Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Adaptive routing with end-to-end feedback: distributed learning and geometric approaches
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Robbing the bandit: less regret in online geometric optimization against an adaptive adversary
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Efficient algorithms for online decision problems
Journal of Computer and System Sciences - Special issue: Learning theory 2003
Approximation algorithms and online mechanisms for item pricing
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Design is as easy as optimization
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Regret minimization and the price of total anarchy
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Multi-armed bandits in metric spaces
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Regret Minimization and Job Scheduling
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Sharp dichotomies for regret minimization in metric spaces
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms for reliable stochastic combinatorial optimization
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Network-wide deployment of intrusion detection and prevention systems
Proceedings of the 6th International COnference
GSP auctions with correlated types
Proceedings of the 12th ACM conference on Electronic commerce
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In an online linear optimization problem, on each period t, an online algorithm chooses st ∈ S from a fixed (possibly infinite) set S of feasible decisions. Nature (who may be adversarial) chooses a weight vector wt ∈ R, and the algorithm incurs cost c(st,wt), where c is a fixed cost function that is linear in the weight vector. In the full-information setting, the vector wt is then revealed to the algorithm, and in the bandit setting, only the cost experienced, c(st,wt), is revealed. The goal of the online algorithm is to perform nearly as well as the best fixed s ∈ S in hindsight. Many repeated decision-making problems with weights fit naturally into this framework, such as online shortest-path, online TSP, online clustering, and online weighted set cover. Previously, it was shown how to convert any efficient exact offline optimization algorithm for such a problem into an efficient online bandit algorithm in both the full-information and the bandit settings, with average cost nearly as good as that of the best fixed s ∈ S in hindsight. However, in the case where the offline algorithm is an approximation algorithm with ratio α 1, the previous approach only worked for special types of approximation algorithms. We show how to convert any offline approximation algorithm for a linear optimization problem into a corresponding online approximation algorithm, with a polynomial blowup in runtime. If the offline algorithm has an α-approximation guarantee, then the expected cost of the online algorithm on any sequence is not much larger than α times that of the best s ∈ S, where the best is chosen with the benefit of hindsight. Our main innovation is combining Zinkevich's algorithm for convex optimization with a geometric transformation that can be applied to any approximation algorithm. Standard techniques generalize the above result to the bandit setting, except that a "Barycentric Spanner" for the problem is also (provably) necessary as input.Our algorithm can also be viewed as a method for playing largerepeated games, where one can only compute approximate best-responses, rather than best-responses.