BAGEL: Projection-Free Algorithm for Adversarially Constrained Online Convex Optimization
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914284266586112 |
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| author | Lu, Yiyang Pedramfar, Mohammad Aggarwal, Vaneet |
| author_facet | Lu, Yiyang Pedramfar, Mohammad Aggarwal, Vaneet |
| contents | Projection-based algorithms for Constrained Online Convex Optimization (COCO) achieve optimal $\mathcal{O}(T^{1/2})$ regret guarantees but face scalability challenges due to the computational complexity of projections. To circumvent this, projection-free methods utilizing Linear Optimization Oracles (LOO) have been proposed, albeit typically achieving slower $\mathcal{O}(T^{3/4})$ regret rates. In this work, we examine whether the $\mathcal{O}(T^{1/2})$ rate can be recovered in the projection-free setting by strengthening the oracle assumption. We introduce BAGEL, an algorithm utilizing a Separation Oracle (SO) that achieves $\mathcal{O}(T^{1/2})$ regret and $\tilde{\mathcal{O}}(T^{1/2})$ cumulative constraint violation (CCV) for convex cost functions. Our analysis shows that by leveraging an infeasible projection via SO, we can match the time-horizon dependence of projection-based methods with $\tilde{\mathcal{O}}(T)$ oracle calls, provided dependence on the geometry of the action set. This establishes a specific regime where projection-free methods can attain the same convergence rates as projection-based counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16744 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | BAGEL: Projection-Free Algorithm for Adversarially Constrained Online Convex Optimization Lu, Yiyang Pedramfar, Mohammad Aggarwal, Vaneet Machine Learning Artificial Intelligence Optimization and Control Projection-based algorithms for Constrained Online Convex Optimization (COCO) achieve optimal $\mathcal{O}(T^{1/2})$ regret guarantees but face scalability challenges due to the computational complexity of projections. To circumvent this, projection-free methods utilizing Linear Optimization Oracles (LOO) have been proposed, albeit typically achieving slower $\mathcal{O}(T^{3/4})$ regret rates. In this work, we examine whether the $\mathcal{O}(T^{1/2})$ rate can be recovered in the projection-free setting by strengthening the oracle assumption. We introduce BAGEL, an algorithm utilizing a Separation Oracle (SO) that achieves $\mathcal{O}(T^{1/2})$ regret and $\tilde{\mathcal{O}}(T^{1/2})$ cumulative constraint violation (CCV) for convex cost functions. Our analysis shows that by leveraging an infeasible projection via SO, we can match the time-horizon dependence of projection-based methods with $\tilde{\mathcal{O}}(T)$ oracle calls, provided dependence on the geometry of the action set. This establishes a specific regime where projection-free methods can attain the same convergence rates as projection-based counterparts. |
| title | BAGEL: Projection-Free Algorithm for Adversarially Constrained Online Convex Optimization |
| topic | Machine Learning Artificial Intelligence Optimization and Control |
| url | https://arxiv.org/abs/2502.16744 |