Achieving PAC Guarantees in Mechanism Design through Multi-Armed Bandits

TL;DR

This paper introduces a novel approach combining mechanism design with multi-armed bandit algorithms to efficiently compute incentive-compatible, budget-balanced mechanisms with PAC guarantees, scaling to large numbers of players.

Contribution

It develops a PAC estimator using MAB techniques to reduce the complexity of mechanism evaluation from exponential to O(N log N), enabling scalable automated mechanism design.

Findings

Efficiently computes mechanisms for up to 128 players.

Reduces evaluation complexity from exponential to O(N log N).

Provides PAC guarantees with asymptotically optimal sample complexity.

Abstract

We analytically derive a class of optimal solutions to a linear program (LP) for automated mechanism design that satisfies efficiency, incentive compatibility, strong budget balance (SBB), and individual rationality (IR), where SBB and IR are enforced in expectation. These solutions can be expressed using a set of essential variables whose cardinality is exponentially smaller than the total number of variables in the original formulation. However, evaluating a key term in the solutions requires exponentially many optimization steps as the number of players $N$ increases. We address this by translating the evaluation of this term into a multi-armed bandit (MAB) problem and develop a probably approximately correct (PAC) estimator with asymptotically optimal sample complexity. This MAB-based approach reduces the optimization complexity from exponential to $O(N\log N)$. Numerical experiments confirm that our method efficiently computes mechanisms with the target properties, scaling to problems with up to $N=128$ players -- substantially improving over prior work.