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Super-Exponential Regret for UCT, AlphaGo and Variants
May 8, 2024, 4:42 a.m. | Laurent Orseau, Remi Munos
cs.LG updates on arXiv.org arxiv.org
Abstract: We improve the proofs of the lower bounds of Coquelin and Munos (2007) that demonstrate that UCT can have $\exp(\dots\exp(1)\dots)$ regret (with $\Omega(D)$ exp terms) on the $D$-chain environment, and that a `polynomial' UCT variant has $\exp_2(\exp_2(D - O(\log D)))$ regret on the same environment -- the original proofs contain an oversight for rewards bounded in $[0, 1]$, which we fix in the present draft. We also adapt the proofs to AlphaGo's MCTS and its …
abstract alphago arxiv cs.ai cs.lg environment polynomial terms type variants
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