Convex Regularization in Monte-Carlo Tree Search

TL;DR

This paper introduces convex regularization techniques into Monte-Carlo Tree Search to improve sample efficiency and computational performance, supported by theoretical guarantees and empirical validation on complex decision problems.

Contribution

It develops a unifying theory for convex regularizers in MCTS, introduces novel regularized backup operators, and demonstrates their effectiveness in advanced RL algorithms.

Findings

Regularized operators outperform baselines in Atari games.

Theoretical guarantees of exponential convergence.

Enhanced exploration efficiency in large decision spaces.

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.