As a branch of quantum machine learning, quantum reinforcement learning (QRL) aims to solve complex sequential decision-making problems more efficiently and effectively than its classical counterpart by exploiting quantum resources. However, in the noisy intermediate-scale quantum (NISQ) era, its realization is challenged by the ubiquitous noise-induced decoherence. Here, we propose a noise-resilient QRL scheme for a quantum eigensolver with a two-level system as an agent. By investigating the non-Markovian decoherence effect on the QRL for solving the eigenstates of the agent-environment interaction Hamiltonian, we find that the formation of a bound state in the energy spectrum of the total agent-noise system restores the QRL performance to that in the noiseless case. Providing a universal physical mechanism to suppress the decoherence effect on quantum machine learning, our result lays the foundation for designing NISQ algorithms and offers a guideline for their practical implementation.