Incremental proximal methods for large scale convex optimization

Laboratory for Information and Decision Systems Report LIDS-P-2847We consider the minimization of a sum∑m [over]i=1 fi (x) consisting of a large number of convex component functions fi . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components.We also discuss applications in a few contexts, including signal processing and inference/machine learning.United States. Air Force Office of Scientific Research (grant FA9550-10-1-0412

Communication-efficient distributed online prediction by dynamic model synchronization

We present the first protocol for distributed online prediction that aims to minimize online prediction loss and network communication at the same time. This protocol can be applied wherever a prediction-based service must be provided timely for each data point of a multitude of high frequency data streams, each of which is observed at a local node of some distributed system. Exemplary applications include social content recommendation and algorithmic trading. The challenge is to balance the joint predictive performance of the nodes by exchanging information between them, while not letting communication overhead deteriorate the responsiveness of the service. Technically, the proposed protocol is based on controlling the variance of the local models in a decentralized way. This approach retains the asymptotic optimal regret of previous algorithms. At the same time, it allows to substantially reduce network communication, and, in contrast to previous approaches, it remain s applicable when the data is non-stationary and shows rapid concept drift. We demonstrate empirically that the protocol is able to hold up a high predictive performance using only a fraction of the communication required by benchmark methods

Aggregating expert judgement

In a paper written some 25 years ago, I distinguished three contexts in which one might wish to combine expert judgements of uncertainty: the expert problem, the group decision problem and the textbook problem. Over the intervening years much has been written on the first two, which have the focus of a single decision context, but little on the third, though the closely related field of meta-analysis has developed considerably. With many developments in internet technology, particularly in relation to interactivity and communication, the textbook problem is gaining in importance since data and expert judgements can be made available over the web to be used by many different individuals to shape their own beliefs in many different contexts. Moreover, applications such as web-based decision support, e-participation and e-democracy are making algorithmic ‘solutions’ to the group decision problem attractive, despite many results showing we know that such solutions are, at best, rare and, at worst, illusory. In this paper I survey developments since my earlier paper and note some unresolved issues. Then I turn to how expert judgement might be used within web-based group decision support, as well as in e-participation and e-democracy contexts. The latter points to a growing importance of the textbook problem and suggests that Cooke’s principles for scientific reporting of expert judgement studies may need enhancing for such studies to be used by a wider audience