## Trading regret for efficiency online convex optimization with long term constraints

Bandit convex optimization is a special case of online convex optimization with regret. Zinkevich (2003) presents a strategy based on gradient descent that 1Both of these results are novel but their proof is omitted due to space constraints . The algorithms we propose are efficient, with the computational complexities  Trading Regret for Efﬁciency: Online Convex Optimization ... • A convex-concave formulation of online convex optimization with long term constraints, and an efﬁcient algorithm based on OGD that attains a regret bound of O(T1/2), and O(T3/4) violation of the constraints. • A modiﬁed OGD based algorithm for online convex optimization with long term constraints

• A convex-concave formulation of online convex optimization with long term constraints, and an efﬁcient algorithm based on OGD that attains a regret bound of O(T1/2), and O(T3/4) violation of the constraints. • A modiﬁed OGD based algorithm for online convex optimization with long term constraints Trading Regret for Efficiency: Online Convex Optimization ... By turning the problem into an online convex-concave optimization problem, we propose an efficient algorithm which achieves O ( √ T) regret bound and O(T 3/4) bound on the violation of constraints. Then, we modify the algorithm in order to guarantee that the constraints are satisfied in the long run. Trading Regret for Efficiency: Online Convex Optimization ... By turning the problem into an online convex-concave optimization problem, we propose an efficient algorithm which achieves $\tilde{\mathcal{O}}(\sqrt{T})$ regret bound and $\tilde{\mathcal{O}}(T^{3/4})$ bound for the violation of constraints. Then we modify the algorithm in order to guarantee that the constraints are satisfied in the long run. Trading Regret for Efficiency: Online Convex Optimization ... By turning the problem into an online convex-concave optimization problem, we propose an efficient algorithm which achieves $\tilde{\mathcal{O}}(\sqrt{T})$ regret bound and $\tilde{\mathcal{O}}(T^{3/4})$ bound for the violation of constraints. Then we modify the algorithm in order to guarantee that the constraints are satisfied in the long run.

## Stochastic convex optimization with multiple objectives with Tianbao Yang and Rong Jin Advances in Neural Information Processing Systems (NeurIPS), 2013. Passive learning with target risk with Rong Jin Conference on Learning Theory (COLT), 2013. Trading regret for efficiency: Online convex optimization with long term constraints

### This "Cited by" count includes citations to the following articles in Scholar. Trading regret for efficiency: online convex optimization with long term constraints. M Mahdavi, R Jin, T Yang. Journal of Machine Learning Research (JMLR) 13, 2503−2528, 2012. 97:

jmlr.csail.mit.edu @article{JMLR:v13:mahdavi12a, author = {Mehrdad Mahdavi and Rong Jin and Tianbao Yang}, title = {Trading Regret for Efficiency: Online Convex Optimization with Long Term Constraints}, journal = {Journal of Machine Learning Research}, year = {2012}, volume = {13}, number = {81}, pages Trading Regret for Efficiency: Online Convex Optimization ... Trading Regret for Efficiency: Online Convex Optimization with Long Term Constraints . Mehrdad Mahdavi, Rong Jin, Tianbao Yang; 13(81):2503−2528, 2012.. Abstract. In this paper we propose efficient algorithms for solving constrained online convex optimization problems. Online Learning in Weakly Coupled Markov Decision ...

### Trading Regret for Efficiency: Online Convex Optimization ...

Portfolio optimization with linear and ﬁxed transaction costs Portfolio optimization with linear and ﬁxed transaction costs Miguel Sousa Lobo · Maryam Fazel · Stephen Boyd Published online: 2 December 2006 Springer ScienceC + Business Media, LLC 2007 Abstract We consider the problem of portfolio selection, with transaction costs and con-straints on … Introducing Convex and Conic Optimization for the ... Introducing Convex and Conic Optimization for the Quantitative Finance Professional Few people are aware of a quiet revolution that has taken place in optimization methods over the last decade O ptimization has played an important role in quantitative finance ever since Markowitz published his original paper on portfolio selection in 19521. Online Convex Optimization with Unconstrained Domains and ...

## [PDF] A Low Complexity Algorithm with $O(\sqrt{T})$ Regret ...

Trading Regret for Efficiency: Online Convex Optimization with Long Term Constraints.pdf: 230.61kB

Nov 25, 2011 · Trading Regret for Efficiency: Online Convex Optimization with Long Term Constraints Article (PDF Available) in Journal of Machine Learning Research 13 · November 2011 with 34 Reads Trading regret for efficiency: online convex optimization ... Mathematics, Computer Science; Published in J. Mach. Learn. Res. 2011 Trading regret for efficiency: online convex optimization with long term constraints @article{Mahdavi2011TradingRF, title={Trading regret for efficiency: online convex optimization with long term constraints}, author={Mehrdad Mahdavi and Rong Jin and Tianbao Yang}, journal={J. Mach. Learn.