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How many parameters are required for a model to execute a given task? It has been argued that large language models, pre-trained via self-supervised learning, exhibit emergent capabilities such as multi-step reasoning as their number of parameters reach a critical scale. In the present work, we explore whether this phenomenon can analogously be replicated in a simple theoretical model. We show that the problem of learning linear dynamical systems -- a simple instance of self-supervised learning -- exhibits a corresponding phase transition. Namely, for every non-ergodic linear system there exists a critical threshold such that a learner using fewer parameters than said threshold cannot achieve bounded error for large sequence lengths. Put differently, in our model we find that tasks exhibiting substantial long-range correlation require a certain critical number of parameters -- a phenomenon akin to emergence. We also investigate the role of the learner's parametrization and consider a simple version of a linear dynamical system with hidden state -- an imperfectly observed random walk in $\mathbb{R}$. For this situation, we show that there exists no learner using a linear filter which can succesfully learn the random walk unless the filter length exceeds a certain threshold depending on the effective memory length and horizon of the problem.

In this survey, we design formal verification and control algorithms for autonomous systems with practical safety guarantees using conformal prediction (CP), a statistical tool for uncertainty quantification. We focus on learning-enabled autonomous systems (LEASs) in which the complexity of learning-enabled components (LECs) is a major bottleneck that hampers the use of existing model-based verification and design techniques. Instead, we advocate for the use of CP, and we will demonstrate its use in formal verification, systems and control theory, and robotics. We argue that CP is specifically useful due to its simplicity (easy to understand, use, and modify), generality (requires no assumptions on learned models and data distributions, i.e., is distribution-free), and efficiency (real-time capable and accurate). We pursue the following goals with this survey. First, we provide an accessible introduction to CP for non-experts who are interested in using CP to solve problems in autonomy. Second, we show how to use CP for the verification of LECs, e.g., for verifying input-output properties of neural networks. Third and fourth, we review recent articles that use CP for safe control design as well as offline and online verification of LEASs. We summarize their ideas in a unifying framework that can deal with the complexity of LEASs in a computationally efficient manner. In our exposition, we consider simple system specifications, e.g., robot navigation tasks, as well as complex specifications formulated in temporal logic formalisms. Throughout our survey, we compare to other statistical techniques (e.g., scenario optimization, PAC-Bayes theory, etc.) and how these techniques have been used in verification and control. Lastly, we point the reader to open problems and future research directions.

Recent research endeavours have theoretically shown the beneficial effect of cooperation in multi-agent reinforcement learning (MARL). In a setting involving $N$ agents, this beneficial effect usually comes in the form of an $N$-fold linear convergence speedup, i.e., a reduction - proportional to $N$ - in the number of iterations required to reach a certain convergence precision. In this paper, we show for the first time that this speedup property also holds for a MARL framework subject to asynchronous delays in the local agents' updates. In particular, we consider a policy evaluation problem in which multiple agents cooperate to evaluate a common policy by communicating with a central aggregator. In this setting, we study the finite-time convergence of \texttt{AsyncMATD}, an asynchronous multi-agent temporal difference (TD) learning algorithm in which agents' local TD update directions are subject to asynchronous bounded delays. Our main contribution is providing a finite-time analysis of \texttt{AsyncMATD}, for which we establish a linear convergence speedup while highlighting the effect of time-varying asynchronous delays on the resulting convergence rate.

In safety-critical robot planning or control, manually specifying safety constraints or learning them from demonstrations can be challenging. In this paper, we propose a certifiable alignment method for a robot to learn a safety constraint in its model predictive control (MPC) policy with human online directional feedback. To our knowledge, it is the first method to learn safety constraints from human feedback. The proposed method is based on an empirical observation: human directional feedback, when available, tends to guide the robot toward safer regions. The method only requires the direction of human feedback to update the learning hypothesis space. It is certifiable, providing an upper bound on the total number of human feedback in the case of successful learning of safety constraints, or declaring the misspecification of the hypothesis space, i.e., the true implicit safety constraint cannot be found within the specified hypothesis space. We evaluated the proposed method using numerical examples and user studies in two developed simulation games. Additionally, we implemented and tested the proposed method on a real-world Franka robot arm performing mobile water-pouring tasks in a user study. The simulation and experimental results demonstrate the efficacy and efficiency of our method, showing that it enables a robot to successfully learn safety constraints with a small handful (tens) of human directional corrections., Comment: 18 pages, submission to T-RO

Operator learning is an emerging area of machine learning which aims to learn mappings between infinite dimensional function spaces. Here we uncover a connection between operator learning architectures and conditioned neural fields from computer vision, providing a unified perspective for examining differences between popular operator learning models. We find that many commonly used operator learning models can be viewed as neural fields with conditioning mechanisms restricted to point-wise and/or global information. Motivated by this, we propose the Continuous Vision Transformer (CViT), a novel neural operator architecture that employs a vision transformer encoder and uses cross-attention to modulate a base field constructed with a trainable grid-based positional encoding of query coordinates. Despite its simplicity, CViT achieves state-of-the-art results across challenging benchmarks in climate modeling and fluid dynamics. Our contributions can be viewed as a first step towards adapting advanced computer vision architectures for building more flexible and accurate machine learning models in physical sciences., Comment: 23 pages, 13 figures

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.

Model-based reinforcement learning is an effective approach for controlling an unknown system. It is based on a longstanding pipeline familiar to the control community in which one performs experiments on the environment to collect a dataset, uses the resulting dataset to identify a model of the system, and finally performs control synthesis using the identified model. As interacting with the system may be costly and time consuming, targeted exploration is crucial for developing an effective control-oriented model with minimal experimentation. Motivated by this challenge, recent work has begun to study finite sample data requirements and sample efficient algorithms for the problem of optimal exploration in model-based reinforcement learning. However, existing theory and algorithms are limited to model classes which are linear in the parameters. Our work instead focuses on models with nonlinear parameter dependencies, and presents the first finite sample analysis of an active learning algorithm suitable for a general class of nonlinear dynamics. In certain settings, the excess control cost of our algorithm achieves the optimal rate, up to logarithmic factors. We validate our approach in simulation, showcasing the advantage of active, control-oriented exploration for controlling nonlinear systems.

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., Comment: 38 pages, added acknowledgements

Jailbreak attacks cause large language models (LLMs) to generate harmful, unethical, or otherwise objectionable content. Evaluating these attacks presents a number of challenges, which the current collection of benchmarks and evaluation techniques do not adequately address. First, there is no clear standard of practice regarding jailbreaking evaluation. Second, existing works compute costs and success rates in incomparable ways. And third, numerous works are not reproducible, as they withhold adversarial prompts, involve closed-source code, or rely on evolving proprietary APIs. To address these challenges, we introduce JailbreakBench, an open-sourced benchmark with the following components: (1) an evolving repository of state-of-the-art adversarial prompts, which we refer to as jailbreak artifacts; (2) a jailbreaking dataset comprising 100 behaviors -- both original and sourced from prior work (Zou et al., 2023; Mazeika et al., 2023, 2024) -- which align with OpenAI's usage policies; (3) a standardized evaluation framework at https://github.com/JailbreakBench/jailbreakbench that includes a clearly defined threat model, system prompts, chat templates, and scoring functions; and (4) a leaderboard at https://jailbreakbench.github.io/ that tracks the performance of attacks and defenses for various LLMs. We have carefully considered the potential ethical implications of releasing this benchmark, and believe that it will be a net positive for the community., Comment: JailbreakBench v1.0: more attack artifacts, more test-time defenses, a more accurate jailbreak judge (Llama-3-70B with a custom prompt), a larger dataset of human preferences for selecting a jailbreak judge (300 examples), an over-refusal evaluation dataset (100 benign/borderline behaviors), a semantic refusal judge based on Llama-3-8B

Prompt engineering is effective for controlling the output of text-to-image (T2I) generative models, but it is also laborious due to the need for manually crafted prompts. This challenge has spurred the development of algorithms for automated prompt generation. However, these methods often struggle with transferability across T2I models, require white-box access to the underlying model, and produce non-intuitive prompts. In this work, we introduce PRISM, an algorithm that automatically identifies human-interpretable and transferable prompts that can effectively generate desired concepts given only black-box access to T2I models. Inspired by large language model (LLM) jailbreaking, PRISM leverages the in-context learning ability of LLMs to iteratively refine the candidate prompts distribution for given reference images. Our experiments demonstrate the versatility and effectiveness of PRISM in generating accurate prompts for objects, styles and images across multiple T2I models, including Stable Diffusion, DALL-E, and Midjourney.

The need for a systematic approach to risk assessment has increased in recent years due to the ubiquity of autonomous systems that alter our day-to-day experiences and their need for safety, e.g., for self-driving vehicles, mobile service robots, and bipedal robots. These systems are expected to function safely in unpredictable environments and interact seamlessly with humans, whose behavior is notably challenging to forecast. We present a survey of risk-aware methodologies for autonomous systems. We adopt a contemporary risk-aware approach to mitigate rare and detrimental outcomes by advocating the use of tail risk measures, a concept borrowed from financial literature. This survey will introduce these measures and explain their relevance in the context of robotic systems for planning, control, and verification applications.

We consider a setting in which $N$ agents aim to speedup a common Stochastic Approximation (SA) problem by acting in parallel and communicating with a central server. We assume that the up-link transmissions to the server are subject to asynchronous and potentially unbounded time-varying delays. To mitigate the effect of delays and stragglers while reaping the benefits of distributed computation, we propose \texttt{DASA}, a Delay-Adaptive algorithm for multi-agent Stochastic Approximation. We provide a finite-time analysis of \texttt{DASA} assuming that the agents' stochastic observation processes are independent Markov chains. Significantly advancing existing results, \texttt{DASA} is the first algorithm whose convergence rate depends only on the mixing time $\tau_{mix}$ and on the average delay $\tau_{avg}$ while jointly achieving an $N$-fold convergence speedup under Markovian sampling. Our work is relevant for various SA applications, including multi-agent and distributed temporal difference (TD) learning, Q-learning and stochastic optimization with correlated data.

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., Comment: 37 pages

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 $\tau_{max}$, and the mixing time $\tau_{mix}$. 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 $\tau_{avg}$, as opposed to $\tau_{max}$ for the vanilla delayed SA rule; here, $\tau_{avg}$ 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., Comment: Accepted to the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024!

In this work, we study statistical learning with dependent ($\beta$-mixing) data and square loss in a hypothesis class $\mathscr{F}\subset L_{\Psi_p}$ where $\Psi_p$ is the norm $\|f\|_{\Psi_p} \triangleq \sup_{m\geq 1} m^{-1/p} \|f\|_{L^m} $ for some $p\in [2,\infty]$. Our inquiry is motivated by the search for a sharp noise interaction term, or variance proxy, in learning with dependent data. Absent any realizability assumption, typical non-asymptotic results exhibit variance proxies that are deflated multiplicatively by the mixing time of the underlying covariates process. We show that whenever the topologies of $L^2$ and $\Psi_p$ are comparable on our hypothesis class $\mathscr{F}$ -- that is, $\mathscr{F}$ is a weakly sub-Gaussian class: $\|f\|_{\Psi_p} \lesssim \|f\|_{L^2}^\eta$ for some $\eta\in (0,1]$ -- the empirical risk minimizer achieves a rate that only depends on the complexity of the class and second order statistics in its leading term. Our result holds whether the problem is realizable or not and we refer to this as a \emph{near mixing-free rate}, since direct dependence on mixing is relegated to an additive higher order term. We arrive at our result by combining the above notion of a weakly sub-Gaussian class with mixed tail generic chaining. This combination allows us to compute sharp, instance-optimal rates for a wide range of problems. Examples that satisfy our framework include sub-Gaussian linear regression, more general smoothly parameterized function classes, finite hypothesis classes, and bounded smoothness classes.

Conformal prediction is a statistical tool for producing prediction regions for machine learning models that are valid with high probability. A key component of conformal prediction algorithms is a \emph{non-conformity score function} that quantifies how different a model's prediction is from the unknown ground truth value. Essentially, these functions determine the shape and the size of the conformal prediction regions. While prior work has gone into creating score functions that produce multi-model prediction regions, such regions are generally too complex for use in downstream planning and control problems. We propose a method that optimizes parameterized \emph{shape template functions} over calibration data, which results in non-conformity score functions that produce prediction regions with minimum volume. Our approach results in prediction regions that are \emph{multi-modal}, so they can properly capture residuals of distributions that have multiple modes, and \emph{practical}, so each region is convex and can be easily incorporated into downstream tasks, such as a motion planner using conformal prediction regions. Our method applies to general supervised learning tasks, while we illustrate its use in time-series prediction. We provide a toolbox and present illustrative case studies of F16 fighter jets and autonomous vehicles, showing an up to $68\%$ reduction in prediction region area compared to a circular baseline region., Comment: Accepted to L4DC 2024. 14 pages, 3 figures. The source code and toolbox are available at https://github.com/nandantumu/conformal_region_designer

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., Comment: 23 pages, 12 figures, and 3 tables. Submitted to: 6th Annual Learning for Dynamics & Control Conference

There is growing interest in ensuring that large language models (LLMs) align with human values. However, the alignment of such models is vulnerable to adversarial jailbreaks, which coax LLMs into overriding their safety guardrails. The identification of these vulnerabilities is therefore instrumental in understanding inherent weaknesses and preventing future misuse. To this end, we propose Prompt Automatic Iterative Refinement (PAIR), an algorithm that generates semantic jailbreaks with only black-box access to an LLM. PAIR -- which is inspired by social engineering attacks -- uses an attacker LLM to automatically generate jailbreaks for a separate targeted LLM without human intervention. In this way, the attacker LLM iteratively queries the target LLM to update and refine a candidate jailbreak. Empirically, PAIR often requires fewer than twenty queries to produce a jailbreak, which is orders of magnitude more efficient than existing algorithms. PAIR also achieves competitive jailbreaking success rates and transferability on open and closed-source LLMs, including GPT-3.5/4, Vicuna, and Gemini.

Despite efforts to align large language models (LLMs) with human intentions, widely-used LLMs such as GPT, Llama, and Claude are susceptible to jailbreaking attacks, wherein an adversary fools a targeted LLM into generating objectionable content. To address this vulnerability, we propose SmoothLLM, the first algorithm designed to mitigate jailbreaking attacks. Based on our finding that adversarially-generated prompts are brittle to character-level changes, our defense randomly perturbs multiple copies of a given input prompt, and then aggregates the corresponding predictions to detect adversarial inputs. Across a range of popular LLMs, SmoothLLM sets the state-of-the-art for robustness against the GCG, PAIR, RandomSearch, and AmpleGCG jailbreaks. SmoothLLM is also resistant against adaptive GCG attacks, exhibits a small, though non-negligible trade-off between robustness and nominal performance, and is compatible with any LLM. Our code is publicly available at \url{https://github.com/arobey1/smooth-llm}.

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.

This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification. We emphasize tools we deem particularly useful for a range of problems in this domain, such as the covering technique, the Hanson-Wright Inequality and the method of self-normalized martingales. We then employ these tools to give streamlined proofs of the performance of various least-squares based estimators for identifying the parameters in autoregressive models. We conclude by sketching out how the ideas presented herein can be extended to certain nonlinear identification problems.

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., Comment: This paper has been accepted to the 2023 62nd IEEE Conference on Decision and Control (CDC)

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., Comment: To appear in IROS 2023

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., Comment: 7 pages, 7 figures. Accepted for publication in the proceedings of the 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2023)

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.

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.

Accurate and robust state estimation is critical for autonomous navigation of robot teams. This task is especially challenging for large groups of size, weight, and power (SWAP) constrained aerial robots operating in perceptually-degraded GPS-denied environments. We can, however, actively increase the amount of perceptual information available to such robots by augmenting them with a small number of more expensive, but less resource-constrained, agents. Specifically, the latter can serve as sources of perceptual information themselves. In this paper, we study the problem of optimally positioning (and potentially navigating) a small number of more capable agents to enhance the perceptual environment for their lightweight,inexpensive, teammates that only need to rely on cameras and IMUs. We propose a numerically robust, computationally efficient approach to solve this problem via nonlinear optimization. Our method outperforms the standard approach based on the greedy algorithm, while matching the accuracy of a heuristic evolutionary scheme for global optimization at a fraction of its running time. Ultimately, we validate our solution in both photorealistic simulations and real-world experiments. In these experiments, we use lidar-based autonomous ground vehicles as the more capable agents, and vision-based aerial robots as their SWAP-constrained teammates. Our method is able to reduce drift in visual-inertial odometry by as much as 90%, and it outperforms random positioning of lidar-equipped agents by a significant margin. Furthermore, our method can be generalized to different types of robot teams with heterogeneous perception capabilities. It has a wide range of applications, such as surveying and mapping challenging dynamic environments, and enabling resilience to large-scale perturbations that can be caused by earthquakes or storms., Comment: To appear in Robotics: Science and Systems (RSS) 2023

We derive upper bounds for random design linear regression with dependent ($\beta$-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.

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GP-PHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems., Comment: Accepted at the IEEE Conference on Decision and Control 2022

Variational autoencoders allow to learn a lower-dimensional latent space based on high-dimensional input/output data. Using video clips as input data, the encoder may be used to describe the movement of an object in the video without ground truth data (unsupervised learning). Even though the object's dynamics is typically based on first principles, this prior knowledge is mostly ignored in the existing literature. Thus, we propose a physics-enhanced variational autoencoder that places a physical-enhanced Gaussian process prior on the latent dynamics to improve the efficiency of the variational autoencoder and to allow physically correct predictions. The physical prior knowledge expressed as linear dynamical system is here reflected by the Green's function and included in the kernel function of the Gaussian process. The benefits of the proposed approach are highlighted in a simulation with an oscillating particle., Comment: Accepted paper at the 5th Annual Learning for Dynamics & Control Conference

Switching physical systems are ubiquitous in modern control applications, for instance, locomotion behavior of robots and animals, power converters with switches and diodes. The dynamics and switching conditions are often hard to obtain or even inaccessible in case of a-priori unknown environments and nonlinear components. Black-box neural networks can learn to approximately represent switching dynamics, but typically require a large amount of data, neglect the underlying axioms of physics, and lack of uncertainty quantification. We propose a Gaussian process based learning approach enhanced by switching Port-Hamiltonian systems (GP-SPHS) to learn physical plausible system dynamics and identify the switching condition. The Bayesian nature of Gaussian processes uses collected data to form a distribution over all possible switching policies and dynamics that allows for uncertainty quantification. Furthermore, the proposed approach preserves the compositional nature of Port-Hamiltonian systems. A simulation with a hopping robot validates the effectiveness of the proposed approach., Comment: Accepted at IFAC World Congress 2023. arXiv admin note: text overlap with arXiv:2305.09017

Federated learning (FL) has recently gained much attention due to its effectiveness in speeding up supervised learning tasks under communication and privacy constraints. However, whether similar speedups can be established for reinforcement learning remains much less understood theoretically. Towards this direction, we study a federated policy evaluation problem where agents communicate via a central aggregator to expedite the evaluation of a common policy. To capture typical communication constraints in FL, we consider finite capacity up-link channels that can drop packets based on a Bernoulli erasure model. Given this setting, we propose and analyze QFedTD - a quantized federated temporal difference learning algorithm with linear function approximation. Our main technical contribution is to provide a finite-sample analysis of QFedTD that (i) highlights the effect of quantization and erasures on the convergence rate; and (ii) establishes a linear speedup w.r.t. the number of agents under Markovian sampling. Notably, while different quantization mechanisms and packet drop models have been extensively studied in the federated learning, distributed optimization, and networked control systems literature, our work is the first to provide a non-asymptotic analysis of their effects in multi-agent and federated reinforcement learning.

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.

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 $1-\delta$, {previous works require that each individual prediction region is valid} with confidence $1-\delta/T$. 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.

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., Comment: This paper is accepted by IEEE CDC 2023

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

We initiate the study of federated reinforcement learning under environmental heterogeneity by considering a policy evaluation problem. Our setup involves $N$ agents interacting with environments that share the same state and action space but differ in their reward functions and state transition kernels. Assuming agents can communicate via a central server, we ask: Does exchanging information expedite the process of evaluating a common policy? To answer this question, we provide the first comprehensive finite-time analysis of a federated temporal difference (TD) learning algorithm with linear function approximation, while accounting for Markovian sampling, heterogeneity in the agents' environments, and multiple local updates to save communication. Our analysis crucially relies on several novel ingredients: (i) deriving perturbation bounds on TD fixed points as a function of the heterogeneity in the agents' underlying Markov decision processes (MDPs); (ii) introducing a virtual MDP to closely approximate the dynamics of the federated TD algorithm; and (iii) using the virtual MDP to make explicit connections to federated optimization. Putting these pieces together, we rigorously prove that in a low-heterogeneity regime, exchanging model estimates leads to linear convergence speedups in the number of agents.

Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network's output. Conversely, there may exist large, meaningful perturbations that do not affect the network's decision (excessive invariance). In our research, we investigate this latter phenomenon in two contexts: (a) discrete-time dynamical system identification, and (b) the calibration of a neural network's output to that of another network. We examine noninvertibility through the lens of mathematical optimization, where the global solution measures the ``safety" of the network predictions by their distance from the non-invertibility boundary. We formulate mixed-integer programs (MIPs) for ReLU networks and $L_p$ norms ($p=1,2,\infty$) that apply to neural network approximators of dynamical systems. We also discuss how our findings can be useful for invertibility certification in transformations between neural networks, e.g. between different levels of network pruning., Comment: 22 pages, 7 figures

In large-scale distributed machine learning, recent works have studied the effects of compressing gradients in stochastic optimization to alleviate the communication bottleneck. These works have collectively revealed that stochastic gradient descent (SGD) is robust to structured perturbations such as quantization, sparsification, and delays. Perhaps surprisingly, despite the surge of interest in multi-agent reinforcement learning, almost nothing is known about the analogous question: Are common reinforcement learning (RL) algorithms also robust to similar perturbations? We investigate this question by studying a variant of the classical temporal difference (TD) learning algorithm with a perturbed update direction, where a general compression operator is used to model the perturbation. Our work makes three important technical contributions. First, we prove that compressed TD algorithms, coupled with an error-feedback mechanism used widely in optimization, exhibit the same non-asymptotic theoretical guarantees as their SGD counterparts. Second, we show that our analysis framework extends seamlessly to nonlinear stochastic approximation schemes that subsume Q-learning. Third, we prove that for multi-agent TD learning, one can achieve linear convergence speedups with respect to the number of agents while communicating just $\tilde{O}(1)$ bits per iteration. Notably, these are the first finite-time results in RL that account for general compression operators and error-feedback in tandem with linear function approximation and Markovian sampling. Our proofs hinge on the construction of novel Lyapunov functions that capture the dynamics of a memory variable introduced by error-feedback., Comment: Accepted to Transactions on Machine Learning Research

This paper proposes an algorithm for motion planning among dynamic agents using adaptive conformal prediction. We consider a deterministic control system and use trajectory predictors to predict the dynamic agents' future motion, which is assumed to follow an unknown distribution. We then leverage ideas from adaptive conformal prediction to dynamically quantify prediction uncertainty from an online data stream. Particularly, we provide an online algorithm uses delayed agent observations to obtain uncertainty sets for multistep-ahead predictions with probabilistic coverage. These uncertainty sets are used within a model predictive controller to safely navigate among dynamic agents. While most existing data-driven prediction approached quantify prediction uncertainty heuristically, we quantify the true prediction uncertainty in a distribution-free, adaptive manner that even allows to capture changes in prediction quality and the agents' motion. We empirically evaluate of our algorithm on a simulation case studies where a drone avoids a flying frisbee.

We are interested in predicting failures of cyber-physical systems during their operation. Particularly, we consider stochastic systems and signal temporal logic specifications, and we want to calculate the probability that the current system trajectory violates the specification. The paper presents two predictive runtime verification algorithms that predict future system states from the current observed system trajectory. As these predictions may not be accurate, we construct prediction regions that quantify prediction uncertainty by using conformal prediction, a statistical tool for uncertainty quantification. Our first algorithm directly constructs a prediction region for the satisfaction measure of the specification so that we can predict specification violations with a desired confidence. The second algorithm constructs prediction regions for future system states first, and uses these to obtain a prediction region for the satisfaction measure. To the best of our knowledge, these are the first formal guarantees for a predictive runtime verification algorithm that applies to widely used trajectory predictors such as RNNs and LSTMs, while being computationally simple and making no assumptions on the underlying distribution. We present numerical experiments of an F-16 aircraft and a self-driving car.

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.

This paper addresses the Multi-Robot Active Information Acquisition (AIA) problem, where a team of mobile robots, communicating through an underlying graph, estimates a hidden state expressing a phenomenon of interest. Applications like target tracking, coverage and SLAM can be expressed in this framework. Existing approaches, though, are either not scalable, unable to handle dynamic phenomena or not robust to changes in the communication graph. To counter these shortcomings, we propose an Information-aware Graph Block Network (I-GBNet), an AIA adaptation of Graph Neural Networks, that aggregates information over the graph representation and provides sequential-decision making in a distributed manner. The I-GBNet, trained via imitation learning with a centralized sampling-based expert solver, exhibits permutation equivariance and time invariance, while harnessing the superior scalability, robustness and generalizability to previously unseen environments and robot configurations. Experiments on significantly larger graphs and dimensionality of the hidden state and more complex environments than those seen in training validate the properties of the proposed architecture and its efficacy in the application of localization and tracking of dynamic targets., Comment: This work has been submitted to the IEEE International Conference on Robotics and Automation (ICRA2023) for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Mariliza Tzes and Nikolaos Bousias equally contributed

This paper addresses a new semantic multi-robot planning problem in uncertain and dynamic environments. Particularly, the environment is occupied with non-cooperative, mobile, uncertain labeled targets. These targets are governed by stochastic dynamics while their current and future positions as well as their semantic labels are uncertain. Our goal is to control mobile sensing robots so that they can accomplish collaborative semantic tasks defined over the uncertain current/future positions and labels of these targets. We express these tasks using Linear Temporal Logic (LTL). We propose a sampling-based approach that explores the robot motion space, the mission specification space, as well as the future configurations of the labeled targets to design optimal paths. These paths are revised online to adapt to uncertain perceptual feedback. To the best of our knowledge, this is the first work that addresses semantic mission planning problems in uncertain and dynamic semantic environments. We provide extensive experiments that demonstrate the efficiency of the proposed method, Comment: arXiv admin note: text overlap with arXiv:2012.10490

This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory is most well-developed when it comes to linear system identification and learning for the linear quadratic regulator, which are the focus of this manuscript. From a theoretical perspective, much of the labor underlying these advances has been in adapting tools from modern high-dimensional statistics and learning theory. While highly relevant to control theorists interested in integrating tools from machine learning, the foundational material has not always been easily accessible. To remedy this, we provide a self-contained presentation of the relevant material, outlining all the key ideas and the technical machinery that underpin recent results. We also present a number of open problems and future directions., Comment: Survey Paper, Submitted to Control Systems Magazine. Second version contains additional motivation for finite sample statistics and more detailed comparison with classical literature

This note studies state estimation in wireless networked control systems with secrecy against eavesdropping. Specifically, a sensor transmits a system state information to the estimator over a legitimate user link, and an eavesdropper overhears these data over its link independent of the user link. Each connection may be affected by packet losses and is modeled by a finite-state Markov channel (FSMC), an abstraction widely used to design wireless communication systems. This paper presents a novel concept of optimal mean square expected secrecy over FSMCs and delineates the design of a secrecy parameter requiring the user mean square estimation error (MSE) to be bounded and eavesdropper MSE unbounded. We illustrate the developed results on an example of an inverted pendulum on a cart whose parameters are estimated remotely over a wireless link exposed to an eavesdropper.

This paper considers the problem of safely coordinating a team of sensor-equipped robots to reduce uncertainty about a dynamical process, where the objective trades off information gain and energy cost. Optimizing this trade-off is desirable, but leads to a non-monotone objective function in the set of robot trajectories. Therefore, common multi-robot planners based on coordinate descent lose their performance guarantees. Furthermore, methods that handle non-monotonicity lose their performance guarantees when subject to inter-robot collision avoidance constraints. As it is desirable to retain both the performance guarantee and safety guarantee, this work proposes a hierarchical approach with a distributed planner that uses local search with a worst-case performance guarantees and a decentralized controller based on control barrier functions that ensures safety and encourages timely arrival at sensing locations. Via extensive simulations, hardware-in-the-loop tests and hardware experiments, we demonstrate that the proposed approach achieves a better trade-off between sensing and energy cost than coordinate-descent-based algorithms., Comment: To appear in Transactions on Robotics; 18 pages and 16 figures. arXiv admin note: text overlap with arXiv:2101.11093

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 $\alpha$-quantile of predictor's risk distribution over domains, QRM seeks predictors that perform well with probability $\alpha$. 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 $\alpha \to 1$. 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., Comment: NeurIPS 2022 camera-ready (+ minor corrections)

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost.