Related papers: On optimal policy in the group testing with incomp…
We study the problem of identifying a small set $k\sim n^\theta$, $0<\theta<1$, of infected individuals within a large population of size $n$ by testing groups of individuals simultaneously. All tests are conducted concurrently. The goal is…
The goal of a sequential decision making problem is to design an interactive policy that adaptively selects a group of items, each selection is based on the feedback from the past, in order to maximize the expected utility of selected…
In the theory of dynamic programming, an optimal policy is a policy whose lifetime value dominates that of all other policies from every possible initial condition in the state space. This raises a natural question: when does optimality…
In group testing, the task is to determine the distinguished members of a set of objects L by asking subset queries of the form ``does the subset Q of L contain a distinguished object?'' The primary biological application of group testing…
We consider the problem of designing affirmative action policies for selecting the top-k candidates from a pool of applicants. We assume that for each candidate we have socio-demographic attributes and a series of variables that serve as…
The main goal of group testing with inhibitors (GTI) is to efficiently identify a small number of defective items and inhibitor items in a large set of items. A test on a subset of items is positive if the subset satisfies some specific…
Affine policies (or control) are widely used as a solution approach in dynamic optimization where computing an optimal adjustable solution is usually intractable. While the worst case performance of affine policies can be significantly bad,…
In this paper, we study a dynamic on/off server scheduling problem in a queueing system with multi-class servers, where servers are heterogeneous and can be classified into $K$ groups. Servers in the same group are homogeneous. A scheduling…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
We study the policy testing problem in discounted Markov decision processes (MDPs) in the fixed-confidence setting under a generative model with static sampling. The goal is to decide whether the value of a given policy exceeds a specified…
We study a ranking and selection problem of learning from choice-based feedback with dynamic assortments. In this problem, a company sequentially displays a set of items to a population of customers and collects their choices as feedback.…
This paper is concerned with the convergence rate of policy iteration for (deterministic) optimal control problems in continuous time. To overcome the problem of ill-posedness due to lack of regularity, we consider a semi-discrete scheme by…
We study Dorfman's classical group testing protocol in a novel setting where individual specimen statuses are modeled as exchangeable random variables. We are motivated by infectious disease screening. In that case, specimens which arrive…
Optimal Markov Decision Process policies for problems with finite state and action space are identified through a partial ordering by comparing the value function across states. This is referred to as state-based optimality. This paper…
We study the fair allocation of indivisible goods with variable groups. In this model, the goal is to partition the agents into groups of given sizes and allocate the goods to the groups in a fair manner. We show that for any number of…
Sequential multi-class diagnosis, also known as multi-hypothesis testing, is a classical sequential decision problem with broad applications. However, the optimal solution remains, in general, unknown as the dynamic program suffers from the…
We address the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem…
In one-stage or non-adaptive group testing, instead of testing every sample unit individually, they are split, bundled in pools, and simultaneously tested. The results are then decoded to infer the states of the individual items. This…
Conferences such as FUN with Algorithms routinely buy goodies (e.g., t-shirts, coffee mugs, etc) for their attendees. Often, said goodies come in different types, varying by color or design, and organizers need to decide how many goodies of…
We study the problem usually referred to as group testing in the context of COVID-19. Given $n$ samples taken from patients, how should we select mixtures of samples to be tested, so as to maximize information and minimize the number of…