For the L-BFGS optimizer, what does the parameter "maxiter" really represent ?

[rapham]

Hello everyone,

I am using the L-BFGS optimizer to solve a forward PDE problem. I am not very familiar with this algorithm, but I wondered what the maxiter parameter really represents. Indeed, I found some differences between the meaning it has in deepxde source code and in the backends documentations:

• deepxde source code: it controls the number of times the method optim.step() will be called:

def _train_pytorch_lbfgs(self):
        prev_n_iter = 0
        while prev_n_iter < optimizers.LBFGS_options["maxiter"]:
            self.callbacks.on_epoch_begin()
            self.callbacks.on_batch_begin()

            self.train_state.set_data_train(
                *self.data.train_next_batch(self.batch_size)
            )
            self._train_step(
                self.train_state.X_train,
                self.train_state.y_train,
                self.train_state.train_aux_vars,
            )

            n_iter = self.opt.state_dict()["state"][0]["n_iter"]
            if prev_n_iter == n_iter:
                # Converged
                break

            self.train_state.epoch += n_iter - prev_n_iter
            self.train_state.step += n_iter - prev_n_iter
            prev_n_iter = n_iter
            self._test()

            self.callbacks.on_batch_end()
            self.callbacks.on_epoch_end()

            if self.stop_training:
                break

• Pytorch documentation: maximal number of iterations per optimization step
• Tensorflow documentation: the maximum number of iterations for L-BFGS updates.
• Paddle documentation: the maximum number of minimization iterations

It seems to me in deepxde maxiter is used to control the number of iterations typically performed on the data (per batch or per epoch) whereas for the backends, it refers to the number of iterations of the L-BFGS algorithm to perform for one step of the optimization.

What do you think ? Thanks in advance for your help !

[lululxvi]

maxiter in DeepXDE means the same as in Pytorch and TensorFlow.

[rapham]

Hi @lululxvi,

First, thank you for your answer.

But then, it seems to be max_iter should only be used as an internal parameter of the backends, and not to control the number of iterations typically performed on the data.

If this example is right, you have to implement two distinct parameters, one for the L-BFGS inner operation and one to control how many times you want to call it on the data.

Does that sound right ?

[lululxvi]

Can you be more specific? Maybe a PR makes it easier to discuss.