Monte-Carlo Tree Search (MCTS) typically uses multi-armed bandit (MAB) strategies designed to minimize cumulative regret, such as UCB1, as its selection strategy. However, in the root node of the search tree, it is more sensible to minimize simple regret. Previous work has proposed using Sequential Halving as selection strategy in the root node, as, in theory, it performs better with respect to simple regret. However, Sequential Halving requires a budget of iterations to be predetermined, which is often impractical. This paper proposes an anytime version of the algorithm, which can be halted at any arbitrary time and still return a satisfactory result, while being designed such that it approximates the behavior of Sequential Halving. Empirical results in synthetic MAB problems and ten different board games demonstrate that the algorithm's performance is competitive with Sequential Halving and UCB1 (and their analogues in MCTS).

In this paper, we investigate the problem of pure exploration in the context of multi-armed bandits, with a specific focus on scenarios where arms are pulled in fixed-size batches. Batching has been shown to enhance computational efficiency, but it can potentially lead to a degradation compared to the original sequential algorithm's performance due to delayed feedback and reduced adaptability. We introduce a simple batch version of the Sequential Halving (SH) algorithm (Karnin et al., 2013) and provide theoretical evidence that batching does not degrade the performance of the original algorithm under practical conditions. Furthermore, we empirically validate our claim through experiments, demonstrating the robust nature of the SH algorithm in fixed-size batch settings.

Monte Carlo Tree Search and Monte Carlo Search have good results for many combinatorial problems. In this paper we propose to use Monte Carlo Search to design mathematical expressions that are used as exploration terms for Monte Carlo Tree Search algorithms. The optimized Monte Carlo Tree Search algorithms are PUCT and SHUSS. We automatically design the PUCT and the SHUSS root exploration terms. For small search budgets of 32 evaluations the discovered root exploration terms make both algorithms competitive with usual PUCT.