Fig. 1. Diagram of the ideal QOC

Fig. 2. Diagram of optimization of the additional driving field by reinforcement learning

Fig. 3. Comparison of energy cost and output work in the optimization additional driving and free evolution schemes.(a) Energy cost $〈C_{\mathrm{t}\mathrm{o}\mathrm{t}}〉$ and irreversible work $〈W_{\mathrm{i}\mathrm{r}\mathrm{r}}〉$ ; (b) Output work $W_{\mathrm{e}\mathrm{d}}^{\mathrm{t}\mathrm{o}\mathrm{t}}$ and $W_{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}}^{\mathrm{t}\mathrm{o}\mathrm{t}}$

Fig. 4. Comparison of performance of QOC of the optimization additional driving and free evolution schemes.(a) Power $P_{\mathrm{e}\mathrm{d}}$ and $P_{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}}$ ; (b) Efficiency ${\eta }_{\mathrm{e}\mathrm{d}}$ and ${\eta }_{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}}$

Fig. 5. Optimization distribution of additional driving field with $\tau =\mathrm{18}$. (a) $f_{\mathrm{e}\mathrm{d}}^{\mathrm{e}\mathrm{x}\mathrm{p}}$ in expansion process; (b) $f_{\mathrm{e}\mathrm{d}}^{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}$ in compression process