Mechanism design with multi-armed bandit
Keywords: mechanism design, incentive compatibility, efficiency, individual rationality, budget balance, multi-armed bandit, probably approximately correct
TL;DR: We analytically derive the optimal solution to a mechanism design problem and evaluate the solution via a bandit algorithm with theoretical guarantee.
Abstract: A popular approach of automated mechanism design is to formulate a linear program (LP) whose solution gives a mechanism with desired properties. We analytically derive a class of optimal solutions for such an LP that gives mechanisms achieving standard properties of efficiency, incentive compatibility, strong budget balance (SBB), and individual rationality (IR), where SBB and IR are satisfied in expectation. Notably, our solutions are represented by an exponentially smaller number of essential variables than the original variables of LP. Our solutions, however, involve a term whose exact evaluation requires solving a certain optimization problem exponentially many times as the number of players grows. We thus evaluate this term by modeling it as the problem of estimating the mean reward of the best arm in multi-armed bandit (MAB), propose a Probably and Approximately Correct estimator, and prove its asymptotic optimality by establishing a lower bound on its sample complexity. This MAB approach reduces the number of times the optimization problem is solved from exponential to linear. Numerical experiments show that the proposed approach finds mechanisms that are guaranteed to achieve desired properties with high probability for environments with up to 128 players, which substantially improves upon the prior work.
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Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 5243
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