We study the worst-case adaptive optimization problem with budget constraint that is useful for modeling various practical applications in artificial intelligence and machine learning. We investigate the near-optimality of greedy algorithms for this problem with both modular and non-modular cost functions. In both cases, we prove that two simple greedy algorithms are not near-optimal but the best between them is near-optimal if the utility function satisfies pointwise submodularity and pointwise cost-sensitive submodularity respectively. This implies a combined algorithm that is near-optimal with respect to the optimal algorithm that uses half of the budget. We discuss applications of our theoretical results and also report experiments comparing the greedy algorithms on the active learning problem.

In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does our algorithm work much faster than the known methods, but it can also handle more complex sparsity constraints, such as average sparsity. Using numerical experiments, we show that our algorithm outperforms the known methods for dictionary selection, achieving competitive performances with dictionary learning algorithms in a smaller running time.

Wegiveasmoothed analysis, showing that evenwhen contexts may be chosen by an adversary, small perturbations of the adversary's choices suffice for the algorithm to achieve "no regret", perhaps (depending on the specifics of the setting) with a constant amount of initial training data.

A number of problems in Computer Vision and Machine Learning involve searching for a set of bounding boxes or rectangular windows.

In this paper, we address the online learning problem when the input to the greedy algorithm is stochastic with unknown parameters that have to be learned over time.

Decision trees are a fundamental workhorse in machine learning. Their logical and hierarchical structure makes them easy to understand and their predictions easy to explain.

Third, we are the first to consider regularized monotone SCP (RMSCP).

Third, we are the first to consider regularized monotone SCP (RMSCP).