Regularization hyperparam tuning during training
As mentioned above you can try a couple of things, depending on which framework you are using and how you want to go with hyperparameter optimisation.
sklearn (with Keras wrappers):

GridSearchCV: slow but sure to find optimal hyperparams
RandomizedSearchCV: faster and almost as good as GridSearch

Keras (with Keras Tuner):

BayesianOptimization: tuning with Gaussian process
Hyperband: Variation of HyperBand algorithm (Li, Lisha, and Kevin Jamieson. Journal of Machine Learning Research 18 (2018): 1-52.)

Pytorch (with RayTune):

Population Based Training: trains a group of models (or agents) in parallel (https://deepmind.com/blog/population-based-training-neural-networks)
HyperBand: as above
ASHA:Compared to the original version of HyperBand, this implementation provides better parallelism and avoids straggler issues during elimination
Median Stopping Rule: implements the simple strategy of stopping a trial if its performance falls below the median of other trials at similar points in time.
FIFOScheduler: Simple scheduler that just runs trials in submission order