Standard approaches for global optimization of non-convex functions, such as branch-and-bound, maintain partition trees to systematically prune the domain. The tree size grows exponentially in the number of dimensions. We propose new sampling-based methods for non-convex optimization that adapts Monte Carlo Tree Search (MCTS) to improve efficiency. Instead of the standard use of visitation count in Upper Confidence Bounds, we utilize numerical overapproximations of the objective as an uncertainty metric, and also take into account of sampled estimates of first-order and second-order information. The Monte Carlo tree in our approach avoids the usual fixed combinatorial patterns in growing the tree, and aggressively zooms into the promising regions, while still balancing exploration and exploitation. We evaluate the proposed algorithms on high-dimensional non-convex optimization benchmarks against competitive baselines and analyze the effects of the hyper parameters.

翻译：针对非凸函数的全局优化标准方法（如分支定界法）通过维护分区树来系统性地剪枝定义域，但树的大小随维度数量呈指数增长。我们提出基于采样的非凸优化新方法，通过自适应蒙特卡洛树搜索（MCTS）提升效率。不同于上置信界算法中标准化的访问计数，我们利用目标函数的数值上近似作为不确定性度量，同时考虑一阶和二阶信息的采样估计值。本方法中的蒙特卡洛树避免了传统树扩展中固定的组合模式，在平衡探索与利用的同时，激进地聚焦于有前景的区域。我们在高维非凸优化基准测试中，将所提算法与竞争基线进行对比评估，并分析了超参数的影响。