  Autonomous quantum error correction (AQEC) protects logical qubits by
engineered dissipation and thus circumvents the necessity of frequent,
error-prone measurement-feedback loops. Bosonic code spaces, where
single-photon loss represents the dominant source of error, are promising
candidates for AQEC due to their flexibility and controllability. While
existing proposals have demonstrated the in-principle feasibility of AQEC with
bosonic code spaces, these schemes are typically based on the exact
implementation of the Knill-Laflamme conditions and thus require the
realization of Hamiltonian distances $d\geq 2$. Implementing such Hamiltonian
distances requires multiple nonlinear interactions and control fields,
rendering these schemes experimentally challenging. Here, we propose a bosonic
code for approximate AQEC by relaxing the Knill-Laflamme conditions. Using
reinforcement learning (RL), we identify the optimal bosonic set of codewords
(denoted here by RL code), which, surprisingly, is composed of the Fock states
$\vert 2\rangle$ and $\vert 4\rangle$. As we show, the RL code, despite its
approximate nature, successfully suppresses single-photon loss, reducing it to
an effective dephasing process that well surpasses the break-even threshold. It
may thus provide a valuable building block toward full error protection. The
error-correcting Hamiltonian, which includes ancilla systems that emulate the
engineered dissipation, is entirely based on the Hamiltonian distance $d=1$,
significantly reducing model complexity. Single-qubit gates are implemented in
the RL code with a maximum distance $d_g=2$.
