Enterprise AI Research Analysis

Background: The Foundation of MCTS

Our work builds upon the well-established framework of Markov Decision Processes (MDPs) and Monte Carlo Tree Search (MCTS). An MDP formally defines the interaction between an agent and its environment, where an optimal policy dictates actions to maximize discounted rewards. MCTS, a best-first search algorithm, iteratively refines a search tree through four steps: selection, expansion, simulation, and backpropagation. The Upper Confidence Bounds for Trees (UCT) algorithm guides this process, balancing exploration of new actions with exploitation of promising ones.

For environments with continuous action spaces, Progressive Widening (PW) and Double Progressive Widening (DPW) are essential. PW allows the search tree to expand the action space gradually, adding new sampled actions only after a node has been visited a sufficient number of times. DPW extends this by also widening the number of successor states, crucial for stochastic environments where the same action can lead to different outcomes. These techniques manage the infinite possibilities of continuous action spaces, making MCTS applicable to a broader range of complex problems.

Methods: GPR2P & Aggregation Strategies

In root-parallel MCTS, multiple independent search threads concurrently explore the action space from the same root state. Upon termination, their individual search trees are aggregated to determine the best action. The effectiveness of this parallelization heavily depends on the aggregation strategy employed. We compare GPR2P against several established methods:

• Max: Selects the action with the highest estimated value across all threads. Simple but ignores visit counts.
• Most Visited: Chooses the action with the highest visit count, assuming more visited actions are more reliable.
• Similarity Vote: Exploits action similarity to weight and update action values. It performs a weighted sum of values from similar actions.
• Similarity Merge: Similar to Similarity Vote, but also incorporates visit counts to reflect reliability, giving more weight to actions with higher visit counts.

Our proposed Gaussian Process Regression for Root Parallel MCTS (GPR2P) fundamentally differs by not merely selecting from sampled actions but by constructing a principled statistical model of the return over the entire continuous action space. This allows GPR2P to estimate values for actions that were never explicitly sampled in the tree, addressing a key limitation of prior methods. GPR2P uses a Radial Basis Function (RBF) kernel to model correlations between actions, with hyperparameters tuned to the environment. It also incorporates a visit-count threshold to filter out insufficiently explored actions before regression, ensuring reliable training data.

Evaluation: Performance Across Diverse Environments

Our comprehensive empirical evaluation compared GPR2P against five other aggregation strategies and single-thread MCTS across six diverse environments: Lunar Lander, Mountain Car, Pendulum (Gymnasium tasks), and custom-designed Random Teleporter, Wide Corridor, and Narrow Corridor (stochastic tasks). This broad evaluation scope ensures the generalizability of our findings across both deterministic and stochastic continuous action problems. Performance was measured using 'steps to goal' (lower is better, displayed as constant minus steps for better visualization) and 'success rate' (higher is better).

The results consistently demonstrate that GPR2P outperforms all other methods, especially in scenarios with limited trial budgets or when high-quality actions are difficult to discover through sparse sampling. Its ability to infer optimal actions across the entire continuous action space provides a distinct advantage. While GPR2P incurs a modest increase in inference time, this overhead is minor compared to the overall time saved and performance gains. The Mean Reciprocal Rank (MRR) analysis confirms GPR2P's superior overall performance, making it the most effective aggregation algorithm for root-parallel MCTS in continuous domains.