. While the benefits of ADS-B are well known, the lack of basic security measures like encryption and authentication introduces various exploitable security vulnerabilities. One practical threat is the ADS-B spoofing attack that targets the ADS-B ground station, in which the ground-based or aircraft-based attacker manipulates the International Civil Aviation Organization (ICAO) address (a unique identifier for each aircraft) in the ADS-B messages to fake the appearance of non-existent aircraft or masquerade as a trusted aircraft. As a result, this attack can confuse the pilots or the air traffic control personnel and cause dangerous maneuvers. In this paper, we introduce SODA - a two-stage Deep Neural Network (DNN)-based spoofing detector for ADS-B that consists of a message classifier and an aircraft classifier. It allows a ground station to examine each incoming message based on the PHY-layer features (e.g., IQ samples and phases) and flag suspicious messages. Our experimental results show that SODA detects ground-based spoofing attacks with a probability of 99.34%, while having a very small false alarm rate (i.e., 0.43%). It outperforms other machine learning techniques such as XGBoost, Logistic Regression, and Support Vector Machine. It further identifies individual aircraft with an average F-score of 96.68% and an accuracy of 96.66%, with a significant improvement over the state-of-the-art detector.

cs.CR↗

arXiv2019

Secure Control under Partial Observability with Temporal Logic Constraints

This paper studies the synthesis of control policies for an agent that has to satisfy a temporal logic specification in a partially observable environment, in the presence of an adversary. The interaction of the agent (defender) with the adversary is modeled as a partially observable stochastic game. The search for policies is limited to over the space of finite state controllers, which leads to a tractable approach to determine policies. The goal is to generate a defender policy to maximize satisfaction of a given temporal logic specification under any adversary policy. We relate the satisfaction of the specification in terms of reaching (a subset of) recurrent states of a Markov chain. We then present a procedure to determine a set of defender and adversary finite state controllers of given sizes that will satisfy the temporal logic specification. We illustrate our approach with an example.

eess.SY↗