Convergence of Unregularized Online Learning Algorithms

In this paper we study the convergence of online gradient descent algorithms in reproducing kernel Hilbert spaces (RKHSs) without regularization. We establish a sufficient condition and a necessary condition for the convergence of excess generalization errors in expectation. A sufficient condition for the almost sure convergence is also given. With high probability, we provide explicit convergence rates of the excess generalization errors for both averaged iterates and the last iterate, which in turn also imply convergence rates with probability one. To our best knowledge, this is the first high-probability convergence rate for the last iterate of online gradient descent algorithms without strong convexity. Without any boundedness assumptions on iterates, our results are derived by a novel use of two measures of the algorithm's one-step progress, respectively by generalization errors and by distances in RKHSs, where the variances of the involved martingales are cancelled out by the descent property of the algorithm

Robust Adaptive LCMV Beamformer Based On An Iterative Suboptimal Solution

The main drawback of closed-form solution of linearly constrained minimum variance (CF-LCMV) beamformer is the dilemma of acquiring long observation time for stable covariance matrix estimates and short observation time to track dynamic behavior of targets, leading to poor performance including low signal-noise-ratio (SNR), low jammer-to-noise ratios (JNRs) and small number of snapshots. Additionally, CF-LCMV suffers from heavy computational burden which mainly comes from two matrix inverse operations for computing the optimal weight vector. In this paper, we derive a low-complexity Robust Adaptive LCMV beamformer based on an Iterative Suboptimal solution (RAIS-LCMV) using conjugate gradient (CG) optimization method. The merit of our proposed method is threefold. Firstly, RAIS-LCMV beamformer can reduce the complexity of CF-LCMV remarkably. Secondly, RAIS-LCMV beamformer can adjust output adaptively based on measurement and its convergence speed is comparable. Finally, RAIS-LCMV algorithm has robust performance against low SNR, JNRs, and small number of snapshots. Simulation results demonstrate the superiority of our proposed algorithms

Collateral Value and Forbearance Lending

We investigate the foreclosure policy of collateral-based loans in which the endogenous collateral value plays a crucial role. If creditors are able to commit, then the equilibrium arrangement is more likely to feature forebearance lending by specifying a lower level of liquidation (or roll over all of the loans) relative to the expost efficiency criterion for each realization of the interim signal. The key is that collateral value may drop too low when banks call in loans by auctioning off borrowers¿ collateral and this makes clearing up non-performing loans less attractive. We attribute the banks¿ leniency as we have observed in Japan during the 1990s to an equilibrium arrangement where banks can commit due to either relationship banking or an implicit lenderborrower contract, such as the arrangement under Japan¿s main-bank system.Collateral value, forbearance lending, government guarantee.

A Compiler and Runtime Infrastructure for Automatic Program Distribution

This paper presents the design and the implementation of a compiler and runtime infrastructure for automatic program distribution. We are building a research infrastructure that enables experimentation with various program partitioning and mapping strategies and the study of automatic distribution's effect on resource consumption (e.g., CPU, memory, communication). Since many optimization techniques are faced with conflicting optimization targets (e.g., memory and communication), we believe that it is important to be able to study their interaction. We present a set of techniques that enable flexible resource modeling and program distribution. These are: dependence analysis, weighted graph partitioning, code and communication generation, and profiling. We have developed these ideas in the context of the Java language. We present in detail the design and implementation of each of the techniques as part of our compiler and runtime infrastructure. Then, we evaluate our design and present preliminary experimental data for each component, as well as for the entire system