Efficient algorithms for online decision problems

Efficient Algorithms for Online Decision Problems

In an online decision problem, one makes a sequence of decisions without knowledge of the future. Tools from learning such as Weighted Majority and its many variants [13, 18, 4] demonstrate that online algorithms can perform nearly as well as the best single decision chosen in hindsight, even when there are exponentially many possible decisions. However, the naive application of these algorithm...

Adaptive Algorithms for Online Decision Problems

We study the notion of learning in an oblivious changing environment. Existing online learning algorithms which minimize regret are shown to converge to the average of all locally optimal solutions. We propose a new performance metric, strengthening the standard metric of regret, to capture convergence to locally optimal solutions, and propose efficient algorithms which provably converge at the...

Eecient Algorithms for Online Decision Problems

In an online decision problem, one makes a sequence of decisions without knowledge of the future. Tools from learning such as Weighted Majority and its many variants 13, 18, 4] demonstrate that online algorithms can perform nearly as well as the best single decision chosen in hindsight, even when there are exponentially many possible decisions. However, the naive application of these algorithms...

Online algorithms for clustering problems

Efficient algorithms for clique problems

The k-clique problem is a cornerstone of NP-completeness and parameterized complexity. When k is a fixed constant, the asymptotically fastest known algorithm for finding a k-clique in an n-node graph runs in O(n) time (given by Nešetřil and Poljak). However, this algorithm is infamously inapplicable, as it relies on Coppersmith and Winograd’s fast matrix multiplication. We present good combinat...