arXiv subjects

Marta Kwiatkowska

Publications and source records attributed to Marta Kwiatkowska.

At least 37 records · Page 2Linked to original sources

arXiv2025

Learning Probabilistic Temporal Logic Specifications for Stochastic Systems

There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly characterise systems with stochastic behaviour, which occur commonly in reinforcement learning and formal verification. We consider the passive learning problem of inferring a Boolean combination of probabilistic LTL (PLTL) formulas from a set of Markov chains, classified as either positive or negative. We propose a novel learning algorithm that infers concise PLTL specifications, leveraging grammar-based enumeration, search heuristics, probabilistic model checking and Boolean set-cover procedures. We demonstrate the effectiveness of our algorithm in two use cases: learning from policies induced by RL algorithms and learning from variants of a probabilistic model. In both cases, our method automatically and efficiently extracts PLTL specifications that succinctly characterise the temporal differences between the policies or model variants.

cs.LO↗

arXiv2025

Learning Algorithms for Verification of Markov Decision Processes

We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs). The primary goal of our techniques is to improve performance by avoiding an exhaustive exploration of the state space, instead focussing on particularly relevant areas of the system, guided by heuristics. Our work builds on the previous results of Br{á}zdil et al., significantly extending it as well as refining several details and fixing errors. The presented framework focuses on probabilistic reachability, which is a core problem in verification, and is instantiated in two distinct scenarios. The first assumes that full knowledge of the MDP is available, in particular precise transition probabilities. It performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP without knowing the exact transition dynamics. Here, we obtain probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. In particular, the latter is an extension of statistical model-checking (SMC) for unbounded properties in MDPs. In contrast to other related approaches, we do not restrict our attention to time-bounded (finite-horizon) or discounted properties, nor assume any particular structural properties of the MDP.

eess.SY↗

arXiv2025

Planning with Linear Temporal Logic Specifications: Handling Quantifiable and Unquantifiable Uncertainty

This work studies the planning problem for robotic systems under both quantifiable and unquantifiable uncertainty. The objective is to enable the robotic systems to optimally fulfill high-level tasks specified by Linear Temporal Logic (LTL) formulas. To capture both types of uncertainty in a unified modelling framework, we utilise Markov Decision Processes with Set-valued Transitions (MDPSTs). We introduce a novel solution technique for the optimal robust strategy synthesis of MDPSTs with LTL specifications. To improve efficiency, our work leverages limit-deterministic Büchi automata (LDBAs) as the automaton representation for LTL to take advantage of their efficient constructions. To tackle the inherent nondeterminism in MDPSTs, which presents a significant challenge for reducing the LTL planning problem to a reachability problem, we introduce the concept of a Winning Region (WR) for MDPSTs. Additionally, we propose an algorithm for computing the WR over the product of the MDPST and the LDBA. Finally, a robust value iteration algorithm is invoked to solve the reachability problem. We validate the effectiveness of our approach through a case study involving a mobile robot operating in the hexagonal world, demonstrating promising efficiency gains.

cs.RO↗

arXiv2024

Risk-Averse Certification of Bayesian Neural Networks

In light of the inherently complex and dynamic nature of real-world environments, incorporating risk measures is crucial for the robustness evaluation of deep learning models. In this work, we propose a Risk-Averse Certification framework for Bayesian neural networks called RAC-BNN. Our method leverages sampling and optimisation to compute a sound approximation of the output set of a BNN, represented using a set of template polytopes. To enhance robustness evaluation, we integrate a coherent distortion risk measure--Conditional Value at Risk (CVaR)--into the certification framework, providing probabilistic guarantees based on empirical distributions obtained through sampling. We validate RAC-BNN on a range of regression and classification benchmarks and compare its performance with a state-of-the-art method. The results show that RAC-BNN effectively quantifies robustness under worst-performing risky scenarios, and achieves tighter certified bounds and higher efficiency in complex tasks.

cs.LG↗

arXiv2024

Expectation vs. Reality: Towards Verification of Psychological Games

Game theory provides an effective way to model strategic interactions among rational agents. In the context of formal verification, these ideas can be used to produce guarantees on the correctness of multi-agent systems, with a diverse range of applications from computer security to autonomous driving. Psychological games (PGs) were developed as a way to model and analyse agents with belief-dependent motivations, opening up the possibility to model how human emotions can influence behaviour. In PGs, players' utilities depend not only on what actually happens (which strategies players choose to adopt), but also on what the players had expected to happen (their belief as to the strategies that would be played). Despite receiving much attention in fields such as economics and psychology, very little consideration has been given to their applicability to problems in computer science, nor to practical algorithms and tool support. In this paper, we start to bridge that gap, proposing methods to solve PGs and implementing them within PRISM-games, a formal verification tool for stochastic games. We discuss how to model these games, highlight specific challenges for their analysis and illustrate the usefulness of our approach on several case studies, including human behaviour in traffic scenarios.

cs.GT↗

arXiv2024

FAST: Boosting Uncertainty-based Test Prioritization Methods for Neural Networks via Feature Selection

Due to the vast testing space, the increasing demand for effective and efficient testing of deep neural networks (DNNs) has led to the development of various DNN test case prioritization techniques. However, the fact that DNNs can deliver high-confidence predictions for incorrectly predicted examples, known as the over-confidence problem, causes these methods to fail to reveal high-confidence errors. To address this limitation, in this work, we propose FAST, a method that boosts existing prioritization methods through guided FeAture SelecTion. FAST is based on the insight that certain features may introduce noise that affects the model's output confidence, thereby contributing to high-confidence errors. It quantifies the importance of each feature for the model's correct predictions, and then dynamically prunes the information from the noisy features during inference to derive a new probability vector for the uncertainty estimation. With the help of FAST, the high-confidence errors and correctly classified examples become more distinguishable, resulting in higher APFD (Average Percentage of Fault Detection) values for test prioritization, and higher generalization ability for model enhancement. We conduct extensive experiments to evaluate FAST across a diverse set of model structures on multiple benchmark datasets to validate the effectiveness, efficiency, and scalability of FAST compared to the state-of-the-art prioritization techniques.

cs.SE↗

arXiv2024

FullCert: Deterministic End-to-End Certification for Training and Inference of Neural Networks

Modern machine learning models are sensitive to the manipulation of both the training data (poisoning attacks) and inference data (adversarial examples). Recognizing this issue, the community has developed many empirical defenses against both attacks and, more recently, certification methods with provable guarantees against inference-time attacks. However, such guarantees are still largely lacking for training-time attacks. In this work, we present FullCert, the first end-to-end certifier with sound, deterministic bounds, which proves robustness against both training-time and inference-time attacks. We first bound all possible perturbations an adversary can make to the training data under the considered threat model. Using these constraints, we bound the perturbations' influence on the model's parameters. Finally, we bound the impact of these parameter changes on the model's prediction, resulting in joint robustness guarantees against poisoning and adversarial examples. To facilitate this novel certification paradigm, we combine our theoretical work with a new open-source library BoundFlow, which enables model training on bounded datasets. We experimentally demonstrate FullCert's feasibility on two datasets.

cs.LG↗

arXiv2024

Safe POMDP Online Planning among Dynamic Agents via Adaptive Conformal Prediction

Online planning for partially observable Markov decision processes (POMDPs) provides efficient techniques for robot decision-making under uncertainty. However, existing methods fall short of preventing safety violations in dynamic environments. This work presents a novel safe POMDP online planning approach that maximizes expected returns while providing probabilistic safety guarantees amidst environments populated by multiple dynamic agents. Our approach utilizes data-driven trajectory prediction models of dynamic agents and applies Adaptive Conformal Prediction (ACP) to quantify the uncertainties in these predictions. Leveraging the obtained ACP-based trajectory predictions, our approach constructs safety shields on-the-fly to prevent unsafe actions within POMDP online planning. Through experimental evaluation in various dynamic environments using real-world pedestrian trajectory data, the proposed approach has been shown to effectively maintain probabilistic safety guarantees while accommodating up to hundreds of dynamic agents.

cs.RO↗

arXiv2024

Point-Based Value Iteration for POMDPs with Neural Perception Mechanisms

The increasing trend to integrate neural networks and conventional software components in safety-critical settings calls for methodologies for their formal modelling, verification and correct-by-construction policy synthesis. We introduce neuro-symbolic partially observable Markov decision processes (NS-POMDPs), a variant of continuous-state POMDPs with discrete observations and actions, in which the agent perceives a continuous-state environment using a neural {\revise perception mechanism} and makes decisions symbolically. The perception mechanism classifies inputs such as images and sensor values into symbolic percepts, which are used in decision making. We study the problem of optimising discounted cumulative rewards for NS-POMDPs. Working directly with the continuous state space, we exploit the underlying structure of the model and the neural perception mechanism to propose a novel piecewise linear and convex representation (P-PWLC) in terms of polyhedra covering the state space and value vectors, and extend Bellman backups to this representation. We prove the convexity and continuity of value functions and present two value iteration algorithms that ensure finite representability. The first is a classical (exact) value iteration algorithm extending the $α$-functions of Porta {\em et al} (2006) to the P-PWLC representation for continuous-state spaces. The second is a point-based (approximate) method called NS-HSVI, which uses the P-PWLC representation and belief-value induced functions to approximate value functions from below and above for two types of beliefs, particle-based and region-based. Using a prototype implementation, we show the practical applicability of our approach on two case studies that employ (trained) ReLU neural networks as perception functions, by synthesising (approximately) optimal strategies.

eess.SY↗

arXiv2024

Strategy Synthesis for Zero-Sum Neuro-Symbolic Concurrent Stochastic Games

Neuro-symbolic approaches to artificial intelligence, which combine neural networks with classical symbolic techniques, are growing in prominence, necessitating formal approaches to reason about their correctness. We propose a novel modelling formalism called neuro-symbolic concurrent stochastic games (NS-CSGs), which comprise two probabilistic finite-state agents interacting in a shared continuous-state environment. Each agent observes the environment using a neural perception mechanism, which converts inputs such as images into symbolic percepts, and makes decisions symbolically. We focus on the class of NS-CSGs with Borel state spaces and prove the existence and measurability of the value function for zero-sum discounted cumulative rewards under piecewise-constant restrictions on the components of this class of models. To compute values and synthesise strategies, we present, for the first time, practical value iteration (VI) and policy iteration (PI) algorithms to solve this new subclass of continuous-state CSGs. These require a finite decomposition of the environment induced by the neural perception mechanisms of the agents and rely on finite abstract representations of value functions and strategies closed under VI or PI. First, we introduce a Borel measurable piecewise-constant (B-PWC) representation of value functions, extend minimax backups to this representation and propose a value iteration algorithm called B-PWC VI. Second, we introduce two novel representations for the value functions and strategies, constant-piecewise-linear (CON-PWL) and constant-piecewise-constant (CON-PWC) respectively, and propose Minimax-action-free PI by extending a recent PI method based on alternating player choices for finite state spaces to Borel state spaces, which does not require normal-form games to be solved.

cs.AI↗

arXiv2024

Partially Observable Stochastic Games with Neural Perception Mechanisms

Stochastic games are a well established model for multi-agent sequential decision making under uncertainty. In practical applications, though, agents often have only partial observability of their environment. Furthermore, agents increasingly perceive their environment using data-driven approaches such as neural networks trained on continuous data. We propose the model of neuro-symbolic partially-observable stochastic games (NS-POSGs), a variant of continuous-space concurrent stochastic games that explicitly incorporates neural perception mechanisms. We focus on a one-sided setting with a partially-informed agent using discrete, data-driven observations and another, fully-informed agent. We present a new method, called one-sided NS-HSVI, for approximate solution of one-sided NS-POSGs, which exploits the piecewise constant structure of the model. Using neural network pre-image analysis to construct finite polyhedral representations and particle-based representations for beliefs, we implement our approach and illustrate its practical applicability to the analysis of pedestrian-vehicle and pursuit-evasion scenarios.

cs.GT↗

arXiv2024

Learning Decision Policies with Instrumental Variables through Double Machine Learning

A common issue in learning decision-making policies in data-rich settings is spurious correlations in the offline dataset, which can be caused by hidden confounders. Instrumental variable (IV) regression, which utilises a key unconfounded variable known as the instrument, is a standard technique for learning causal relationships between confounded action, outcome, and context variables. Most recent IV regression algorithms use a two-stage approach, where a deep neural network (DNN) estimator learnt in the first stage is directly plugged into the second stage, in which another DNN is used to estimate the causal effect. Naively plugging the estimator can cause heavy bias in the second stage, especially when regularisation bias is present in the first stage estimator. We propose DML-IV, a non-linear IV regression method that reduces the bias in two-stage IV regressions and effectively learns high-performing policies. We derive a novel learning objective to reduce bias and design the DML-IV algorithm following the double/debiased machine learning (DML) framework. The learnt DML-IV estimator has strong convergence rate and $O(N^{-1/2})$ suboptimality guarantees that match those when the dataset is unconfounded. DML-IV outperforms state-of-the-art IV regression methods on IV regression benchmarks and learns high-performing policies in the presence of instruments.

cs.LG↗

arXiv2024

Automated Design of Linear Bounding Functions for Sigmoidal Nonlinearities in Neural Networks

The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification techniques offer provable guarantees for all robustness queries but struggle to scale beyond small neural networks. To overcome this computational intractability, incomplete verification methods often rely on convex relaxation to over-approximate the nonlinearities in neural networks. Progress in tighter approximations has been achieved for piecewise linear functions. However, robustness verification of neural networks for general activation functions (e.g., Sigmoid, Tanh) remains under-explored and poses new challenges. Typically, these networks are verified using convex relaxation techniques, which involve computing linear upper and lower bounds of the nonlinear activation functions. In this work, we propose a novel parameter search method to improve the quality of these linear approximations. Specifically, we show that using a simple search method, carefully adapted to the given verification problem through state-of-the-art algorithm configuration techniques, improves the average global lower bound by 25% on average over the current state of the art on several commonly used local robustness verification benchmarks.

cs.LG↗

arXiv2024

The Trembling-Hand Problem for LTLf Planning

Consider an agent acting to achieve its temporal goal, but with a "trembling hand". In this case, the agent may mistakenly instruct, with a certain (typically small) probability, actions that are not intended due to faults or imprecision in its action selection mechanism, thereby leading to possible goal failure. We study the trembling-hand problem in the context of reasoning about actions and planning for temporally extended goals expressed in Linear Temporal Logic on finite traces (LTLf), where we want to synthesize a strategy (aka plan) that maximizes the probability of satisfying the LTLf goal in spite of the trembling hand. We consider both deterministic and nondeterministic (adversarial) domains. We propose solution techniques for both cases by relying respectively on Markov Decision Processes and on Markov Decision Processes with Set-valued Transitions with LTLf objectives, where the set-valued probabilistic transitions capture both the nondeterminism from the environment and the possible action instruction errors from the agent. We formally show the correctness of our solution techniques and demonstrate their effectiveness experimentally through a proof-of-concept implementation.

cs.RO↗

arXiv2024

HSVI-based Online Minimax Strategies for Partially Observable Stochastic Games with Neural Perception Mechanisms

We consider a variant of continuous-state partially-observable stochastic games with neural perception mechanisms and an asymmetric information structure. One agent has partial information, with the observation function implemented as a neural network, while the other agent is assumed to have full knowledge of the state. We present, for the first time, an efficient online method to compute an $\varepsilon$-minimax strategy profile, which requires only one linear program to be solved for each agent at every stage, instead of a complex estimation of opponent counterfactual values. For the partially-informed agent, we propose a continual resolving approach which uses lower bounds, pre-computed offline with heuristic search value iteration (HSVI), instead of opponent counterfactual values. This inherits the soundness of continual resolving at the cost of pre-computing the bound. For the fully-informed agent, we propose an inferred-belief strategy, where the agent maintains an inferred belief about the belief of the partially-informed agent based on (offline) upper bounds from HSVI, guaranteeing $\varepsilon$-distance to the value of the game at the initial belief known to both agents.

cs.GT↗

arXiv2024

Provable Preimage Under-Approximation for Neural Networks (Full Version)

Neural network verification mainly focuses on local robustness properties, which can be checked by bounding the image (set of outputs) of a given input set. However, often it is important to know whether a given property holds globally for the input domain, and if not then for what proportion of the input the property is true. To analyze such properties requires computing preimage abstractions of neural networks. In this work, we propose an efficient anytime algorithm for generating symbolic under-approximations of the preimage of any polyhedron output set for neural networks. Our algorithm combines a novel technique for cheaply computing polytope preimage under-approximations using linear relaxation, with a carefully-designed refinement procedure that iteratively partitions the input region into subregions using input and ReLU splitting in order to improve the approximation. Empirically, we validate the efficacy of our method across a range of domains, including a high-dimensional MNIST classification task beyond the reach of existing preimage computation methods. Finally, as use cases, we showcase the application to quantitative verification and robustness analysis. We present a sound and complete algorithm for the former, which exploits our disjoint union of polytopes representation to provide formal guarantees. For the latter, we find that our method can provide useful quantitative information even when standard verifiers cannot verify a robustness property.

cs.SE↗

arXiv2023

STR-Cert: Robustness Certification for Deep Text Recognition on Deep Learning Pipelines and Vision Transformers

Robustness certification, which aims to formally certify the predictions of neural networks against adversarial inputs, has become an integral part of important tool for safety-critical applications. Despite considerable progress, existing certification methods are limited to elementary architectures, such as convolutional networks, recurrent networks and recently Transformers, on benchmark datasets such as MNIST. In this paper, we focus on the robustness certification of scene text recognition (STR), which is a complex and extensively deployed image-based sequence prediction problem. We tackle three types of STR model architectures, including the standard STR pipelines and the Vision Transformer. We propose STR-Cert, the first certification method for STR models, by significantly extending the DeepPoly polyhedral verification framework via deriving novel polyhedral bounds and algorithms for key STR model components. Finally, we certify and compare STR models on six datasets, demonstrating the efficiency and scalability of robustness certification, particularly for the Vision Transformer.

cs.CV↗

arXiv2023

Probabilistic Reach-Avoid for Bayesian Neural Networks

Model-based reinforcement learning seeks to simultaneously learn the dynamics of an unknown stochastic environment and synthesise an optimal policy for acting in it. Ensuring the safety and robustness of sequential decisions made through a policy in such an environment is a key challenge for policies intended for safety-critical scenarios. In this work, we investigate two complementary problems: first, computing reach-avoid probabilities for iterative predictions made with dynamical models, with dynamics described by Bayesian neural network (BNN); second, synthesising control policies that are optimal with respect to a given reach-avoid specification (reaching a "target" state, while avoiding a set of "unsafe" states) and a learned BNN model. Our solution leverages interval propagation and backward recursion techniques to compute lower bounds for the probability that a policy's sequence of actions leads to satisfying the reach-avoid specification. Such computed lower bounds provide safety certification for the given policy and BNN model. We then introduce control synthesis algorithms to derive policies maximizing said lower bounds on the safety probability. We demonstrate the effectiveness of our method on a series of control benchmarks characterized by learned BNN dynamics models. On our most challenging benchmark, compared to purely data-driven policies the optimal synthesis algorithm is able to provide more than a four-fold increase in the number of certifiable states and more than a three-fold increase in the average guaranteed reach-avoid probability.

cs.LG↗