Online Newton Step Algorithm with Estimated Gradient

Online learning with limited information feedback (bandit) tries to solve the problem where an online learner receives partial feedback information from the environment in the course of learning. Under this setting, Flaxman extends Zinkevich's classical Online Gradient Descent (OGD) algorithm Zinkevich [2003] by proposing the Online Gradient Descent with Expected Gradient (OGDEG) algorithm. Specifically, it uses a simple trick to approximate the gradient of the loss function $f_t$ by evaluating it at a single point and bounds the expected regret as $\mathcal{O}(T^{5/6})$ Flaxman et al. [2005]. It has been shown that compared with the first-order algorithms, second-order online learning algorithms such as Online Newton Step (ONS) Hazan et al. [2007] can significantly accelerate the convergence rate in traditional online learning. Motivated by this, this paper aims to exploit second-order information to speed up the convergence of OGDEG. In particular, we extend the ONS algorithm with the trick of expected gradient and develop a novel second-order online learning algorithm, i.e., Online Newton Step with Expected Gradient (ONSEG). Theoretically, we show that the proposed ONSEG algorithm significantly reduces the expected regret of OGDEG from $\mathcal{O}(T^{5/6})$ to $\mathcal{O}(T^{2/3})$ in the bandit feedback scenario. Empirically, we demonstrate the advantages of the proposed algorithm on several real-world datasets.

Efficient online learning for large-scale peptide identification

Motivation: Post-database searching is a key procedure in peptide dentification with tandem mass spectrometry (MS/MS) strategies for refining peptide-spectrum matches (PSMs) generated by database search engines. Although many statistical and machine learning-based methods have been developed to improve the accuracy of peptide identification, the challenge remains on large-scale datasets and datasets with an extremely large proportion of false positives (hard datasets). A more efficient learning strategy is required for improving the performance of peptide identification on challenging datasets. Results: In this work, we present an online learning method to conquer the challenges remained for exiting peptide identification algorithms. We propose a cost-sensitive learning model by using different loss functions for decoy and target PSMs respectively. A larger penalty for wrongly selecting decoy PSMs than that for target PSMs, and thus the new model can reduce its false discovery rate on hard datasets. Also, we design an online learning algorithm, OLCS-Ranker, to solve the proposed learning model. Rather than taking all training data samples all at once, OLCS-Ranker iteratively feeds in only one training sample into the learning model at each round. As a result, the memory requirement is significantly reduced for large-scale problems. Experimental studies show that OLCS-Ranker outperforms benchmark methods, such as CRanker and Batch-CS-Ranker, in terms of accuracy and stability. Furthermore, OLCS-Ranker is 15--85 times faster than CRanker method on large datasets. Availability and implementation: OLCS-Ranker software is available at no charge for non-commercial use at https://github.com/Isaac-QiXing/CRanker.