A Unified View of Large-scale Zero-sum Equilibrium Computation

The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and seemingly different approaches emerged---one an application of no-regret online learning, the other a sophisticated gradient method applied to a convex-concave saddle-point formulation. Since then, both approaches have grown in relative isolation with advancements on one side not effecting the other. In this paper, we rectify this by dissecting and, in a sense, unify the two views.Comment: AAAI Workshop on Computer Poker and Imperfect Informatio

Generalized Boosting Algorithms for Convex Optimization

Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting with respect to any convex objective and introduce a new measure of weak learner performance into this setting which generalizes existing work. We present the weak to strong learning guarantees for the existing gradient boosting work for strongly-smooth, strongly-convex objectives under this new measure of performance, and also demonstrate that this work fails for non-smooth objectives. To address this issue, we present new algorithms which extend this boosting approach to arbitrary convex loss functions and give corresponding weak to strong convergence results. In addition, we demonstrate experimental results that support our analysis and demonstrate the need for the new algorithms we present.Comment: Extended version of paper presented at the International Conference on Machine Learning, 2011. 9 pages + appendix with proof

Experimental Investigation and Computer Modeling of Optical Switching in Distributed Bragg Reflector and Vertical Cavity Surface Emitting Laser Structures

The optical switching capabilities of Distributed Bragg Reflector (DBR) structures, including Vertical Cavity Surface Emitting Lasers (VCSELs) are examined. Reflectivity switching is demonstrated using both thermal and carrier generated effects to alter the DBR/VCSEL layers\u27 refractive indices. Optical bistability is demonstrated at room temperature, under CW photopumped excitation. The optical bistability hysteresis is controllable by spectral location of the pump on the stop band edge. In the VCSEL, reflective bistability is also evidenced; additionally, this bistability is accompanied by a bistability in the VCSEL lasing output intensity, spot size, and wavelength. Modeling of the DBR/VCSEL thermally induced bistability was accomplished using an iterative, three dimensional Green\u27s function solution to the laser induced heat equation. The model predicts thermally generated bistability, indicating a wavelength dependence, reflectivity jump, self focusing induced spot size change, and wavelength jump commensurate with the experimental data. Reflectivity switching due to carrier effects is also demonstrated, the DBR and VCSELs exhibiting subpicosecond switching speeds and contrast ratios of 3:1. Carrier heating, two photon absorption, and thermal components of the reflectivity switching capabilities are examined and found to be consistent with measured nonlinear response characteristics for the refractive index in AlGaAs