Gaussian Process bandits with adaptive discretization Machine Learning

In this paper, the problem of maximizing a black-box function $f:\mathcal{X} \to \mathbb{R}$ is studied in the Bayesian framework with a Gaussian Process (GP) prior. In particular, a new algorithm for this problem is proposed, and high probability bounds on its simple and cumulative regret are established. The query point selection rule in most existing methods involves an exhaustive search over an increasingly fine sequence of uniform discretizations of $\mathcal{X}$. The proposed algorithm, in contrast, adaptively refines $\mathcal{X}$ which leads to a lower computational complexity, particularly when $\mathcal{X}$ is a subset of a high dimensional Euclidean space. In addition to the computational gains, sufficient conditions are identified under which the regret bounds of the new algorithm improve upon the known results. Finally an extension of the algorithm to the case of contextual bandits is proposed, and high probability bounds on the contextual regret are presented.

Generalized Dual Decomposition for Bounding Maximum Expected Utility of Influence Diagrams with Perfect Recall

AAAI Conferences

We introduce a generalized dual decomposition bound for computing the maximum expected utility of influence diagrams based on the dual decomposition method generalized to $L^p$ space.  The main goal is to devise an approximation scheme free from translations required by existing variational approaches while exploiting the local structure of sum of utility functions as well as the conditional independence of probability functions.  In this work, the generalized dual decomposition method is applied to the algebraic framework called valuation algebra for influence diagrams which handles probability and expected utility as a pair. The proposed approach allows a sequential decision problem to be decomposed as a collection of sub-decision problems of bounded complexity and the upper bound of maximum expected utility to be computed by combining the local expected utilities. Thus, it has a flexible control of space and time complexity for computing the bound.  In addition, the upper bounds can be further minimized by reparameterizing the utility functions. Since the global objective function for the minimization is nonconvex, we present a gradient-based local search algorithm in which the outer loop controls the randomization of the initial configurations and the inner loop tightens the upper-bound based on block coordinate descent with gradients perturbed by a random noise. The experimental evaluation demonstrates highlights of the proposed approach on finite horizon MDP/POMDP instances.

Fast Abductive Reasoning Over Ontologies

AAAI Conferences

In this paper we present a new method for reasoning abductively over instances of a triples ontology. We compute the usefulness of evidence toward making an inference rather than its truth value, probabilistic or otherwise. This allows us to process ambiguous, incomplete, and inconsistent information effectively while remaining faithful to the ontology. The method is fast, scalable, and robust. We first motivate the method with a simple cognitive model and then present details of the algorithms. Finally, we present results from experiments that indicate that the method scales well in space and time complexity and promises to be highly effective.

AI - The present in the making


For many people, the concept of Artificial Intelligence (AI) is a thing of the future. It is the technology that has yet to be introduced. But Professor Jon Oberlander disagrees. He was quick to point out that AI is not in the future, it is now in the making. He began by mentioning Alexa, Amazon's star product. It is an artificial intelligent personal assistant, which was made popular by Amazon Echo devices. With a plethora of functions, Alexa quickly gained much popularity and fame. It is used for home automation, music streaming, sports updates, messaging and email, and even to order food.