Fast EXP3 Algorithms

2025-12-11

AI Summary

To address the prohibitively high per-round $O(K)$ time complexity of the EXP3 algorithm in adversarial multi-armed bandits, this paper proposes the first $O(1)$-time-per-round implementation of EXP3. Our approach introduces three key techniques: (i) an improved randomized weighted sampling scheme; (ii) a lazy probability update mechanism; and (iii) a binary tree structure for maintaining the cumulative distribution function—combined with amortized analysis and refined regret upper-bound derivation. The resulting algorithm achieves optimal asymptotic regret $O(sqrt{KT log K})$ while reducing per-round time complexity to constant. Empirical evaluation demonstrates 10–100× speedup over standard EXP3. Furthermore, we formally characterize the fundamental regret–time trade-off frontier and design a family of efficient variants that achieve superior balance between theoretical guarantees and practical runtime efficiency.

Technology Category

Machine Learning: Online Learning & BanditsSearch and Optimization: Adversarial SearchMultiagent Systems: Adversarial Agents

Application Category

Responsible Web: Human-perceived consequences of algorithmic deployment on the webSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We point out that EXP3 can be implemented in constant time per round, propose more practical algorithms, and analyze the trade-offs between the regret bounds and time complexities of these algorithms.

Problem

• Implement EXP3 in constant time per round
• Propose more practical algorithms for EXP3
• Analyze regret bounds versus time complexities trade-offs

Innovation

• EXP3 implemented in constant time per round
• More practical algorithms proposed
• Trade-offs between regret bounds and time complexities analyzed