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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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We present S+t-SNE, an adaptation of the t-SNE algorithm designed to handle infinite data streams. The core idea behind S+t-SNE is to update the t-SNE embedding incrementally as new data arrives, ensuring scalability and adaptability to handle streaming scenarios. By selecting the most important points at each step, the algorithm ensures scalability while keeping informative visualisations. By employing a blind method for drift management, the algorithm adjusts the embedding space, which facilitates the visualisation of evolving data dynamics. Our experimental evaluations demonstrate the effectiveness and efficiency of S+t-SNE, whilst highlighting its ability to capture patterns in a streaming scenario. We hope our approach offers researchers and practitioners a real-time tool for understanding and interpreting high-dimensional data.

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