arXiv subjects

George J. Pappas

Publications and source records attributed to George J. Pappas.

At least 73 records · Page 4Linked to original sources

arXiv2024

Recursively Feasible Shrinking-Horizon MPC in Dynamic Environments with Conformal Prediction Guarantees

In this paper, we focus on the problem of shrinking-horizon Model Predictive Control (MPC) in uncertain dynamic environments. We consider controlling a deterministic autonomous system that interacts with uncontrollable stochastic agents during its mission. Employing tools from conformal prediction, existing works derive high-confidence prediction regions for the unknown agent trajectories, and integrate these regions in the design of suitable safety constraints for MPC. Despite guaranteeing probabilistic safety of the closed-loop trajectories, these constraints do not ensure feasibility of the respective MPC schemes for the entire duration of the mission. We propose a shrinking-horizon MPC that guarantees recursive feasibility via a gradual relaxation of the safety constraints as new prediction regions become available online. This relaxation enforces the safety constraints to hold over the least restrictive prediction region from the set of all available prediction regions. In a comparative case study with the state of the art, we empirically show that our approach results in tighter prediction regions and verify recursive feasibility of our MPC scheme.

eess.SY↗

arXiv2024

Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Method

We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve the optimal rate for a wide range of problems, there have been no non-asymptotic results matching these optimal rates outside of a select few, typically linear, model classes. By leveraging modern tools from learning with dependent data, we provide the first rate-optimal non-asymptotic analysis of this method for our more general setting of nonlinearly parametrized model classes. Moreover, we show that our results can be applied to a particular class of identifiable AutoRegressive Moving Average (ARMA) models, resulting in the first optimal non-asymptotic rates for identification of ARMA models.

math.ST↗

arXiv2024

Stochastic Approximation with Delayed Updates: Finite-Time Rates under Markovian Sampling

Motivated by applications in large-scale and multi-agent reinforcement learning, we study the non-asymptotic performance of stochastic approximation (SA) schemes with delayed updates under Markovian sampling. While the effect of delays has been extensively studied for optimization, the manner in which they interact with the underlying Markov process to shape the finite-time performance of SA remains poorly understood. In this context, our first main contribution is to show that under time-varying bounded delays, the delayed SA update rule guarantees exponentially fast convergence of the \emph{last iterate} to a ball around the SA operator's fixed point. Notably, our bound is \emph{tight} in its dependence on both the maximum delay $τ_{max}$, and the mixing time $τ_{mix}$. To achieve this tight bound, we develop a novel inductive proof technique that, unlike various existing delayed-optimization analyses, relies on establishing uniform boundedness of the iterates. As such, our proof may be of independent interest. Next, to mitigate the impact of the maximum delay on the convergence rate, we provide the first finite-time analysis of a delay-adaptive SA scheme under Markovian sampling. In particular, we show that the exponent of convergence of this scheme gets scaled down by $τ_{avg}$, as opposed to $τ_{max}$ for the vanilla delayed SA rule; here, $τ_{avg}$ denotes the average delay across all iterations. Moreover, the adaptive scheme requires no prior knowledge of the delay sequence for step-size tuning. Our theoretical findings shed light on the finite-time effects of delays for a broad class of algorithms, including TD learning, Q-learning, and stochastic gradient descent under Markovian sampling.

cs.LG↗

arXiv2024

Adversarial Training Should Be Cast as a Non-Zero-Sum Game

One prominent approach toward resolving the adversarial vulnerability of deep neural networks is the two-player zero-sum paradigm of adversarial training, in which predictors are trained against adversarially chosen perturbations of data. Despite the promise of this approach, algorithms based on this paradigm have not engendered sufficient levels of robustness and suffer from pathological behavior like robust overfitting. To understand this shortcoming, we first show that the commonly used surrogate-based relaxation used in adversarial training algorithms voids all guarantees on the robustness of trained classifiers. The identification of this pitfall informs a novel non-zero-sum bilevel formulation of adversarial training, wherein each player optimizes a different objective function. Our formulation yields a simple algorithmic framework that matches and in some cases outperforms state-of-the-art attacks, attains comparable levels of robustness to standard adversarial training algorithms, and does not suffer from robust overfitting.

cs.LG↗

arXiv2024

Defending Large Language Models against Jailbreak Attacks via Semantic Smoothing

Aligned large language models (LLMs) are vulnerable to jailbreaking attacks, which bypass the safeguards of targeted LLMs and fool them into generating objectionable content. While initial defenses show promise against token-based threat models, there do not exist defenses that provide robustness against semantic attacks and avoid unfavorable trade-offs between robustness and nominal performance. To meet this need, we propose SEMANTICSMOOTH, a smoothing-based defense that aggregates the predictions of multiple semantically transformed copies of a given input prompt. Experimental results demonstrate that SEMANTICSMOOTH achieves state-of-the-art robustness against GCG, PAIR, and AutoDAN attacks while maintaining strong nominal performance on instruction following benchmarks such as InstructionFollowing and AlpacaEval. The codes will be publicly available at https://github.com/UCSB-NLP-Chang/SemanticSmooth.

cs.CL↗

arXiv2024

Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networks

Lipschitz constants of neural networks allow for guarantees of robustness in image classification, safety in controller design, and generalizability beyond the training data. As calculating Lipschitz constants is NP-hard, techniques for estimating Lipschitz constants must navigate the trade-off between scalability and accuracy. In this work, we significantly push the scalability frontier of a semidefinite programming technique known as LipSDP while achieving zero accuracy loss. We first show that LipSDP has chordal sparsity, which allows us to derive a chordally sparse formulation that we call Chordal-LipSDP. The key benefit is that the main computational bottleneck of LipSDP, a large semidefinite constraint, is now decomposed into an equivalent collection of smaller ones: allowing Chordal-LipSDP to outperform LipSDP particularly as the network depth grows. Moreover, our formulation uses a tunable sparsity parameter that enables one to gain tighter estimates without incurring a significant computational cost. We illustrate the scalability of our approach through extensive numerical experiments.

cs.LG↗

arXiv2024

Conformal Prediction Regions for Time Series using Linear Complementarity Programming

Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction regions. In fact, to obtain prediction regions over $T$ time steps with confidence $1-δ$, {previous works require that each individual prediction region is valid} with confidence $1-δ/T$. We propose an optimization-based method for reducing this conservatism to enable long horizon planning and verification when using learning-enabled time series predictors. Instead of considering prediction errors individually at each time step, we consider a parameterized prediction error over multiple time steps. By optimizing the parameters over an additional dataset, we find prediction regions that are not conservative. We show that this problem can be cast as a mixed integer linear complementarity program (MILCP), which we then relax into a linear complementarity program (LCP). Additionally, we prove that the relaxed LP has the same optimal cost as the original MILCP. Finally, we demonstrate the efficacy of our method on case studies using pedestrian trajectory predictors and F16 fighter jet altitude predictors.

eess.SY↗

arXiv2023

Data-Driven Modeling and Verification of Perception-Based Autonomous Systems

This paper addresses the problem of data-driven modeling and verification of perception-based autonomous systems. We assume the perception model can be decomposed into a canonical model (obtained from first principles or a simulator) and a noise model that contains the measurement noise introduced by the real environment. We focus on two types of noise, benign and adversarial noise, and develop a data-driven model for each type using generative models and classifiers, respectively. We show that the trained models perform well according to a variety of evaluation metrics based on downstream tasks such as state estimation and control. Finally, we verify the safety of two systems with high-dimensional data-driven models, namely an image-based version of mountain car (a reinforcement learning benchmark) as well as the F1/10 car, which uses LiDAR measurements to navigate a racing track.

eess.SY↗

arXiv2023

The noise level in linear regression with dependent data

We derive upper bounds for random design linear regression with dependent ($β$-mixing) data absent any realizability assumptions. In contrast to the strictly realizable martingale noise regime, no sharp instance-optimal non-asymptotics are available in the literature. Up to constant factors, our analysis correctly recovers the variance term predicted by the Central Limit Theorem -- the noise level of the problem -- and thus exhibits graceful degradation as we introduce misspecification. Past a burn-in, our result is sharp in the moderate deviations regime, and in particular does not inflate the leading order term by mixing time factors.

cs.LG↗

arXiv2023

Resilient Temporal Logic Planning in the Presence of Robot Failures

Several task and motion planning algorithms have been proposed recently to design paths for mobile robot teams with collaborative high-level missions specified using formal languages, such as Linear Temporal Logic (LTL). However, the designed paths often lack reactivity to failures of robot capabilities (e.g., sensing, mobility, or manipulation) that can occur due to unanticipated events (e.g., human intervention or system malfunctioning) which in turn may compromise mission performance. To address this novel challenge, in this paper, we propose a new resilient mission planning algorithm for teams of heterogeneous robots with collaborative LTL missions. The robots are heterogeneous with respect to their capabilities while the mission requires applications of these skills at certain areas in the environment in a temporal/logical order. The proposed method designs paths that can adapt to unexpected failures of robot capabilities. This is accomplished by re-allocating sub-tasks to the robots based on their currently functioning skills while minimally disrupting the existing team motion plans. We provide experiments and theoretical guarantees demonstrating the efficiency and resiliency of the proposed algorithm.

cs.RO↗

arXiv2023

Structural Risk Minimization for Learning Nonlinear Dynamics

Recent advances in learning or identification of nonlinear dynamics focus on learning a suitable model within a pre-specified model class. However, a key difficulty that remains is the choice of the model class from which the dynamics will be learned. The fundamental challenge is trading the richness of the model class with the learnability within the model class. Toward addressing the so-called model selection problem, we introduce a novel notion of Structural Risk Minimization (SRM) for learning nonlinear dynamics. Inspired by classical SRM for classification, we minimize a bound on the true prediction error over hierarchies of model classes. The class selected by our SRM scheme is shown to achieve a nearly optimal learning guarantee among all model classes contained in the hierarchy. Employing the proposed scheme along with computable model class complexity bounds, we derive explicit SRM schemes for learning nonlinear dynamics under hierarchies of: i) norm-constrained Reproducing Kernel Hilbert Spaces, and ii) norm-constrained Neural Network classes. We empirically show that even though too loose to be used as absolute estimates, our SRM bounds on the true prediction error are able to track its relative behavior across different model classes of the hierarchy.

eess.SY↗

arXiv2023

Safety Filter Design for Neural Network Systems via Convex Optimization

With the increase in data availability, it has been widely demonstrated that neural networks (NN) can capture complex system dynamics precisely in a data-driven manner. However, the architectural complexity and nonlinearity of the NNs make it challenging to synthesize a provably safe controller. In this work, we propose a novel safety filter that relies on convex optimization to ensure safety for a NN system, subject to additive disturbances that are capable of capturing modeling errors. Our approach leverages tools from NN verification to over-approximate NN dynamics with a set of linear bounds, followed by an application of robust linear MPC to search for controllers that can guarantee robust constraint satisfaction. We demonstrate the efficacy of the proposed framework numerically on a nonlinear pendulum system.

eess.SY↗

arXiv2023

Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Prediction

We consider perception-based control using state estimates that are obtained from high-dimensional sensor measurements via learning-enabled perception maps. However, these perception maps are not perfect and result in state estimation errors that can lead to unsafe system behavior. Stochastic sensor noise can make matters worse and result in estimation errors that follow unknown distributions. We propose a perception-based control framework that i) quantifies estimation uncertainty of perception maps, and ii) integrates these uncertainty representations into the control design. To do so, we use conformal prediction to compute valid state estimation regions, which are sets that contain the unknown state with high probability. We then devise a sampled-data controller for continuous-time systems based on the notion of measurement robust control barrier functions. Our controller uses idea from self-triggered control and enables us to avoid using stochastic calculus. Our framework is agnostic to the choice of the perception map, independent of the noise distribution, and to the best of our knowledge the first to provide probabilistic safety guarantees in such a setting. We demonstrate the effectiveness of our proposed perception-based controller for a LiDAR-enabled F1/10th car.

eess.SY↗

arXiv2023

Probable Domain Generalization via Quantile Risk Minimization

Domain generalization (DG) seeks predictors which perform well on unseen test distributions by leveraging data drawn from multiple related training distributions or domains. To achieve this, DG is commonly formulated as an average- or worst-case problem over the set of possible domains. However, predictors that perform well on average lack robustness while predictors that perform well in the worst case tend to be overly-conservative. To address this, we propose a new probabilistic framework for DG where the goal is to learn predictors that perform well with high probability. Our key idea is that distribution shifts seen during training should inform us of probable shifts at test time, which we realize by explicitly relating training and test domains as draws from the same underlying meta-distribution. To achieve probable DG, we propose a new optimization problem called Quantile Risk Minimization (QRM). By minimizing the $α$-quantile of predictor's risk distribution over domains, QRM seeks predictors that perform well with probability $α$. To solve QRM in practice, we propose the Empirical QRM (EQRM) algorithm and provide: (i) a generalization bound for EQRM; and (ii) the conditions under which EQRM recovers the causal predictor as $α\to 1$. In our experiments, we introduce a more holistic quantile-focused evaluation protocol for DG and demonstrate that EQRM outperforms state-of-the-art baselines on datasets from WILDS and DomainBed.

stat.ML↗

arXiv2023

Robust Localization of Aerial Vehicles via Active Control of Identical Ground Vehicles

This paper addresses the problem of active collaborative localization in heterogeneous robot teams with unknown data association. It involves positioning a small number of identical unmanned ground vehicles (UGVs) at desired positions so that an unmanned aerial vehicle (UAV) can, through unlabelled measurements of UGVs, uniquely determine its global pose. We model the problem as a sequential two player game, in which the first player positions the UGVs and the second identifies the two distinct hypothetical poses of the UAV at which the sets of measurements to the UGVs differ by as little as possible. We solve the underlying problem from the vantage point of the first player for a subclass of measurement models using a mixture of local optimization and exhaustive search procedures. Real-world experiments with a team of UAV and UGVs show that our method can achieve centimeter-level global localization accuracy. We also show that our method consistently outperforms random positioning of UGVs by a large margin, with as much as a 90% reduction in position and angular estimation error. Our method can tolerate a significant amount of random as well as non-stochastic measurement noise. This indicates its potential for reliable state estimation on board size, weight, and power (SWaP) constrained UAVs. This work enables robust localization in perceptually-challenged GPS-denied environments, thus paving the road for large-scale multi-robot navigation and mapping.

cs.RO↗

arXiv2023

Enhancing Sample Efficiency and Uncertainty Compensation in Learning-based Model Predictive Control for Aerial Robots

The recent increase in data availability and reliability has led to a surge in the development of learning-based model predictive control (MPC) frameworks for robot systems. Despite attaining substantial performance improvements over their non-learning counterparts, many of these frameworks rely on an offline learning procedure to synthesize a dynamics model. This implies that uncertainties encountered by the robot during deployment are not accounted for in the learning process. On the other hand, learning-based MPC methods that learn dynamics models online are computationally expensive and often require a significant amount of data. To alleviate these shortcomings, we propose a novel learning-enhanced MPC framework that incorporates components from $\mathcal{L}_1$ adaptive control into learning-based MPC. This integration enables the accurate compensation of both matched and unmatched uncertainties in a sample-efficient way, enhancing the control performance during deployment. In our proposed framework, we present two variants and apply them to the control of a quadrotor system. Through simulations and physical experiments, we demonstrate that the proposed framework not only allows the synthesis of an accurate dynamics model on-the-fly, but also significantly improves the closed-loop control performance under a wide range of spatio-temporal uncertainties.

cs.RO↗

arXiv2023

Safe Planning in Dynamic Environments using Conformal Prediction

We propose a framework for planning in unknown dynamic environments with probabilistic safety guarantees using conformal prediction. Particularly, we design a model predictive controller (MPC) that uses i) trajectory predictions of the dynamic environment, and ii) prediction regions quantifying the uncertainty of the predictions. To obtain prediction regions, we use conformal prediction, a statistical tool for uncertainty quantification, that requires availability of offline trajectory data - a reasonable assumption in many applications such as autonomous driving. The prediction regions are valid, i.e., they hold with a user-defined probability, so that the MPC is provably safe. We illustrate the results in the self-driving car simulator CARLA at a pedestrian-filled intersection. The strength of our approach is compatibility with state of the art trajectory predictors, e.g., RNNs and LSTMs, while making no assumptions on the underlying trajectory-generating distribution. To the best of our knowledge, these are the first results that provide valid safety guarantees in such a setting.

cs.RO↗

arXiv2023

Combined Left and Right Temporal Robustness for Control under STL Specifications

Many modern autonomous systems, particularly multi-agent systems, are time-critical and need to be robust against timing uncertainties. Previous works have studied left and right time robustness of signal temporal logic specifications by considering time shifts in the predicates that are either only to the left or only to the right. We propose a combined notion of temporal robustness which simultaneously considers left and right time shifts. For instance, in a scenario where a robot plans a trajectory around a pedestrian, this combined notion can now capture uncertainty of the pedestrian arriving earlier or later than anticipated. We first derive desirable properties of this new notion with respect to left and right time shifts and then design control laws for linear systems that maximize temporal robustness using mixed-integer linear programming. Finally, we present two case studies to illustrate how the proposed temporal robustness accounts for timing uncertainties.

eess.SY↗