Graph-Based Stochastic Power-UCT: Monte-Carlo Graph Search with Power Mean Estimation
Read the original on arXiv Machine Learning →Graph-Based Stochastic-Power-UCT (GS-Power-UCT) is a Monte‑Carlo graph search algorithm that shares states reached at the same planning depth while keeping separate values for different depths, thereby reducing duplicate simulations in stochastic MDPs. The method guarantees that, for a fixed horizon, the root estimate converges to the finite‑horizon value at an $O(n^{-1/2})$ rate, matching tree‑based Stochastic‑Power‑UCT but with improved sample reuse. Two full‑state variants—GS‑Power‑UCT‑F and GS‑Power‑UCT‑F$^+$—extend the approach to single‑node per physical state and adaptive horizons, respectively, with the latter converging to the optimal infinite‑horizon discounted value when cross‑depth bias vanishes. Experiments on stochastic planning benchmarks demonstrate that GS‑Power‑UCT outperforms both tree‑based and other graph‑based baselines in sample efficiency.
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