Reviewerly/exHarmony huggingface dataset:
Fraud Detection and Deterrence in Electronic Voting Machines: A Game-Theoretic Approach

We study a setting where a detector wishes to detect and deter adversarial manipulation in an electronic voting machine. An adversary tries to win the election by tampering the votes while obfuscating its manipulation. We pose this problem as a game between the detector and the adversary and characterize the equilibrium payoffs for the players and the asymptotic nature of these payoffs. We find that if the detector is too cautious, then in equilibrium the adversary wins with a probability higher than its prior probability of winning. We derive an expression for the deterrence threshold, i.e., the minimum level of false-alarm that the detector should endure so that the adversary is not any better off by the manipulation. With this, asymptotically, the detector can ensure that the probability of missed-detection becomes zero by appropriately adjusting the rate of decay of probability of false-alarm. But if this rate of decay is too ‘fast’, then the adversary can get an arbitrarily high probability of winning in spite of having a vanishing prior probability of winning. We then extend the results to a setting where the detector has incomplete information about the adversary.
Performance of Noisy Three-Step Accelerated First-Order Optimization Algorithms for Strongly Convex Quadratic Problems

We study the class of first-order algorithms in which the optimization variable is updated using information from three previous iterations. While two-step momentum algorithms akin to heavy-ball and Nesterov's accelerated methods achieve the optimal convergence rate, it is an open question if the three-step momentum method can offer advantages for problems in which exact gradients are not available. For strongly convex quadratic problems, we identify algorithmic parameters which achieve the optimal convergence rate and examine how additional momentum terms affects the trade-offs between acceleration and noise amplification. Our results suggest that for parameters that optimize the convergence rate, introducing additional momentum terms does not provide improvement in variance amplification relative to standard accelerated algorithms.
Exact and Cost-Effective Automated Transformation of Neural Network Controllers to Decision Tree Controllers

Over the past decade, neural network (NN)-based controllers have demonstrated remarkable efficacy in a variety of decision-making tasks. However, their black-box nature and the risk of unexpected behaviors and surprising results pose a challenge to their deployment in real-world systems with strong guarantees of correctness and safety. We address these limitations by investigating the transformation of NN-based controllers into equivalent soft decision tree (SDT)-based controllers and its impact on verifiability. Differently from previous approaches, we focus on discrete-output NN controllers including rectified linear unit (ReLU) activation functions as well as argmax operations. We then devise an exact but cost-effective transformation algorithm, in that it can automatically prune redundant branches. We evaluate our approach using two benchmarks from the OpenAI Gym environment. Our results indicate that the SDT transformation can benefit formal verification, showing runtime improvements of up to 21x and 2x for MountainCar-v0 and CartPole-v1, respectively.
Hybrid Zonotopes Exactly Represent ReLU Neural Networks

We show that hybrid zonotopes offer an equivalent representation of feed-forward fully connected neural networks with ReLU activation functions. Our approach demonstrates that the complexity of binary variables is equal to the total number of neurons in the network and hence grows linearly in the size of the network, regardless of the architecture. We demonstrate the utility of the hybrid zonotope formulation through three case studies including nonlinear function approximation, MPC closed-loop reachability and verification, and robustness of classification on the MNIST dataset.
Safe Neural Control for Non-Affine Control Systems with Differentiable Control Barrier Functions

This paper addresses the problem of safety-critical control for non-affine control systems. It has been shown that optimizing quadratic costs subject to state and control constraints can be sub-optimally reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs). Our recently proposed High Order CBFs (HOCBFs) can accommodate constraints of arbitrary relative degree. The main challenges in this approach are that it requires affine control dynamics and the solution of the CBF-based QP is sub-optimal since it is solved point-wise. To address these challenges, we incorporate higher-order CBFs into neural ordinary differential equation-based learning models as differentiable CBFs to guarantee safety for non-affine control systems. The differentiable CBFs are trainable in terms of their parameters, and thus, they can address the conservativeness of CBFs such that the system state will not stay unnecessarily far away from safe set boundaries. Moreover, the imitation learning model is capable of learning complex and optimal control policies that are usually intractable online. We illustrate the effectiveness of the proposed framework on LiDAR-based autonomous driving and compare it with existing methods.
Robust Decentralised Proof-of-Position Algorithms for Smart City Applications

Motivated by the ever growing use of location-based services, we present a decentralised class of algorithms called Tree-Proof-of-Position (T-PoP). Most of the current proofs of location are centralised, thus forgoing verifiablity and privacy for the users. Decentralised solutions also exist, but they suffer from drawbacks that make them unsuitable for realistic, adversarial use cases. T-PoP algorithms rely on the web of interconnected devices in a smart city to establish how likely it is that an agent is in their claimed position. T-PoP operates under adversarial assumptions, where some agents are incentivised to be dishonest. We present a theoretical model for T-PoP and its security properties, and we validate this model through a large number of Monte-Carlo simulations. We specifically focus on two instances of T-PoP and analyse their security and reliability properties under a range of adversarial conditions. Use-cases and applications are discussed towards the end of the paper.
Soft-Bellman Equilibrium in Affine Markov Games: Forward Solutions and Inverse Learning

Markov games model interactions among multiple players in a stochastic, dynamic environment. Each player in a Markov game maximizes its expected total discounted reward, which depends upon the policies of the other players. We formulate a class of Markov games, termed affine Markov games, where an affine reward function couples the players' actions. We introduce a novel solution concept, the soft-Bellman equilibrium, where each player is boundedly rational and chooses a soft-Bellman policy rather than a purely rational policy as in the well-known Nash equilibrium concept. We provide conditions for the existence and uniqueness of the soft-Bellman equilibrium and propose a nonlinear least-squares algorithm to compute such an equilibrium in the forward problem. We then solve the inverse game problem of inferring the players' reward parameters from observed state-action trajectories via a projected-gradient algorithm. Experiments in a predator-prey OpenAI Gym environment show that the reward parameters inferred by the proposed algorithm outper- form those inferred by a baseline algorithm: they reduce the Kullback-Leibler divergence between the equilibrium policies and observed policies by at least two orders of magnitude.
Abstraction-Based Safety Analysis of Linear Dynamical Systems with Neural Network Controllers

We consider the safety verification problem of a closed-loop discrete-time linear dynamical system with a neural network controller. The crux of safety verification relies on computing output reachable sets of the dynamical system and the neural network. Reachable set computation time of the neural network grows with the network size. To address the scalability issue, our main approach consists of abstracting the neural network controller into a smaller annotated interval neural network (AINN), and using this to compute an over- approximation of the reachable set of the closed-loop system. We present a novel approach for output reachable set computation of an AINN by decomposing it into two reachable set computation problems on neural networks, which we then compute using star-sets. Our experimental analysis on two benchmarks demonstrate the trade-off in the precision and time for reachable set computation.
On Iterative Parameter Identification of FIR Systems with Batched Possibly Incorrect Binary-Valued Observations

This paper considers the problem of parameter identification for a binary output finite impulse response (FIR) system with measurement error, where the measurement error makes the binary measurement values take opposite values with a certain probability. First, the maximum likelihood estimation (MLE) of the parameters is given and an iterative algorithm with projection based on the Expectation-Maximization algorithm is presented to calculate the MLE. Furthermore, the necessary and sufficient condition for the likelihood function to have a unique maximum point is obtained. It is proved that the iterative estimation error converges to zero at an exponential rate under persistently excitation input conditions. Finally, some numerical simulation results based on a typical system show the effectiveness of the proposed algorithm.
Dynamic System Identification from Scarce and Noisy Data Using Symbolic Regression

A framework for dynamic system model identification from scarce and noisy data is proposed. This framework uses symbolic regression via genetic programming with a gradient-based parameter estimation step to identify a differential equation model and its parameters from available system data. The effectiveness of the method is demonstrated by identifying four synthetic systems: an ideal plug flow reactor (PFR) with an irreversible chemical reaction, an ideal continuously stirred tank reactor (CSTR) with an irreversible chemical reaction, a system described by Burgers' Equation, and an ideal PFR with a reversible chemical reaction. The results show that this framework can identify PDE models of systems from broadly spaced and noisy data. When the data was not sufficiently rich, the framework discovered a surrogate model that described the observations in equal or fewer terms than the true system model. Additionally, the method can select relevant physics terms to describe a system from a list of candidate arguments, providing valuable models for use in controls applications.
Optimizing Field-of-View for Multi-Agent Path Finding via Reinforcement Learning: A Performance and Communication Overhead Study

This work investigates the impact of Field-of-View (FOV) on the performance of Reinforcement Learning (RL) models in Multi-Agent Path Finding (MAPF) problems. The study measures the effects of different FOV settings on RL performance, communication overhead, and computation time. Results show that the tested smallest FOV <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(3\times 3)$</tex> reduces communication frequency by 28.9% with only a 1.65% reduction in success rate compared to the baseline <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(9\times 9)$</tex> . The study also compares computation time for different FOV for efficiency analysis and provides insights into FOV selection considering computation cost.
Differentially-Private Distributed Optimization with Guaranteed Optimality

Privacy protection is gaining increased attention in distributed optimization and learning. As differential privacy is becoming a de facto standard for privacy preservation, recently results have emerged integrating differential privacy with distributed optimization. However, to ensure differential privacy (with a finite cumulative privacy budget), all existing approaches have to sacrifice provable convergence to the optimal solution. In this paper, we propose a differentially-private distributed optimization algorithm that can ensure, for the first time, both <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\epsilon$</tex> -differential privacy and optimality, even on the infinite time horizon. Numerical simulation results confirm the effectiveness of the proposed approach.
Gradient Tracking with Multiple Local SGD for Decentralized Non-Convex Learning

The stochastic Gradient Tracking (GT) method for distributed optimization, is known to be robust against the inter-client variance caused by data heterogeneity. However, the stochastic GT method can be communication-intensive, requiring a large number of communication rounds of message exchange for convergence. To address this challenge, this paper proposes a new communication-efficient stochastic GT algorithm called the Local Stochastic GT(LSGT) algorithm, which adopts the local stochastic gradient descent (local SGD) technique in the GT method. With LSGT, each agent can perform multiple SGD updates locally within each communication round. Although it is not known previously whether the stochastic GT method can benefit from the local SGD, we establish the conditions under which our proposed LSGT algorithm enjoys the linear speedup brought by local SGD. Compared with the existing work, our analysis requires less restrictive conditions on the mixing matrix and algorithm stepsize. Moreover, it reveals that the local SGD does not only reserve the resilience of the stochastic GT method against the data heterogeneity but also speeds up reducing the tracking error reduction in the optimization process. The experimental results demonstrate that the proposed LSGT exhibits improved convergence speed and robust performance in various heterogeneous environments.
Boosting Exploration in Actor-Critic Algorithms by Incentivizing Plausible Novel States

Improvement of exploration and exploitation using more efficient samples is a critical issue in reinforcement learning algorithms. A basic strategy of a learning algorithm is to facilitate indiscriminate exploration of the entire environment state space, as well as to encourage exploration of rarely visited states rather than frequently visited ones. Under this strategy, we propose a new method to boost exploration through an intrinsic reward, based on the measurement of a state's novelty and the associated benefit of exploring the state, collectively called plausible novelty. By incentivizing exploration of plausible novel states, an actor-critic (AC) algorithm can improve its sample efficiency and, consequently, its training performance. The new method is verified through extensive simulations of continuous control tasks in MuJoCo environments, using a variety of prominent off-policy AC algorithms.
Differential Privacy for Stochastic Matrices Using the Matrix Dirichlet Mechanism

Stochastic matrices are commonly used to analyze Markov chains, but revealing them can leak sensitive information. Therefore, in this paper we introduce a technique to privatize stochastic matrices in a way that (i) conceals the probabilities they contain, and (ii) still allows for accurate analyses of Markov chains. Specifically, we use differential privacy, which is a statistical framework for protecting sensitive data. To implement it, we introduce the Matrix Dirichlet Mechanism, which is a probabilistic mapping that perturbs a stochastic matrix to provide privacy. We prove that this mechanism provides differential privacy, and we quantify the error induced in private stochastic matrices as a function of the strength of privacy being provided. We then bound the distance between the stationary distribution of the underlying, sensitive stochastic matrix and the stationary distribution of its privatized form. Numerical results show that, under typical conditions, privacy introduces error as low as 5.05% in the stationary distribution of a stochastic matrix.
Safe Non-Stochastic Control of Linear Dynamical Systems

We study the problem of safe control of linear dynamical systems corrupted with non-stochastic noise, and provide an algorithm that guarantees (i) zero constraint violation of convex time-varying constraints, and (ii) bounded dynamic regret, i.e., bounded suboptimality against an optimal clairvoyant controller that knows the future noise a priori. The constraints bound the values of the state and of the control input such as to ensure collision avoidance and bounded control effort. We are motivated by the future of autonomy where robots will safely perform complex tasks despite real- world unpredictable disturbances such as wind and wake disturbances. To develop the algorithm, we capture our problem as a sequential game between a linear feedback controller and an adversary, assuming a known upper bound on the noise's magnitude. Particularly, at each step <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$t=1, \ldots, T$</tex> , first the controller chooses a linear feedback control gain <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K_{t}\in \mathcal{K}_{t}$</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{K}_{t}$</tex> is constructed such that it guarantees that the safety constraints will be satisfied; then, the adversary reveals the current noise <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$w_{t}$</tex> and the controller suffers a loss <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{t}(K_{t})$</tex> - e.g., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{t}$</tex> represents the system's tracking error at upon the realization of the noise. The controller aims to minimize its cumulative loss, despite knowing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$w_{t}$</tex> only after <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K_{t}$</tex> has been chosen. We validate our algorithm in simulated scenarios of safe control of linear dynamical systems in the presence of bounded noise.
Online Variable-Length Source Coding for Minimum Bitrate LQG Control

We propose an adaptive coding approach to achieve linear-Quadratic-Gaussian (LQG) control with near-minimum bitrate prefix-free feedback. Our approach combines a recent analysis of a quantizer design for minimum rate LQG control with work on universal lossless source coding for sources on countable alphabets. It was recently demonstrated that the aforementioned quantizer's outputs are an asymptotically stationary, ergodic process. To enable LQG control with provably near-minimum bitrate, the quantizer outputs must be encoded into binary codewords efficiently. This is possible given knowledge of the quantizations' probability distributions, or of their limiting distribution. Obtaining such knowledge is challenging; the distributions do not readily admit closed form descriptions. This motivates the application of universal source coding. Our main theoretical contribution in this work is a proof that (after an invertible transformation), the quantizer outputs are random variables that fall within an exponential or power-law envelope class (depending on the plant dimension). Using ideas from universal coding on envelope classes, we develop a practical, zero-delay, fixed precision source code for the quantizer outputs. We evaluate the performance of this approach numerically, and demonstrate competitive results with respect to fundamental tradeoffs between bitrate and LQG control performance.
Robust Stability of Gaussian Process Based Moving Horizon Estimation

In this paper, we introduce a Gaussian process based moving horizon estimation (MHE) framework. The scheme is based on offline collected data and offline hyperparameter optimization. In particular, compared to standard MHE schemes, we replace the mathematical model of the system by the posterior mean of the Gaussian process. To account for the uncertainty of the learned model, we exploit the posterior variance of the learned Gaussian process in the weighting matrices of the cost function of the proposed MHE scheme. We prove practical robust exponential stability of the resulting estimator using a recently proposed Lyapunov-based proof technique. Finally, the performance of the Gaussian process based MHE scheme is illustrated via a nonlinear system.
Asynchronous Byzantine-Robust Stochastic Aggregation with Variance Reduction for Distributed Learning

We consider Byzantine-robust distributed learning with asynchronous participation of clients at a certain probability, where Byzantine clients can send malicious messages to the server. Instead of relying on traditional robust aggregation rules, such as Krum and Median, that can only tolerate a limited proportion of Byzantine clients, we propose an asynchronous Byzantine-robust stochastic aggregation method that employs regularization-based techniques to mitigate Byzantine attacks, and adopts variance-reduced techniques to eliminate the effect of stochastic noise of gradient sampling. Leveraging a properly designed Lyapunov function, we show that the proposed algorithm converges linearly to an error ball that is independent of stochastic gradient variance. Extensive experiments are conducted to show its efficacy in dealing with Byzantine attacks compared to the existing counterparts.
Out of Distribution Detection via Domain-Informed Gaussian Process State Space Models

In order for robots to safely navigate in unseen scenarios using learning-based methods, it is important to accurately detect out-of-training-distribution (OoD) situations online. Recently, Gaussian process state-space models (GPSSMs) have proven useful to discriminate unexpected observations by comparing them against probabilistic predictions. However, the capability for the model to correctly distinguish between in- and out-of-training distribution observations hinges on the accuracy of these predictions, primarily affected by the class of functions the GPSSM kernel can represent. In this paper, we propose (i) a novel approach to embed existing domain knowledge in the kernel and (ii) an OoD online runtime monitor, based on receding-horizon predictions. Domain knowledge is provided in the form of a dataset, collected either in simulation or by using a nominal model. Numerical results show that the informed kernel yields better regression quality with smaller datasets, as compared to standard kernel choices. We demonstrate the effectiveness of the OoD monitor on a real quadruped navigating an indoor setting, which reliably classifies previously unseen terrains.
Quantum Privacy and Hypothesis-Testing

A novel definition for quantum privacy based on hypothesis testing is presented. This privacy notion possesses an operational interpretation based on the false positive and negative rates of adversaries attempting to distinguish among private categories to which quantum states belong using arbitrary measurements. Important properties of post processing and composition are established. The relationship between privacy against hypothesis-testing adversaries and quantum differential privacy are then examined. This enables analysis of hypothesis testing under differential privacy and in noisy quantum systems. It also provides an operational interpretation for quantum differential privacy.