We study a sequential resource allocation problem where, at each round, the decision-maker needs to allocate its limited budget among different available entities. In doing so, the decision-maker obtains the reward for each entity in that round. The goal of the decision-maker is to maximize the expected cumulative reward or equivalently minimize cumulative regret over a total of T rounds. Sequential resource allocation can be modeled as a combinatorial bandit by viewing the allocation of a budget to an entity as a base arm. In the context of resource allocation, the rewards received under different budget allocations are likely to be correlated. We propose a novel correlated combinatorial bandit framework that explicitly models such correlations. We develop a novel Correlated-UCB algorithm for online resource allocation, which yields significantly reduced regret relative to correlation-agnostic algorithms. In certain cases, our proposed algorithm even achieves bounded regret, which is an order-wise reduction in the regret relative to the correlation-agnostic approach, which incurs logarithmic regret under all scenarios. We validate these performance gains through experiments on several applications such as online power allocation across wireless channels, job scheduling in multi-server systems and online channel assignment for the slotted ALOHA protocol.

We study the problem of scalable design of Error-Correcting Output Codes (ECOC) for multi-class classification. Prior works on ECOC-based classifiers are limited to codebooks with small number of rows (classes) or columns, and do not provide optimality guarantees for the codebook design problem. We address these limitations by developing a codebook design approach based on a Mixed-Integer Quadratically Constrained Program (MIQCP). This discrete formulation is naturally suited for maximizing the error-correction capability of ECOC-based classifiers and incorporates various design criteria in a flexible manner. Our solution approach is tractable in that it incrementally increases the codebook size by adding columns to maximize the gain in error-correcting capability. In particular, we show that the maximal gain in error-correction can be upper bounded by solving a graph-coloring problem. As a result, we can efficiently generate near-optimal codebooks for very large problem instances. These codebooks provide competitive multi-class classification performance on small class datasets such as MNIST and CIFAR10. Moreover, by leveraging transfer-learned binary classifiers, we achieve better classification performance over transfer-learned multi-class CNNs on large class datasets such as CIFAR100, Caltech-101/256. Our results highlight the advantages of simple and modular ECOC-based classifiers in improving classification accuracy without the risk of overfitting.

We consider a finite-armed structured bandit problem in which mean rewards of different arms are known functions of a common hidden parameter θ*. This problem setting subsumes several previously studied frameworks that assume linear or invertible reward functions. We propose a novel approach to gradually estimate the hidden θ*and use the estimate together with the mean reward functions to substantially reduce exploration of sub-optimal arms. This approach enables us to fundamentally generalize any classic bandit algorithm including UCB and Thompson Sampling to the structured bandit setting. We prove via regret analysis that our proposed UCB-C and TS-C algorithms (structured bandit versions of UCB and Thompson Sampling, respectively) pull only a subset of the sub-optimal arms O(log T ) times while the other sub-optimal arms (referred to as non-competitive arms) are pulled O(1) times. As a result, in cases where all sub-optimal arms are noncompetitive, which can happen in many practical scenarios, the proposed algorithms achieve bounded regret.

Error-Correcting Output Codes (ECOCs) offer a principled approach for combining binary classifiers into multiclass classifiers. In this paper, we study the problem of designing optimal ECOCs to achieve both nominal and adversarial accuracy using Support Vector Machines (SVMs) and binary deep neural networks. We develop a scalable Integer Programming (IP) formulation to design minimal codebooks with desirable error correcting properties. Our work leverages the advances in IP solution techniques to generate codebooks with optimality guarantees. To achieve tractability, we exploit the underlying graph-theoretic structure of the constraint set. Particularly, the size of the constraint set can be significantly reduced using edge clique covers. Using this reduction technique along with Plotkin’s bound in coding theory, we demonstrate that our approach is scalable to a large number of classes. The resulting codebooks achieve a high nominal accuracy relative to standard codebooks (e.g., one-vs-all, one-vs-one, and dense/sparse codes). Interestingly, our codebooks provide non-trivial robustness to white-box attacks without any adversarial training.

We consider a multi-armed bandit framework where the rewards obtained by pulling different arms are correlated. We develop a unified approach to leverage these reward correlations and present fundamental generalizations of classic bandit algorithms to the correlated setting. We present a unified proof technique to analyze the proposed algorithms. Rigorous analysis of C-UCB (the correlated bandit versions of Upper-confidence-bound) reveals that the algorithm end up pulling certain sub-optimal arms, termed as non-competitive, only O(1) times, as opposed to the O(logT) pulls required by classic bandit algorithms such as UCB, TS etc. We present regret-lower bound and show that when arms are correlated through a latent random source, our algorithms obtain order-optimal regret. We validate the proposed algorithms via experiments on the MovieLens and Goodreads datasets, and show significant improvement over classical bandit algorithms.

Multi-armed bandit models are widely studied sequential decision-making problems that exemplify the exploration-exploitation trade-off. We study a novel correlated multi-armed bandit model where the rewards obtained from the arms are functions of a common latent random variable. We propose and analyze the performance of the C-UCB algorithm that leverages the correlations between arms to reduce the cumulative regret (i.e., to increase the total reward obtained after T rounds). Unlike the standard UCB algorithm that pulls all sub-optimal arms O(log T) times, the C-UCB algorithm takes only O(1) times to identify that some arms, which we refer to as non-competitive arms, are optimal. Thus, we effectively reduce a K-armed bandit problem to a C + 1-armed bandit problem with C <; K denoting the number of competitive, where C can be computed from the reward functions. A key consequence is that when C = 0, our algorithm achieves a constant (i.e., O(1)) regret instead of the standard O(log T) scaling with the number of rounds T . Establishing lower bounds for the regret, we show that the C-UCB algorithm is order-wise optimal and demonstrate its superiority against other algorithms via numerical simulations.

We consider the task of content replication in distributed content delivery systems used by Video-on-Demand (VoD) services with large content catalogs. The prior work in this area focuses on the setting where each request is generated independent of all past requests. Motivated by the fact that most popular VoD services offer recommendations to users based on their viewing history, in a departure from existing studies, we study the setting where there is time-correlation in requests coming from each user.

Multi-Objective Evolutionary Algorithms(MOEAs) have been gaining increased popularity and usage in different fields of engineering. For real world large scale optimization problems with large variable/search space, using a large population of individuals in proportion to the size of search space is ubiquitous. Solving such problems with current state of the art algorithms like NSGA-II [1] is pervasive. The strength of NSGA-II lies in its non-dominance selection procedure and non-dominance based sorting of a population of individuals. Although, the non-dominated sort is computationally efficient for a small population (102- 103) of solutions but becomes computationally expensive and slow for a large population (104- 105) of solutions. Also, various archive based algorithms [2], [3] have been proposed in past which make use of a large population apart from the principal population. Therefore, there is a huge need for a scalable and parallel implementation of NSGA-II. With advent of consumer level Graphics processing units(GPUs) and advancement of CUDA framework we try to fill this research gap using GPGPU architecture. In this paper we propose a parallel GPU based implementation of NSGA-II with major focus on non-dominated sorting. The proposed approach can be easily coupled with the original form of NSGA-II to solve real world problems using large populations.