I don't know if this is what you'd call Hot, but I've been hearing talk about using Neural Networks for Bermudan and American options pricing in high dimension.
a few papers :
Kohler, M. , Krzyzak, A. and Todorovic, N. (2010), Pricing Of High-Dimensional American Options By Neural Networks. Mathematical Finance, Vol. 20. MC approach with NN to estimate the continuation values; Consider at most 5-d basket.
Ludkovski M., (2018). Kriging Metamodels and Experimental Design for Bermudan Option Pricing. Journal of Computational Finance, Vol. 22. Use of GPR and MC approach; Consider at most 5-d basket.
Becker S., Cheridito P., and Jentzen A., (2019) Deep Optimal Stopping. Journal of Machine Learning Research, Vol. 20. Deep learning method for optimal stopping problems; Consider at most 500-d basket.
Lapeyre, B., Lelong, J. (2019). Neural Network Regression for Bermudan Option Pricing. arXiv preprint arXiv:1907.06474. Prove the convergence of the Longstaff-Schwartz algorithm when the LS regression is replaced by NN.