# Convex Regularization in Monte-Carlo Tree Search Source: [Convex Regularization in Monte-Carlo Tree Search]() Collection index: [llms.txt]() Data updated: 2025-10-25T22:56:51.523Z Authors: Tuan Dam, Carlo D'Eramo, Jan Peters, Joni Pajarinen Published: 2020-07-01T11:29:08.000Z ## Abstract Monte-Carlo planning and Reinforcement Learning (RL) are essential to sequential decision making. The recent AlphaGo and AlphaZero algorithms have shown how to successfully combine these two paradigms in order to solve large scale sequential decision problems. These methodologies exploit a variant of the well-known UCT algorithm to trade off exploitation of good actions and exploration of unvisited states, but their empirical success comes at the cost of poor sample-efficiency and high computation time. In this paper, we overcome these limitations by considering convex regularization in Monte-Carlo Tree Search (MCTS), which has been successfully used in RL to efficiently drive exploration. First, we introduce a unifying theory on the use of generic convex regularizers in MCTS, deriving the regret analysis and providing guarantees of exponential convergence rate. Second, we exploit our theoretical framework to introduce novel regularized backup operators for MCTS, based on the relative entropy of the policy update, and on the Tsallis entropy of the policy. Finally, we empirically evaluate the proposed operators in AlphaGo and AlphaZero on problems of increasing dimensionality and branching factor, from a toy problem to several Atari games, showing their superiority w.r.t. representative baselines. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Game Playing on Go (round-robin)](): Game Playing; Go (round-robin); Avg Trials per Move: 5206. ## Original sources and implementation [Original paper]() [PDF]()