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.

Monte Carlo Tree Search can be used for automated theorem proving. Holophrasm is a neural theorem prover using MCTS combined with neural networks for the policy and the evaluation. In this paper we propose to improve the performance of the Holophrasm theorem prover using other game tree search algorithms.

This paper presents a new approach for controlling emotion in symbolic music generation with Monte Carlo Tree Search. We use Monte Carlo Tree Search as a decoding mechanism to steer the probability distribution learned by a language model towards a given emotion. At every step of the decoding process, we use Predictor Upper Confidence for Trees (PUCT) to search for sequences that maximize the average values of emotion and quality as given by an emotion classifier and a discriminator, respectively. We use a language model as PUCT's policy and a combination of the emotion classifier and the discriminator as its value function. To decode the next token in a piece of music, we sample from the distribution of node visits created during the search. We evaluate the quality of the generated samples with respect to human-composed pieces using a set of objective metrics computed directly from the generated samples. We also perform a user study to evaluate how human subjects perceive the generated samples' quality and emotion. We compare PUCT against Stochastic Bi-Objective Beam Search (SBBS) and Conditional Sampling (CS). Results suggest that PUCT outperforms SBBS and CS in almost all metrics of music quality and emotion.

The use of a policy and a heuristic function for guiding search can be quite effective in adversarial problems, as demonstrated by AlphaGo and its successors, which are based on the PUCT search algorithm. While PUCT can also be used to solve single-agent deterministic problems, it lacks guarantees on its search effort and it can be computationally inefficient in practice. Combining the A* algorithm with a learned heuristic function tends to work better in these domains, but A* and its variants do not use a policy. Moreover, the purpose of using A* is to find solutions of minimum cost, while we seek instead to minimize the search loss (e.g., the number of search steps). LevinTS is guided by a policy and provides guarantees on the number of search steps that relate to the quality of the policy, but it does not make use of a heuristic function. In this work we introduce Policy-guided Heuristic Search (PHS), a novel search algorithm that uses both a heuristic function and a policy and has theoretical guarantees on the search loss that relates to both the quality of the heuristic and of the policy. We show empirically on the sliding-tile puzzle, Sokoban, and a puzzle from the commercial game `The Witness' that PHS enables the rapid learning of both a policy and a heuristic function and compares favorably with A*, Weighted A*, Greedy Best-First Search, LevinTS, and PUCT in terms of number of problems solved and search time in all three domains tested.

The standard for Deep Reinforcement Learning in games, following Alpha Zero, is to use residual networks and to increase the depth of the network to get better results. We propose to improve mobile networks as an alternative to residual networks and experimentally show the playing strength of the networks according to both their width and their depth. We also propose a generalization of the PUCT search algorithm that improves on PUCT.