relative_epsilon for entropic Gromov-Wasserstein solver

[theouscidda6]

Suppose we solve the entropic regularized Gromov-Wasserstein problem for two cost matrices $C$ and $C'$, with regularization strength $\varepsilon$ and weights $a,b$. Then, each iteration of the algorithm updates the coupling via ((http://proceedings.mlr.press/v48/peyre16.pdf, Eq. 9):
$$P^{t+1} \leftarrow \mathrm{Sinkhorn}(\mathcal{L}(C, C') \otimes P^t, a, b, \varepsilon)$$

Is there a feature to choose the $\varepsilon$ of each iteration relatively to $\mathcal{L}(C, C') \otimes P^t$? So that we perform for instance $P^{t+1} \leftarrow \mathrm{Sinkhorn}(\mathcal{L}(C, C') \otimes P^t, a, b, \varepsilon_t)$ where $\varepsilon_t =\varepsilon_0 \cdot \mathrm{mean}(\mathcal{L}(C, C') \otimes P^t)$ where $\varepsilon_0$ is passed while instantiating the solver.