Is Monte Carlo Tree Search Just Every-Visit Monte Carlo Control?

Monte Carlo Tree Search (MCTS) and every-visit Monte Carlo (MC) control are usually presented as different methods. MCTS is described in the language of search (selection, expansion, simulation, and backup), whereas MC control is described in the language of reinforcement learning (trajectory sampling, return estimation, action-value updating, and policy improvement). This note argues that, at the level of trajectory generation and action-value updating, the distinction is largely terminological. The tree policy and rollout policy can be viewed as the learned and not-yet-learned parts of a single evolving policy; expansion corresponds to first visit and initialization; and backup is the ordinary every-visit Monte Carlo update. Under this interpretation, the four stages of MCTS reduce to two basic operations: trajectory sampling under the current policy and every-visit Monte Carlo updating. In this sense, MCTS is simply every-visit Monte Carlo control expressed in the language and data structure of search. The purpose of this note is expository: to make this equivalence explicit and easier to recognize.

Variance Driven Exploration: A Provable and Efficient Methodology for Pure Exploration in Highly Stochastic Environments

We propose Variance Driven Exploration (VarDE), a principled approach for pure exploration in highly stochastic environments, where the exploration process is dominated by stochastic variance. VarDE is built on a fundamental principle: sampling effort should be allocated to minimize the uncertainty of the final decision. We formalize the uncertainty of the final decision through a smooth decision function and derive allocation rules that explicitly capture how stochastic noise in individual components affects the reliability of the final output. We apply this methodology to three core problems of pure exploration -- Best Arm Identification (BAI), Monte Carlo Tree Search (MCTS), and Best-Policy Identification (BPI) -- with theoretical guarantees on variance decay and simple regret. Empirically, we demonstrate consistent and significant improvements of VarDE over existing methods, with especially strong gains in highly stochastic environments.

Learning to Run Power Networks: Effective AlphaZero-inspired Topological Control

As the integration of volatile renewable energy sources increases the strain on modern power grids, the use of Reinforcement Learning (RL) for autonomous topological reconfiguration has emerged as a promising research field to keep strained grids stable and operational. Compared to traditional redispatching measures, topological actions offer a cheaper and more cost-effective way to manage grid congestion. However, their implementation is hindered by a vast combinatorial action space and strict operational constraints. This paper investigates the effectiveness of model-based AlphaZero-inspired approaches that utilize Monte Carlo Tree Search (MCTS) for proactive grid management. We systematically evaluate how reward functions, observation density, and search guidance influence an agent's survivability. Our results demonstrate that the optimized AlphaZero approach achieves a peak survivability of 98.43%, significantly outperforming the proximal policy optimization (PPO) variant. We find that conducting the MCTS without guidance from a prior learned policy or value function can enhance training efficiency, and that a straightforward binary survival reward provides more effective search guidance than complex, multi-objective functions. Our findings demonstrate that while AlphaZero is a powerful framework for topological control, pure reinforcement learning is not sufficient; rather, an effective and reliable system requires a 'minimalist' integration of domain-specific heuristics, binary rewards, and a restricted observation space of line loads.

Belief-Guided Decision Making with Uncertainty Gating in the Game of Go

Recent advancements in Computer Go, driven by AlphaZero and MuZero, rely heavily on Monte Carlo Tree Search (MCTS) to correct the errors of the neural network policy. While effective on massive computational clusters, this dependence creates a critical bottleneck on consumer-grade hardware, where the computational cost of tree management severely limits inference rates. Furthermore, without deep search, these models suffer from hallucination, proposing moves with high confidence that are strategically fatal. This paper introduces a novel Belief-Guided architecture that disentangles the Policy head from a distinct Belief head. Unlike traditional value functions, the Belief head acts as an internal simulator and independent critic, modeling epistemic uncertainty and strategic stability. By integrating memory mechanisms (Transformer/GRU) to handle long-term dependencies and the Ko rule, and utilizing a gating mechanism to filter overconfident policy errors, our model shifts the burden of intelligence from runtime search to parametric "intuition." Experimental results demonstrate that this approach significantly improves search-free win rates and reduces hallucination, enabling professional-level play on limited hardware where massive MCTS is infeasible.

Dynamic Resource Allocation for Ensemble Determinization MCTS

Simulation-based algorithms are especially suited for high-uncertainty environments such as adversarial board games with significant elements of randomness and hidden information. In particular, several Monte Carlo Tree Search (MCTS) variants are commonly used in such domains. In this paper, we propose a series of enhancements for Ensemble Determinization MCTS, introducing two axes for dynamic resource allocation. First, Dynamic Number of Determinizations, increases or decreases the number of currently used determinization trees depending on the behavior of so-far search. Second, Dynamic Simulation Allocation, splits the simulation budget nonuniformly across the determinization trees, using simulation-to-simulation decisions to choose the tree with potentially the best knowledge gain. As benchmark domains, we used three popular tabletop games: Jaipur, Lost Cities, and Splendor. Testing our proposed enhancements in iteration- and time-based settings showed that particular configurations yield a statistically significant increase in the algorithm's strength.

AlphaZero in Sparsely Rewarded Games: Limits and Auxiliary Supervision

AlphaZero has demonstrated that a neural-guided Monte Carlo Tree Search can achieve superhuman performance, but strong play does not necessarily imply perfect play. We study this gap in two oracle-evaluable domains with contrasting structure: Connect Four, a solved partisan game with exact game-theoretic values, and Chomp, an impartial game whose optimal play is governed by Grundy-number structure. Under a unified self-play $+$ MCTS pipeline, we compare vanilla AlphaZero, a multi-frame variant (limited to Chomp), and an AlphaZero Auxiliary Loss (AZAL) that adds oracle-derived policy supervision. We find that vanilla AlphaZero achieves strong play across both domains but cannot preserve the exact trajectories required for optimal play: in Connect Four, it fails to maintain the optimal line of play, while in Chomp, it fails to consistently restore the $g=0$ invariant. On rectangular Chomp boards, multi-frame inputs alone do not remove this gap. Nevertheless, AZAL substantially improves oracle consistency across multi-seeded full-game traces and sampled-state evaluations. On Chomp, AZAL reaches perfect full-game oracle consistency on 10x11 and high but not complete consistency on 9x10; on Connect Four, AZAL improves oracle-match rate and delays the first oracle mistake, but does not reach perfect play.

Causal Object-Centric Models for Planning with Monte Carlo Tree Search

We introduce COMET (Causal Object-centric Model for Efficient Tree search), a model-based reinforcement learning algorithm that performs Monte Carlo Tree Search in a slot-structured latent space. COMET pairs a frozen unsupervised object-centric encoder with a transformer-based world model, in which actions are bound to objects through a novel action-slot fusion mechanism that is used in slot transition prediction. Policy and value heads use object-causal attention, modulating token interactions by learned per-slot relevance scores so that decision-making concentrates on task-relevant entities. COMET adds an explicit object-level inductive bias to MuZero-style latent planning. Across eight visually and dynamically diverse tasks from the Object-Centric Visual RL benchmark, ManiSkill, Robosuite, and VizDoom, COMET achieves a higher mean normalized score during the early stages of training compared to object-centric and monolithic baselines.

Two-Fidelity Best-Action Identification for Stochastic Minimax Tree

We study fixed-confidence best-action identification (BAI) in stochastic minimax trees. This problem is increasingly relevant in modern AI planning, where deep minimax search and Monte Carlo Tree Search (MCTS) with language model long rollouts face a fundamental tradeoff: heuristic evaluations are cheap but biased, while accurate rollouts are reliable but prohibitively expensive. We propose 2FFS, a two-fidelity tree-search algorithm that brings multi-fidelity flat bandit ideas into trees. The algorithm combines minimax-style fast expansion with MCTS-style stochastic sampling, adaptively deciding when to exploit cheap biased evaluations and when to invoke expensive accurate evaluations for local certification. We prove fixed-confidence correctness, establish finite stopping for exact identification, and give a polynomial-depth cost upper bound for general-depth trees. Across numerical stochastic-tree experiments, 2FFS uses substantially fewer samples and computational operations comparing to existing BAI-MCTS baseline.