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cloud.google.com·8h ago
AI Research
arXiv CS.AI·Aug 6·5 min read
Efficient Online Lexicographic Generalized Low-Rank Matrix Bandits
TL;DR
Lexi-LowGLM is a novel online algorithm for generalized low-rank matrix bandits that prioritizes multiple objectives using a lexicographic approach. It significantly reduces the complexity of estimator updates, achieving a regret bound that depends on effective low-rank dimensions rather than ambient dimensions.
✦ Why It Matters
Implement Lexi-LowGLM to efficiently handle multi-objective optimization in your matrix bandit applications today.
Key Takeaways
- Utilize Lexi-LowGLM for efficient multi-objective optimization.
- Reduce estimator update complexity from O(T^2) to O(T).
- Focus on effective low-rank dimensions for better performance.
- Apply lexicographic learning to prioritize objectives effectively.
How It Works
Lexi-LowGLM operates by first estimating low-rank subspaces for each objective, allowing it to focus on the most relevant features. It then updates each objective-specific estimator using an online Newton step, which is computationally efficient and avoids the need for batch processing of historical data.