Best of both worlds: Stochastic & adversarial best-arm identification

2026-04-16 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new study investigates best-arm identification in bandit problems, specifically addressing scenarios with arbitrary and potentially adversarial rewards. While a simple random uniform learner achieves optimal error rates in adversarial settings, it performs suboptimally with stochastically sampled rewards. The research explores the feasibility of designing a single learner that performs optimally in both stochastic and adversarial reward environments without prior knowledge of the reward nature. The authors demonstrate that such a universal optimal learner is generally impossible, establishing a lower bound that characterizes the optimal rate for stochastic problems when the strategy is constrained to be robust against adversarial rewards. They then propose a simple, parameter-free algorithm that matches this lower bound (up to logarithmic factors) in stochastic problems and maintains robustness against adversarial rewards.

Key takeaway

For research scientists developing bandit algorithms, you should recognize the inherent trade-off between optimal performance in stochastic environments and robustness against adversarial rewards. Your design choices must prioritize one over the other or accept a constrained optimal rate for stochastic problems if adversarial robustness is critical. Consider implementing the proposed parameter-free algorithm for a balanced approach.

Key insights

Designing a single optimal learner for both stochastic and adversarial bandit best-arm identification is generally impossible.

Principles

• Adversarial robustness limits stochastic optimality.
• Random uniform learners excel in adversarial settings.

Method

The study establishes a lower bound for stochastic problems under adversarial robustness constraints, then designs a parameter-free algorithm matching this bound.

In practice

• Use random uniform learners for adversarial bandits.
• Consider trade-offs between robustness and stochastic performance.

Topics

• Bandit Best-Arm Identification
• Stochastic Rewards
• Adversarial Rewards
• Optimal Error Rate
• Parameter-Free Algorithms

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.