Quantum-Inspired Neural Networks for Reinforcement Learning with Delayed Rewards

Abstract

Reinforcement learning (RL) faces significant challenges when dealing with environments characterized by delayed rewards and sparse feedback. Traditional RL algorithms often struggle to efficiently learn optimal policies in such scenarios due to the difficulty in associating actions with their eventual consequences. This research proposes a novel approach to RL leveraging quantum-inspired concepts – superposition and entanglement – to improve exploration and exploitation within the state space. The core idea involves designing a neural network architecture where nodes exist in a superposition of states, allowing the agent to concurrently evaluate multiple actions. Furthermore, entangled node interactions are implemented to facilitate the rapid and efficient transfer of information across the network, effectively addressing the problem of delayed rewards. We demonstrate, theoretically and through a conceptual framework, the potential benefits of this approach, highlighting its capacity to improve learning speed and robustness in complex RL environments. The network architecture is defined as follows: Let $N = (n_1, n_2, ..., n_K)$ represent the neural network, where $n_i$ denotes the i-th node. Each node $n_i$ is associated with a state vector $s_i = (s_{i1}, s_{i2}, ..., s_{id})$ and an associated potential $V_i$. The superposition state of node $n_i$ is denoted as $|n_i\rangle = \alpha_i |0\rangle + \beta_i |1\rangle$, where $\alpha_i$ and $\beta_i$ are complex amplitudes. Entanglement is represented by a correlation function $C(n_i, n_j)$ which quantifies the degree of interconnectedness between nodes $n_i$ and $n_j$. The learning process involves updating the node potentials based on the expected future reward, considering the superposition state and entanglement interactions. The central focus is on the theoretical framework and the design principles, rather than a fully realized experimental implementation.