Arun Verma

Zhongxiang Dai, Gregory Kang Ruey Lau, Arun Verma et al.

Kernelized bandits, also known as Bayesian optimization (BO), has been a prevalent method for optimizing complicated black-box reward functions. Various BO algorithms have been theoretically shown to enjoy upper bounds on their cumulative regret which are sub-linear in the number T of iterations, and a regret lower bound of Omega(sqrt(T)) has been derived which represents the unavoidable regrets for any classical BO algorithm. Recent works on quantum bandits have shown that with the aid of quantum computing, it is possible to achieve tighter regret upper bounds better than their corresponding classical lower bounds. However, these works are restricted to either multi-armed or linear bandits, and are hence not able to solve sophisticated real-world problems with non-linear reward functions. To this end, we introduce the quantum-Gaussian process-upper confidence bound (Q-GP-UCB) algorithm. To the best of our knowledge, our Q-GP-UCB is the first BO algorithm able to achieve a regret upper bound of O(polylog T), which is significantly smaller than its regret lower bound of Omega(sqrt(T)) in the classical setting. Moreover, thanks to our novel analysis of the confidence ellipsoid, our Q-GP-UCB with the linear kernel achieves a smaller regret than the quantum linear UCB algorithm from the previous work. We use simulations, as well as an experiment using a real quantum computer, to verify that the theoretical quantum speedup achieved by our Q-GP-UCB is also potentially relevant in practice.

Arun Verma, Indrajit Saha, Makoto Yokoo et al.

This paper considers a novel variant of the online fair division problem involving multiple agents in which a learner sequentially observes an indivisible item that has to be irrevocably allocated to one of the agents while satisfying a fairness and efficiency constraint. Existing algorithms assume a small number of items with a sufficiently large number of copies, which ensures a good utility estimation for all item-agent pairs from noisy bandit feedback. However, this assumption may not hold in many real-life applications, for example, an online platform that has a large number of users (items) who use the platform's service providers (agents) only a few times (a few copies of items), which makes it difficult to accurately estimate utilities for all item-agent pairs. To address this, we assume utility is an unknown function of item-agent features. We then propose algorithms that model online fair division as a contextual bandit problem, with sub-linear regret guarantees. Our experimental results further validate the effectiveness of the proposed algorithms.

Arun Verma, Indrajit Saha, Makoto Yokoo et al.

This paper considers a contextual bandit problem involving multiple agents, where a learner sequentially observes the contexts and the agent's reported arms, and then selects the arm that maximizes the system's overall reward. Existing work in contextual bandits assumes that agents truthfully report their arms, which is unrealistic in many real-life applications. For instance, consider an online platform with multiple sellers; some sellers may misrepresent product quality to gain an advantage, such as having the platform preferentially recommend their products to online users. To address this challenge, we propose an algorithm, COBRA, for contextual bandit problems involving strategic agents that disincentivize their strategic behavior without using any monetary incentives, while having incentive compatibility and a sub-linear regret guarantee. Our experimental results also validate the different performance aspects of our proposed algorithm.

Arun Verma, Manjesh K. Hanawal

In this paper, we study a novel Stochastic Network Utility Maximization (NUM) problem where the utilities of agents are unknown. The utility of each agent depends on the amount of resource it receives from a network operator/controller. The operator desires to do a resource allocation that maximizes the expected total utility of the network. We consider threshold type utility functions where each agent gets non-zero utility if the amount of resource it receives is higher than a certain threshold. Otherwise, its utility is zero (hard real-time). We pose this NUM setup with unknown utilities as a regret minimization problem. Our goal is to identify a policy that performs as `good' as an oracle policy that knows the utilities of agents. We model this problem setting as a bandit setting where feedback obtained in each round depends on the resource allocated to the agents. We propose algorithms for this novel setting using ideas from Multiple-Play Multi-Armed Bandits and Combinatorial Semi-Bandits. We show that the proposed algorithm is optimal when all agents have the same utility. We validate the performance guarantees of our proposed algorithms through numerical experiments.

Arun Verma, Manjesh K. Hanawal, Nandyala Hemachandra

In medical diagnosis, physicians predict the state of a patient by checking measurements (features) obtained from a sequence of tests, e.g., blood test, urine test, followed by invasive tests. As tests are often costly, one would like to obtain only those features (tests) that can establish the presence or absence of the state conclusively. Another aspect of medical diagnosis is that we are often faced with unsupervised prediction tasks as the true state of the patients may not be known. Motivated by such medical diagnosis problems, we consider a {\it Cost-Sensitive Medical Diagnosis} (CSMD) problem, where the true state of patients is unknown. We formulate the CSMD problem as a feature selection problem where each test gives a feature that can be used in a prediction model. Our objective is to learn strategies for selecting the features that give the best trade-off between accuracy and costs. We exploit the `Weak Dominance' property of problem to develop online algorithms that identify a set of features which provides an `optimal' trade-off between cost and accuracy of prediction without requiring to know the true state of the medical condition. Our empirical results validate the performance of our algorithms on problem instances generated from real-world datasets.