In this paper, a collection of value-based quantum reinforcement learning algorithms are introduced which use Grover’s algorithm to update the policy, which is stored as a superposition of qubits associated with each possible action, and their parameters are explored. These algorithms may be grouped in two classes, one class which uses value functions (V(s)) and new class which uses action value functions (Q(s,a)). The new (Q(s,a))-based quantum algorithms are found to converge faster than V(s)-based algorithms, and in general the quantum algorithms are found to converge in fewer iterations than their classical counterparts, netting larger returns during training. This is due to fact that the (Q(s,a)) algorithms are more precise than those based on V(s), meaning that updates are incorporated into the value function more efficiently. This effect is also enhanced by the observation that the Q(s,a)-based algorithms may be trained with higher learning rates. These algorithms are then extended by adding multiple value functions, which are observed to allow larger learning rates and have improved convergence properties in environments with stochastic rewards, the latter of which is further improved by the probabilistic nature of the quantum algorithms. Finally, the quantum algorithms were found to use less CPU time than their classical counterparts overall, meaning that their benefits may be realized even without a full quantum computer.
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