The field of Monte Carlo methods is moving towards more efficient and innovative sampling techniques. Recent developments have focused on improving the accuracy and speed of sampling from complex distributions, with a particular emphasis on posterior sampling and combinatorial optimization problems. One notable direction is the use of reinforcement learning to optimize nonlocal Monte Carlo algorithms, which has shown promising results in escaping suboptimal basins of attraction and sampling high-quality solutions. Another area of research is the development of novel frameworks for training neural samplers, which can accurately sample from target distributions despite high problem dimensions. Noteworthy papers include:

• Efficient Approximate Posterior Sampling with Annealed Langevin Monte Carlo, which presents a polynomial-time algorithm for approximate posterior sampling.
• Nonlocal Monte Carlo via Reinforcement Learning, which demonstrates the effectiveness of reinforcement learning in optimizing nonlocal Monte Carlo algorithms.
• MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control, which proposes a novel framework for training discrete neural samplers.