arXiv subjects

Alessandro Abate

Publications and source records attributed to Alessandro Abate.

At least 91 records · Page 5Linked to original sources

arXiv2024

Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems

Ensuring that AI systems reliably and robustly avoid harmful or dangerous behaviours is a crucial challenge, especially for AI systems with a high degree of autonomy and general intelligence, or systems used in safety-critical contexts. In this paper, we will introduce and define a family of approaches to AI safety, which we will refer to as guaranteed safe (GS) AI. The core feature of these approaches is that they aim to produce AI systems which are equipped with high-assurance quantitative safety guarantees. This is achieved by the interplay of three core components: a world model (which provides a mathematical description of how the AI system affects the outside world), a safety specification (which is a mathematical description of what effects are acceptable), and a verifier (which provides an auditable proof certificate that the AI satisfies the safety specification relative to the world model). We outline a number of approaches for creating each of these three core components, describe the main technical challenges, and suggest a number of potential solutions to them. We also argue for the necessity of this approach to AI safety, and for the inadequacy of the main alternative approaches.

cs.AI↗

arXiv2024

Stochastic Omega-Regular Verification and Control with Supermartingales

We present for the first time a supermartingale certificate for $ω$-regular specifications. We leverage the Robbins & Siegmund convergence theorem to characterize supermartingale certificates for the almost-sure acceptance of Streett conditions on general stochastic processes, which we call Streett supermartingales. This enables effective verification and control of discrete-time stochastic dynamical models with infinite state space under $ω$-regular and linear temporal logic specifications. Our result generalises reachability, safety, reach-avoid, persistence and recurrence specifications; our contribution applies to discrete-time stochastic dynamical models and probabilistic programs with discrete and continuous state spaces and distributions, and carries over to deterministic models and programs. We provide a synthesis algorithm for control policies and Streett supermartingales as proof certificates for $ω$-regular objectives, which is sound and complete for supermartingales and control policies with polynomial templates and any stochastic dynamical model whose post-expectation is expressible as a polynomial. We additionally provide an optimisation of our algorithm that reduces the problem to satisfiability modulo theories, under the assumption that templates and post-expectation are in piecewise linear form. We have built a prototype and have demonstrated the efficacy of our approach on several exemplar $ω$-regular verification and control synthesis problems.

cs.LO↗

arXiv2024

Bisimulation Learning

We introduce a data-driven approach to computing finite bisimulations for state transition systems with very large, possibly infinite state space. Our novel technique computes stutter-insensitive bisimulations of deterministic systems, which we characterize as the problem of learning a state classifier together with a ranking function for each class. Our procedure learns a candidate state classifier and candidate ranking functions from a finite dataset of sample states; then, it checks whether these generalise to the entire state space using satisfiability modulo theory solving. Upon the affirmative answer, the procedure concludes that the classifier constitutes a valid stutter-insensitive bisimulation of the system. Upon a negative answer, the solver produces a counterexample state for which the classifier violates the claim, adds it to the dataset, and repeats learning and checking in a counterexample-guided inductive synthesis loop until a valid bisimulation is found. We demonstrate on a range of benchmarks from reactive verification and software model checking that our method yields faster verification results than alternative state-of-the-art tools in practice. Our method produces succinct abstractions that enable an effective verification of linear temporal logic without next operator, and are interpretable for system diagnostics.

cs.LO↗

arXiv2024

Learning-based Rigid Tube Model Predictive Control

This paper is concerned with model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and mixed constraints on the state and input, whereas the true disturbance set is unknown. Unlike most existing work on robust MPC, we propose an algorithm incorporating online learning that builds on prior knowledge of the disturbance, i.e., a known but conservative disturbance set. We approximate the true disturbance set at each time step with a parameterised set, which is referred to as a quantified disturbance set, using disturbance realisations. A key novelty is that the parameterisation of these quantified disturbance sets enjoys desirable properties such that the quantified disturbance set and its corresponding rigid tube bounding disturbance propagation can be efficiently updated online. We provide statistical gaps between the true and quantified disturbance sets, based on which, probabilistic recursive feasibility of MPC optimisation problems is discussed. Numerical simulations are provided to demonstrate the effectiveness of our proposed algorithm and compare with conventional robust MPC algorithms.

math.OC↗

arXiv2024

Learning Robust Policies for Uncertain Parametric Markov Decision Processes

Synthesising verifiably correct controllers for dynamical systems is crucial for safety-critical problems. To achieve this, it is important to account for uncertainty in a robust manner, while at the same time it is often of interest to avoid being overly conservative with the view of achieving a better cost. We propose a method for verifiably safe policy synthesis for a class of finite state models, under the presence of structural uncertainty. In particular, we consider uncertain parametric Markov decision processes (upMDPs), a special class of Markov decision processes, with parameterised transition functions, where such parameters are drawn from a (potentially) unknown distribution. Our framework leverages recent advancements in the so-called scenario approach theory, where we represent the uncertainty by means of scenarios, and provide guarantees on synthesised policies satisfying probabilistic computation tree logic (PCTL) formulae. We consider several common benchmarks/problems and compare our work to recent developments for verifying upMDPs.

eess.SY↗

arXiv2024

Data-driven memory-dependent abstractions of dynamical systems via a Cantor-Kantorovich metric

Abstractions of dynamical systems enable their verification and the design of feedback controllers using simpler, usually discrete, models. In this paper, we propose a data-driven abstraction mechanism based on a novel metric between Markov models. Our approach is based purely on observing output labels of the underlying dynamics, thus opening the road for a fully data-driven approach to construct abstractions. Another feature of the proposed approach is the use of memory to better represent the dynamics in a given region of the state space. We show through numerical examples the usefulness of the proposed methodology.

eess.SY↗

arXiv2024

Safe Reach Set Computation via Neural Barrier Certificates

We present a novel technique for online safety verification of autonomous systems, which performs reachability analysis efficiently for both bounded and unbounded horizons by employing neural barrier certificates. Our approach uses barrier certificates given by parameterized neural networks that depend on a given initial set, unsafe sets, and time horizon. Such networks are trained efficiently offline using system simulations sampled from regions of the state space. We then employ a meta-neural network to generalize the barrier certificates to state space regions that are outside the training set. These certificates are generated and validated online as sound over-approximations of the reachable states, thus either ensuring system safety or activating appropriate alternative actions in unsafe scenarios. We demonstrate our technique on case studies from linear models to nonlinear control-dependent models for online autonomous driving scenarios.

eess.SY↗

arXiv2024

Fossil 2.0: Formal Certificate Synthesis for the Verification and Control of Dynamical Models

This paper presents Fossil 2.0, a new major release of a software tool for the synthesis of certificates (e.g., Lyapunov and barrier functions) for dynamical systems modelled as ordinary differential and difference equations. Fossil 2.0 is much improved from its original release, including new interfaces, a significantly expanded certificate portfolio, controller synthesis and enhanced extensibility. We present these new features as part of this tool paper. Fossil implements a counterexample-guided inductive synthesis (CEGIS) loop ensuring the soundness of the method. Our tool uses neural networks as templates to generate candidate functions, which are then formally proven by an SMT solver acting as an assertion verifier. Improvements with respect to the first release include a wider range of certificates, synthesis of control laws, and support for discrete-time models.

eess.SY↗

arXiv2024

Data-driven Interval MDP for Robust Control Synthesis

The abstraction of dynamical systems is a powerful tool that enables the design of feedback controllers using a correct-by-design framework. We investigate a novel scheme to obtain data-driven abstractions of discrete-time stochastic processes in terms of richer discrete stochastic models, whose actions lead to nondeterministic transitions over the space of probability measures. The data-driven component of the proposed methodology lies in the fact that we only assume samples from an unknown probability distribution. We also rely on the model of the underlying dynamics to build our abstraction through backward reachability computations. The nondeterminism in the probability space is captured by a collection of Markov Processes, and we identify how this model can improve upon existing abstraction techniques in terms of satisfying temporal properties, such as safety or reach-avoid. The connection between the discrete and the underlying dynamics is made formal through the use of the scenario approach theory. Numerical experiments illustrate the advantages and main limitations of the proposed techniques with respect to existing approaches.

eess.SY↗

arXiv2024

A Stability-Based Abstraction Framework for Reach-Avoid Control of Stochastic Dynamical Systems with Unknown Noise Distributions

Finite-state abstractions are widely studied for the automated synthesis of correct-by-construction controllers for stochastic dynamical systems. However, existing abstraction methods often lead to prohibitively large finite-state models. To address this issue, we propose a novel abstraction scheme for stochastic linear systems that exploits the system's stability to obtain significantly smaller abstract models. As a unique feature, we first stabilize the open-loop dynamics using a linear feedback gain. We then use a model-based approach to abstract a known part of the stabilized dynamics while using a data-driven method to account for the stochastic uncertainty. We formalize abstractions as Markov decision processes (MDPs) with intervals of transition probabilities. By stabilizing the dynamics, we can further constrain the control input modeled in the abstraction, which leads to smaller abstract models while retaining the correctness of controllers. Moreover, when the stabilizing feedback controller is aligned with the property of interest, then a good trade-off is achieved between the reduction in the abstraction size and the performance loss. The experiments show that our approach can reduce the size of the graph of abstractions by up to 90% with negligible performance loss.

eess.SY↗

arXiv2024

Policy Evaluation in Distributional LQR (Extended Version)

Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard reinforcement learning. Meanwhile, a challenge in DRL is that the policy evaluation typically relies on the representation of the return distribution, which needs to be carefully designed. In this paper, we address this challenge for the special class of DRL problems that rely on a discounted linear quadratic regulator (LQR), which we call \emph{distributional LQR}. Specifically, we provide a closed-form expression for the distribution of the random return, which is applicable for all types of exogenous disturbance as long as it is independent and identically distributed (i.i.d.). We show that the variance of the random return is bounded if the fourth moment of the exogenous disturbance is bounded. Furthermore, we investigate the sensitivity of the return distribution to model perturbations. While the proposed exact return distribution consists of infinitely many random variables, we show that this distribution can be well approximated by a finite number of random variables. The associated approximation error can be analytically bounded under mild assumptions. When the model is unknown, we propose a model-free approach for estimating the return distribution, supported by sample complexity guarantees. Finally, we extend our approach to partially observable linear systems. Numerical experiments are provided to illustrate the theoretical results.

math.OC↗

arXiv2024

Quantifying the Sensitivity of Inverse Reinforcement Learning to Misspecification

Inverse reinforcement learning (IRL) aims to infer an agent's preferences (represented as a reward function $R$) from their behaviour (represented as a policy $π$). To do this, we need a behavioural model of how $π$ relates to $R$. In the current literature, the most common behavioural models are optimality, Boltzmann-rationality, and causal entropy maximisation. However, the true relationship between a human's preferences and their behaviour is much more complex than any of these behavioural models. This means that the behavioural models are misspecified, which raises the concern that they may lead to systematic errors if applied to real data. In this paper, we analyse how sensitive the IRL problem is to misspecification of the behavioural model. Specifically, we provide necessary and sufficient conditions that completely characterise how the observed data may differ from the assumed behavioural model without incurring an error above a given threshold. In addition to this, we also characterise the conditions under which a behavioural model is robust to small perturbations of the observed policy, and we analyse how robust many behavioural models are to misspecification of their parameter values (such as e.g.\ the discount rate). Our analysis suggests that the IRL problem is highly sensitive to misspecification, in the sense that very mild misspecification can lead to very large errors in the inferred reward function.

cs.LG↗

arXiv2024

Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.

stat.ML↗

arXiv2024

On the Limitations of Markovian Rewards to Express Multi-Objective, Risk-Sensitive, and Modal Tasks

In this paper, we study the expressivity of scalar, Markovian reward functions in Reinforcement Learning (RL), and identify several limitations to what they can express. Specifically, we look at three classes of RL tasks; multi-objective RL, risk-sensitive RL, and modal RL. For each class, we derive necessary and sufficient conditions that describe when a problem in this class can be expressed using a scalar, Markovian reward. Moreover, we find that scalar, Markovian rewards are unable to express most of the instances in each of these three classes. We thereby contribute to a more complete understanding of what standard reward functions can and cannot express. In addition to this, we also call attention to modal problems as a new class of problems, since they have so far not been given any systematic treatment in the RL literature. We also briefly outline some approaches for solving some of the problems we discuss, by means of bespoke RL algorithms.

cs.AI↗

arXiv2023

Distributionally Robust Optimal and Safe Control of Stochastic Systems via Kernel Conditional Mean Embedding

We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the state evolution into an associated repreducing kernel Hilbert space. Our key idea lies in combining conditional mean embedding with the maximum mean discrepancy distance to construct an ambiguity set, and then design a robust control policy using techniques from distributionally robust optimization. The main theoretical contribution of this paper is to leverage functional analytic tools to prove that optimal policies for this infinite-dimensional min-max problem are Markovian and deterministic. Additionally, we discuss approximation schemes based on state and input discretization to make the approach computationally tractable. To validate the theoretical findings, we conduct an experiment on safe control for thermostatically controlled loads (TCL).

eess.SY↗

arXiv2023

Safeguarded Progress in Reinforcement Learning: Safe Bayesian Exploration for Control Policy Synthesis

This paper addresses the problem of maintaining safety during training in Reinforcement Learning (RL), such that the safety constraint violations are bounded at any point during learning. In a variety of RL applications the safety of the agent is particularly important, e.g. autonomous platforms or robots that work in proximity of humans. As enforcing safety during training might severely limit the agent's exploration, we propose here a new architecture that handles the trade-off between efficient progress and safety during exploration. As the exploration progresses, we update via Bayesian inference Dirichlet-Categorical models of the transition probabilities of the Markov decision process that describes the environment dynamics. This paper proposes a way to approximate moments of belief about the risk associated to the action selection policy. We construct those approximations, and prove the convergence results. We propose a novel method for leveraging the expectation approximations to derive an approximate bound on the confidence that the risk is below a certain level. This approach can be easily interleaved with RL and we present experimental results to showcase the performance of the overall architecture.

cs.LG↗

arXiv2023

Stability Analysis of Switched Linear Systems with Neural Lyapunov Functions

Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely model-free, data-driven approach, but also for handling arbitrary complex functions via their power of representation (as opposed to, e.g. algebraic optimization techniques that are restricted to polynomial functions). Whilst classical Lyapunov techniques allow to provide a formal and robust guarantee of stability of a switched dynamical system, very little is yet known about correctness guarantees for Neural Lyapunov functions, nor about their performance (amount of data needed for a certain accuracy). We thus formally introduce neural Lyapunov functions for the stability analysis of switched linear systems: we benchmark them on this paradigmatic problem, which is notoriously difficult (and in general Turing-undecidable), but which admits recently-developed technologies and theoretical results. Inspired by switched systems theory, we provide theoretical guarantees on the representative power of neural networks, leveraging recent results from the ML community. We additionally experimentally display how neural Lyapunov functions compete with state-of-the-art results and techniques, while admitting a wide range of improvement, both in theory and in practice. This study intends to improve our understanding of the opportunities and current limitations of neural-based data-driven analysis and control of complex dynamical systems.

math.OC↗

arXiv2023

Bounded Robustness in Reinforcement Learning via Lexicographic Objectives

Policy robustness in Reinforcement Learning may not be desirable at any cost: the alterations caused by robustness requirements from otherwise optimal policies should be explainable, quantifiable and formally verifiable. In this work we study how policies can be maximally robust to arbitrary observational noise by analysing how they are altered by this noise through a stochastic linear operator interpretation of the disturbances, and establish connections between robustness and properties of the noise kernel and of the underlying MDPs. Then, we construct sufficient conditions for policy robustness, and propose a robustness-inducing scheme, applicable to any policy gradient algorithm, that formally trades off expected policy utility for robustness through lexicographic optimisation, while preserving convergence and sub-optimality in the policy synthesis.

cs.LG↗