Fighting Bandits with a New Kind of Smoothness

We define a novel family of algorithms for the adversarial multi-armed bandit problem, and provide a simple analysis technique based on convex smoothing. We prove two main results. First, we show that regularization via the \emph{Tsallis entropy}, which includes EXP3 as a special case, achieves the $\Theta(\sqrt{TN})$ minimax regret. Second, we show that a wide class of perturbation methods achieve a near-optimal regret as low as $O(\sqrt{TN \log N})$ if the perturbation distribution has a bounded hazard rate. For example, the Gumbel, Weibull, Frechet, Pareto, and Gamma distributions all satisfy this key property.Comment: In Proceedings of NIPS, 201

Analysis of Perturbation Techniques in Online Learning

The most commonly used regularization technique in machine learning is to directly add a penalty function to the optimization objective. For example, $L_2$ regularization is universally applied to a wide range of models including linear regression and neural networks. The alternative regularization technique, which has become essential in modern applications of machine learning, is implicit regularization by injecting random noise into the training data. In fact, this idea of using random perturbations as regularizer has been one of the first algorithms for online learning, where a learner chooses actions iteratively on a data sequence that may be designed adversarially to thwart learning process. One such classical algorithm is known as Follow The Perturbed Leader (FTPL). This dissertation presents new interpretations of FTPL. In the first part, we show that FTPL is equivalent to playing the gradients of a stochastically smoothed potential function in the dual space. In the second part, we show that FTPL is the extension of a differentially private mechanism that has inherent stability guarantees. These perspectives lead to novel frameworks for FTPL regret analysis, which not only prove strong performance guarantees but also help characterize the optimal choice of noise distributions. Furthermore, they extend to the partial information setting where the learner observes only part of the input data.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143968/1/chansool_1.pd

Bespoke Nanoparticle Synthesis and Chemical Knowledge Discovery Via Autonomous Experimentations

The optimization of nanomaterial synthesis using numerous synthetic variables is considered to be extremely laborious task because the conventional combinatorial explorations are prohibitively expensive. In this work, we report an autonomous experimentation platform developed for the bespoke design of nanoparticles (NPs) with targeted optical properties. This platform operates in a closed-loop manner between a batch synthesis module of NPs and a UV- Vis spectroscopy module, based on the feedback of the AI optimization modeling. With silver (Ag) NPs as a representative example, we demonstrate that the Bayesian optimizer implemented with the early stopping criterion can efficiently produce Ag NPs precisely possessing the desired absorption spectra within only 200 iterations (when optimizing among five synthetic reagents). In addition to the outstanding material developmental efficiency, the analysis of synthetic variables further reveals a novel chemistry involving the effects of citrate in Ag NP synthesis. The amount of citrate is a key to controlling the competitions between spherical and plate-shaped NPs and, as a result, affects the shapes of the absorption spectra as well. Our study highlights both capabilities of the platform to enhance search efficiencies and to provide a novel chemical knowledge by analyzing datasets accumulated from the autonomous experimentations