Related papers: Formally Verified Approximate Policy Iteration

Probabilistic model checkers like PRISM only check probabilistic systems of a fixed size. To guarantee the desired properties for an arbitrary size, mathematical analysis is necessary. We show for two case studies how this can be done in…

The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…

Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…

We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…

Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…

Automatic and efficient verification of multiplier designs, especially through a provably correct method, is a difficult problem. We show how to utilize a theorem prover, ACL2, to implement an efficient rewriting algorithm for multiplier…

In this paper we discuss $\l$-policy iteration, a method for exact and approximate dynamic programming. It is intermediate between the classical value iteration (VI) and policy iteration (PI) methods, and it is closely related to optimistic…

While policy-based reinforcement learning (RL) achieves tremendous successes in practice, it is significantly less understood in theory, especially compared with value-based RL. In particular, it remains elusive how to design a provably…

Formal verification of traditional algorithms are of great significance due to their wide application in state-of-the-art software. Timsort is a complicated and hybrid stable sorting algorithm, derived from merge sort and insertion sort.…

Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…

Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…

The use of autonomous vehicles in real-world applications is often precluded by the difficulty of providing safety guarantees for their complex controllers. The simulation-based testing of these controllers cannot deliver sufficient safety…

Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…

This paper presents a formal approach to specify and verify object-oriented programs written in the `programming to interfaces' paradigm. Besides the methods to be invoked by its clients, an interface also declares a set of abstract…

We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…

We present a system for interactive examination of learned security policies. It allows a user to traverse episodes of Markov decision processes in a controlled manner and to track the actions triggered by security policies. Similar to a…

We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…

Assurance cases are often required to certify critical systems. The use of formal methods in assurance can improve automation, increase confidence, and overcome errant reasoning. However, assurance cases can never be fully formalised, as…

To guarantee that machine learning models yield outputs that are not only accurate, but also robust, recent works propose formally verifying robustness properties of machine learning models. To be applicable to realistic safety-critical…

Training models through self-play alone (without any human data) has been a longstanding goal in AI, but its effectiveness for training large language models remains unclear, particularly in code generation where rewards based on unit tests…