9 research outputs found
Accelerated Method for Stochastic Composition Optimization with Nonsmooth Regularization
Stochastic composition optimization draws much attention recently and has
been successful in many emerging applications of machine learning, statistical
analysis, and reinforcement learning. In this paper, we focus on the
composition problem with nonsmooth regularization penalty. Previous works
either have slow convergence rate or do not provide complete convergence
analysis for the general problem. In this paper, we tackle these two issues by
proposing a new stochastic composition optimization method for composition
problem with nonsmooth regularization penalty. In our method, we apply variance
reduction technique to accelerate the speed of convergence. To the best of our
knowledge, our method admits the fastest convergence rate for stochastic
composition optimization: for strongly convex composition problem, our
algorithm is proved to admit linear convergence; for general composition
problem, our algorithm significantly improves the state-of-the-art convergence
rate from to . Finally, we apply
our proposed algorithm to portfolio management and policy evaluation in
reinforcement learning. Experimental results verify our theoretical analysis.Comment: AAAI 201
Stochastic Optimization of Areas UnderPrecision-Recall Curves with Provable Convergence
Areas under ROC (AUROC) and precision-recall curves (AUPRC) are common
metrics for evaluating classification performance for imbalanced problems.
Compared with AUROC, AUPRC is a more appropriate metric for highly imbalanced
datasets. While stochastic optimization of AUROC has been studied extensively,
principled stochastic optimization of AUPRC has been rarely explored. In this
work, we propose a principled technical method to optimize AUPRC for deep
learning. Our approach is based on maximizing the averaged precision (AP),
which is an unbiased point estimator of AUPRC. We cast the objective into a sum
of {\it dependent compositional functions} with inner functions dependent on
random variables of the outer level. We propose efficient adaptive and
non-adaptive stochastic algorithms named SOAP with {\it provable convergence
guarantee under mild conditions} by leveraging recent advances in stochastic
compositional optimization. Extensive experimental results on image and graph
datasets demonstrate that our proposed method outperforms prior methods on
imbalanced problems in terms of AUPRC. To the best of our knowledge, our work
represents the first attempt to optimize AUPRC with provable convergence. The
SOAP has been implemented in the libAUC library at~\url{https://libauc.org/}.Comment: 24 pages, 10 figure