Summary of Tight Bounds For Online Convex Optimization with Adversarial Constraints, by Abhishek Sinha and Rahul Vaze
Tight Bounds for Online Convex Optimization with Adversarial Constraints
by Abhishek Sinha, Rahul Vaze
First submitted to arxiv on: 15 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This research paper tackles constrained online convex optimization (COCO), a generalization of standard online convex optimization (OCO). In COCO, the learner faces adaptive adversaries that reveal convex cost functions and constraint functions after each action is taken. The goal is to design an online policy that balances small regret with small cumulative constraint violation (CCV) without restrictive assumptions. The authors show that this can be achieved simultaneously for the first time, achieving O(sqrt(T)) regret and tilde{O}(sqrt{T}) CCV using a combination of AdaGrad’s adaptive regret bound and Lyapunov optimization from control theory. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper solves a long-standing problem in constrained online convex optimization (COCO). The goal is to find an online policy that balances small regret with small cumulative constraint violation. The authors show that this can be achieved for the first time, without restrictive assumptions. They use a combination of algorithms to achieve O(sqrt(T)) regret and tilde{O}(sqrt{T}) constraint violation. |
Keywords
» Artificial intelligence » Generalization » Optimization
