arXiv subjects

Jan Křetínský

Publications and source records attributed to Jan Křetínský.

At least 19 recordsLinked to original sources

arXiv2026

FoSeRL: Formal Sequential Robustness Certification for Reinforcement Learning Policies

Even a few action perturbations can substantially degrade the performance of a deployed decision policy. Certifying the resulting return loss is challenging in stochastic environments, where returns vary even without an attack. We introduce FoSeRL, a framework for certifying deployed RL policies against precommitted, temporally sparse action attacks. The deployed policy is unchanged, with no smoothing or retraining. Certification requires a resettable simulator supporting shared randomness and independent one-step successor queries, but no analytical dynamics model. FoSeRL certifies that an attacked episode loses no more than a prescribed amount of return relative to the same episode unattacked, with at least a target probability and at a user-specified confidence level. Both runs share the initial state and randomness, so the measured loss reflects the attack, not the episode; carrying the running return gap as a state coordinate makes it the terminal value, reducing trajectory-level certification to terminal safety. Time-dependent barrier conditions on the augmented state bound the terminal failure probability: satisfied exactly, they certify every admissible precommitted attack; learned from sampled trajectories and verified on held-out data, they certify the same guarantee under a specified attack-episode setting. Across six stochastic continuous-control environments and three RL policy families (TD3, SAC, and PPO), FoSeRL certifies non-trivial cardinality--magnitude robustness frontiers, achieves substantially larger certified budgets than policy smoothing, and reveals marked robustness differences among policies with comparable nominal performance.

cs.LG↗

arXiv2026

Robust Risk Under Evolving Uncertainty: A Wasserstein Counterpart of the Entropic Value-at-Risk

An agent still learning its environment should be cautious while ignorant and bold once confident. The entropic value-at-risk captures this through a robust-optimization identity---a confidence level fixes the radius of a relative-entropy ball of alternative models---but that ball cannot reach catastrophes the nominal deems impossible, precisely what a safe agent must hedge. We instead use an optimal-transport ball and study the coherent risk measure it induces, the Wasserstein entropic value-at-risk. It has a variational dual mirroring the entropic formula (an inverse temperature becomes a transport price), occupies a definite place in the risk hierarchy, and provably accounts for the reachable catastrophes the entropic measure ignores; we verify both dualities numerically. Driving the transport radius by belief entropy then yields a closed-form robust dynamic-programming operator whose caution contracts as the belief sharpens, with a certified safety sandwich and a sharp safety switch.

cs.AI↗

arXiv2026

dtControl2+$\varepsilon$: Trading Optimality for Explainability in MDPs via Decision Trees

Over the past decade, decision trees have been used to represent controllers (a.k.a. policies) in an explainable way, with dtControl2 as a current state-of-the-art tool. However, for systems that are large or have many corner cases, even such representations tend to be too complex and not human-comprehensible. Unfortunately, reducing the size of the decision tree is not straightforward, as missing just a single crucial case might result in an incorrect controller. We tackle this issue in the setting of Markov decision processes, extending dtControl2 by "$\varepsilon$" functionality: Given an allowed imprecision $\varepsilon \geq 0$, we construct a smaller decision tree, distilling the essence of the controller, while still guaranteeing its $\varepsilon$-optimality. This enables us to provide tunably simpler explanations, omitting a controllable amount of detail. Our tool constructs decision trees that are orders of magnitude smaller than the state of the art.

cs.AI↗

arXiv2026

Explainably Safe Reinforcement Learning

Trust in a decision-making system requires both safety guarantees and the ability to interpret and understand its behavior. This is particularly important for learned systems, whose decision-making processes are often highly opaque. Shielding is a prominent model-based technique for enforcing safety in reinforcement learning. However, because shields are automatically synthesized using rigorous formal methods, their decisions are often similarly difficult for humans to interpret. Recently, decision trees became customary to represent controllers and policies. However, since shields are inherently non-deterministic, their decision tree representations become too large to be explainable in practice. To address this challenge, we propose a novel approach for explainable safe RL that enhances trust by providing human-interpretable explanations of the shield's decisions. Our method represents the shielding policy as a hierarchy of decision trees, offering top-down, case-based explanations. At design time, we use a world model to analyze the safety risks of executing actions in given states. Based on this analysis, we construct both the shield and a high-level decision tree that classifies states into risk categories (safe, critical, dangerous, unsafe), explaining why a situation may be safety-critical. At runtime, we generate localized decision trees that explain which actions are allowed and why others are deemed unsafe. Our method facilitates explainability of the safety aspect in safe-by-shielding reinforcement learning, requires no additional information beyond what is already used for shielding, incurs minimal overhead, and integrates readily into existing shielded RL pipelines. In our experiments, we compute explanations using decision trees that are several orders of magnitude smaller than the original shield.

cs.LG↗

arXiv2026

SemML 2.0: Synthesizing Controllers for LTL

Synthesizing a reactive system from specifications given in linear temporal logic (LTL) is a classical problem, finding its applications in safety-critical systems design. These systems are typically represented using either Mealy machines or AIGER circuits. We present the second version of SemML, which outperforms all state-of-the-art tools for finding either solution. Aside from implementing the classical automata-theoretic approach, our tool utilizes partial exploration and machine-learning guidance for obtaining solutions efficiently, and numerous heuristics and improvements of classic algorithms for extracting small representations of these solutions. We evaluate our tool against the existing state-of-the-art tools (in particular Strix, LtlSynt, and the previous version of SemML) on the dataset of the synthesis competition SYNTCOMP. We show that we solve significantly more instances and do so much faster than other tools, while maintaining state-of-the-art solution quality.

cs.AI↗

arXiv2026

Logic of Fuzzy Paths

We introduce a new family of temporal logics intended for specifications in motion planning (MP). It builds upon the signal temporal logic (STL), which is a linear-time logic over real-valued signals that possess quantitative semantics and thus became popular in the areas of cyber-physical systems, robotics, and specifically robot MP. However, in contrast to STL, the proposed logic works with paths as first-class citizens, separating the concerns of geometry and of logic. This in turn leads to simpler and more understandable formulae, and a more refined notion of satisfaction being able to reflect also preferences over behaviours. Technically, the logic is built on fuzzy, time-varying signal constraints. As a consequence of this expressivity, it is (i) more usable for human-given specifications in MP and (ii) more amenable to learning specifications from demonstrations than other logics. The former is important for the traditional style of verification in robot MP; the latter is becoming recognized as crucial for mining data-given tasks and controller synthesis in human-aware MP. We expose the advantages of our proposed logic on examples and show the versatility and flexibility of the framework on a number of scenarios. Finally, we give a learning algorithm with a prototype implementation and discuss the possibilities of model checking and monitoring.

cs.LO↗

arXiv2026

Talking with Verifiers: Automatic Specification Generation for Neural Network Verification

Neural network verification tools currently support only a narrow class of specifications, typically expressed as low-level constraints over raw inputs and outputs. This limitation significantly hinders their adoption and practical applicability across diverse application domains where correctness requirements are naturally expressed at a higher semantic level. This challenge is rooted in the inherent nature of deep neural networks, which learn internal representations that lack an explicit mapping to human-understandable features. To address this, we bridge this gap by introducing a novel component to the verification pipeline, making existing verification tools applicable to a broader range of domains and specification styles. Our framework enables users to formulate specifications in natural language, which are then automatically analyzed and translated into formal verification queries compatible with state-of-the-art neural network verifiers. We evaluate our approach on both structured and unstructured datasets, demonstrating that it successfully verifies complex semantic specifications that were previously inaccessible. Our results show that this translation process maintains high fidelity to user intent while incurring low computational overhead, thereby substantially extending the applicability of formal DNN verification to real-world, high-level requirements.

cs.LG↗

arXiv2025

Stopping Criteria for Value Iteration on Concurrent Stochastic Reachability and Safety Games

We consider two-player zero-sum concurrent stochastic games (CSGs) played on graphs with reachability and safety objectives. These include degenerate classes such as Markov decision processes or turn-based stochastic games, which can be solved by linear or quadratic programming; however, in practice, value iteration (VI) outperforms the other approaches and is the most implemented method. Similarly, for CSGs, this practical performance makes VI an attractive alternative to the standard theoretical solution via the existential theory of reals. VI starts with an under-approximation of the sought values for each state and iteratively updates them, traditionally terminating once two consecutive approximations are $ε$-close. However, this stopping criterion lacks guarantees on the precision of the approximation, which is the goal of this work. We provide bounded (a.k.a. interval) VI for CSGs: it complements standard VI with a converging sequence of over-approximations and terminates once the over- and under-approximations are $ε$-close.

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↗

arXiv2024

Gaussian-Based and Outside-the-Box Runtime Monitoring Join Forces

Since neural networks can make wrong predictions even with high confidence, monitoring their behavior at runtime is important, especially in safety-critical domains like autonomous driving. In this paper, we combine ideas from previous monitoring approaches based on observing the activation values of hidden neurons. In particular, we combine the Gaussian-based approach, which observes whether the current value of each monitored neuron is similar to typical values observed during training, and the Outside-the-Box monitor, which creates clusters of the acceptable activation values, and, thus, considers the correlations of the neurons' values. Our experiments evaluate the achieved improvement.

cs.LG↗

arXiv2024

stl2vec: Semantic and Interpretable Vector Representation of Temporal Logic

Integrating symbolic knowledge and data-driven learning algorithms is a longstanding challenge in Artificial Intelligence. Despite the recognized importance of this task, a notable gap exists due to the discreteness of symbolic representations and the continuous nature of machine-learning computations. One of the desired bridges between these two worlds would be to define semantically grounded vector representation (feature embedding) of logic formulae, thus enabling to perform continuous learning and optimization in the semantic space of formulae. We tackle this goal for knowledge expressed in Signal Temporal Logic (STL) and devise a method to compute continuous embeddings of formulae with several desirable properties: the embedding (i) is finite-dimensional, (ii) faithfully reflects the semantics of the formulae, (iii) does not require any learning but instead is defined from basic principles, (iv) is interpretable. Another significant contribution lies in demonstrating the efficacy of the approach in two tasks: learning model checking, where we predict the probability of requirements being satisfied in stochastic processes; and integrating the embeddings into a neuro-symbolic framework, to constrain the output of a deep-learning generative model to comply to a given logical specification.

cs.AI↗

arXiv2024

Tools at the Frontiers of Quantitative Verification

The analysis of formal models that include quantitative aspects such as timing or probabilistic choices is performed by quantitative verification tools. Broad and mature tool support is available for computing basic properties such as expected rewards on basic models such as Markov chains. Previous editions of QComp, the comparison of tools for the analysis of quantitative formal models, focused on this setting. Many application scenarios, however, require more advanced property types such as LTL and parameter synthesis queries as well as advanced models like stochastic games and partially observable MDPs. For these, tool support is in its infancy today. This paper presents the outcomes of QComp 2023: a survey of the state of the art in quantitative verification tool support for advanced property types and models. With tools ranging from first research prototypes to well-supported integrations into established toolsets, this report highlights today's active areas and tomorrow's challenges in tool-focused research for quantitative verification.

cs.LO↗

arXiv2024

MULTIGAIN 2.0: MDP controller synthesis for multiple mean-payoff, LTL and steady-state constraints

We present MULTIGAIN 2.0, a major extension to the controller synthesis tool MULTIGAIN, built on top of the probabilistic model checker PRISM. This new version extends MULTIGAIN's multi-objective capabilities, by allowing for the formal verification and synthesis of controllers for probabilistic systems with multi-dimensional long-run average reward structures, steady-state constraints, and linear temporal logic properties. Additionally, MULTIGAIN 2.0 can modify the underlying linear program to prevent unbounded-memory and other unintuitive solutions and visualizes Pareto curves, in the two- and three-dimensional cases, to facilitate trade-off analysis in multi-objective scenarios.

cs.AI↗

arXiv2023

Syntactic vs Semantic Linear Abstraction and Refinement of Neural Networks

Abstraction is a key verification technique to improve scalability. However, its use for neural networks is so far extremely limited. Previous approaches for abstracting classification networks replace several neurons with one of them that is similar enough. We can classify the similarity as defined either syntactically (using quantities on the connections between neurons) or semantically (on the activation values of neurons for various inputs). Unfortunately, the previous approaches only achieve moderate reductions, when implemented at all. In this work, we provide a more flexible framework where a neuron can be replaced with a linear combination of other neurons, improving the reduction. We apply this approach both on syntactic and semantic abstractions, and implement and evaluate them experimentally. Further, we introduce a refinement method for our abstractions, allowing for finding a better balance between reduction and precision.

cs.LO↗

arXiv2023

Stopping Criteria for Value Iteration on Stochastic Games with Quantitative Objectives

A classic solution technique for Markov decision processes (MDP) and stochastic games (SG) is value iteration (VI). Due to its good practical performance, this approximative approach is typically preferred over exact techniques, even though no practical bounds on the imprecision of the result could be given until recently. As a consequence, even the most used model checkers could return arbitrarily wrong results. Over the past decade, different works derived stopping criteria, indicating when the precision reaches the desired level, for various settings, in particular MDP with reachability, total reward, and mean payoff, and SG with reachability. In this paper, we provide the first stopping criteria for VI on SG with total reward and mean payoff, yielding the first anytime algorithms in these settings. To this end, we provide the solution in two flavours: First through a reduction to the MDP case and second directly on SG. The former is simpler and automatically utilizes any advances on MDP. The latter allows for more local computations, heading towards better practical efficiency. Our solution unifies the previously mentioned approaches for MDP and SG and their underlying ideas. To achieve this, we isolate objective-specific subroutines as well as identify objective-independent concepts. These structural concepts, while surprisingly simple, form the very essence of the unified solution.

cs.AI↗

arXiv2022

Algebraically Explainable Controllers: Decision Trees and Support Vector Machines Join Forces

Recently, decision trees (DT) have been used as an explainable representation of controllers (a.k.a. strategies, policies, schedulers). Although they are often very efficient and produce small and understandable controllers for discrete systems, complex continuous dynamics still pose a challenge. In particular, when the relationships between variables take more complex forms, such as polynomials, they cannot be obtained using the available DT learning procedures. In contrast, support vector machines provide a more powerful representation, capable of discovering many such relationships, but not in an explainable form. Therefore, we suggest to combine the two frameworks in order to obtain an understandable representation over richer, domain-relevant algebraic predicates. We demonstrate and evaluate the proposed method experimentally on established benchmarks.

cs.LG↗

arXiv2022

Optimistic and Topological Value Iteration for Simple Stochastic Games

While value iteration (VI) is a standard solution approach to simple stochastic games (SSGs), it suffered from the lack of a stopping criterion. Recently, several solutions have appeared, among them also "optimistic" VI (OVI). However, OVI is applicable only to one-player SSGs with no end components. We lift these two assumptions, making it available to general SSGs. Further, we utilize the idea in the context of topological VI, where we provide an efficient precise solution. In order to compare the new algorithms with the state of the art, we use not only the standard benchmarks, but we also design a random generator of SSGs, which can be biased towards various types of models, aiding in understanding the advantages of different algorithms on SSGs.

cs.GT↗

arXiv2022

Satisfiability Bounds for $ω$-Regular Properties in Bounded-Parameter Markov Decision Processes

We consider the problem of computing minimum and maximum probabilities of satisfying an $ω$-regular property in a bounded-parameter Markov decision process (BMDP). BMDP arise from Markov decision processes (MDP) by allowing for uncertainty on the transition probabilities in the form of intervals where the actual probabilities are unknown. $ω$-regular languages form a large class of properties, expressible as, e.g., Rabin or parity automata, encompassing rich specifications such as linear temporal logic. In a BMDP the probability to satisfy the property depends on the unknown transitions probabilities as well as on the policy. In this paper, we compute the extreme values. This solves the problem specifically suggested by Dutreix and Coogan in CDC 2018, extending their results on interval Markov chains with no adversary. The main idea is to reinterpret their work as analysis of interval MDP and accordingly the BMDP problem as analysis of an $ω$-regular stochastic game, where a solution is provided. This method extends smoothly further to bounded-parameter stochastic games.

cs.LO↗