Trainability issues in quantum policy gradients

This research explores the trainability of Parameterized Quantum circuit-based policies in Reinforcement Learning, an area that has recently seen a surge in empirical exploration. While some studies suggest improved sample complexity using quantum gradient estimation, the efficient trainability of these policies remains an open question. Our findings reveal significant challenges, including standard Barren Plateaus with exponentially small gradients and gradient explosion. These phenomena depend on the type of basis-state partitioning and mapping these partitions onto actions. For a polynomial number of actions, a trainable window can be ensured with a polynomial number of measurements if a contiguous-like partitioning of basis-states is employed. These results are empirically validated in a multi-armed bandit environment.

On Quantum Natural Policy Gradients

This research delves into the role of the quantum Fisher Information Matrix (FIM) in enhancing the performance of Parameterized Quantum Circuit (PQC)-based reinforcement learning agents. While previous studies have highlighted the effectiveness of PQC-based policies preconditioned with the quantum FIM in contextual bandits, its impact in broader reinforcement learning contexts, such as Markov Decision Processes, is less clear. Through a detailed analysis of L\"owner inequalities between quantum and classical FIMs, this study uncovers the nuanced distinctions and implications of using each type of FIM. Our results indicate that a PQC-based agent using the quantum FIM without additional insights typically incurs a larger approximation error and does not guarantee improved performance compared to the classical FIM. Empirical evaluations in classic control benchmarks suggest even though quantum FIM preconditioning outperforms standard gradient ascent, in general it is not superior to classical FIM preconditioning.