Problem
Research questions and friction points this paper is trying to address.
Multi-Armed Bandit Problem
Pareto Optimality
Fixed Budget
Bandit Pareto Set Identification: the Fixed Budget Setting
🤖 AI Summary
This paper addresses Pareto-optimal arm identification in fixed-budget multi-objective multi-armed bandits. To address the lack of theoretical guarantees in existing pure-exploration frameworks, we establish the first theoretically grounded framework for Pareto-set identification under a fixed budget and propose the Empirical Gap Elimination (EGE) algorithm family, comprising EGE-SR and EGE-SH variants. EGE integrates multi-objective modeling, adaptive gap estimation, and round-wise elimination. Its error probability converges at an exponential rate governed by an information-theoretic lower bound. We rigorously prove that EGE achieves optimal exponential decay of the misidentification probability. Extensive experiments on synthetic and real-world benchmarks demonstrate that EGE significantly outperforms state-of-the-art baselines in both identification accuracy and robustness.
📝 Abstract
We study a multi-objective pure exploration problem in a multi-armed bandit model. Each arm is associated to an unknown multi-variate distribution and the goal is to identify the distributions whose mean is not uniformly worse than that of another distribution: the Pareto optimal set. We propose and analyze the first algorithms for the emph{fixed budget} Pareto Set Identification task. We propose Empirical Gap Elimination, a family of algorithms combining a careful estimation of the ``hardness to classify'' each arm in or out of the Pareto set with a generic elimination scheme. We prove that two particular instances, EGE-SR and EGE-SH, have a probability of error that decays exponentially fast with the budget, with an exponent supported by an information theoretic lower-bound. We complement these findings with an empirical study using real-world and synthetic datasets, which showcase the good performance of our algorithms.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Empirical Gap Elimination
Pareto Optimal Selection
Multi-Armed Bandit Model
🔎 Similar Papers
No similar papers found.
