Selecting Computations: Theory and Applications
This work addresses the challenge of efficient computation selection in decision-making processes, offering a more appropriate theoretical framework than existing bandit approaches, though it is incremental in advancing metalevel decision theory.
The paper tackled the problem of selecting which action sequences to simulate in sequential decision problems by developing a theoretical basis for metalevel decisions using Bayesian selection problems, and demonstrated that heuristic approximations derived from this framework outperform bandit-based methods in one-shot decision problems and Go.
Sequential decision problems are often approximately solvable by simulating possible future action sequences. {\em Metalevel} decision procedures have been developed for selecting {\em which} action sequences to simulate, based on estimating the expected improvement in decision quality that would result from any particular simulation; an example is the recent work on using bandit algorithms to control Monte Carlo tree search in the game of Go. In this paper we develop a theoretical basis for metalevel decisions in the statistical framework of Bayesian {\em selection problems}, arguing (as others have done) that this is more appropriate than the bandit framework. We derive a number of basic results applicable to Monte Carlo selection problems, including the first finite sampling bounds for optimal policies in certain cases; we also provide a simple counterexample to the intuitive conjecture that an optimal policy will necessarily reach a decision in all cases. We then derive heuristic approximations in both Bayesian and distribution-free settings and demonstrate their superiority to bandit-based heuristics in one-shot decision problems and in Go.