Abstract
This research addresses the trainability of Parameterized Quantum Circuit-based Softmax policies in Reinforcement Learning. We assess the trainability of these policies by examining the scaling of the expected value of the partial derivative of the log policy objective function. Here, we assume the hardware-efficient ansatz with blocks forming local 2-designs. In this setting, we show that if each expectation value representing the action's numerical preference is composed of a global observable, it leads to exponentially vanishing gradients. In contrast, for n-qubit systems, if the observables are log(n)-local, the gradients vanish polynomially with the number of qubits provided O(log n) depth. We also show that the expectation of the gradient of the log policy objective depend on the entire action space. Thus, even though global observables lead to concentration, the gradient signal can still be propagated in the presence of at least a single local observable. We validate the theoretical predictions in a series of ansatze and evaluate the performance of local and global observables in a multi-armed bandit setting.

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This paper reports on the development and validation of a formal model for an automotive adaptive exterior lights system (ELS) with multiple variants in Alloy 6, which is the most recent version of the Alloy lightweight formal specification language that supports mutable relations and temporal logic. We explore different strategies to address variability, one in pure Alloy and another through an annotative language extension. We then show how Alloy and its Analyzer can be used to validate systems of this nature, namely by checking that the reference scenarios are admissible, and to automatically verify whether the established requirements hold. A prototype was developed to translate the provided validation sequences into Alloy and back to further automate the validation process. The resulting ELS model was validated against the provided validation sequences and verified for most of requirements for all variants.

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