In the realm of multi-armed bandit problems, the Gittins index policy is known to be optimal in maximizing the expected total discounted reward obtained from pulling the Markovian arms. In most realistic scenarios however, the Markovian state transition probabilities are unknown and therefore the Gittins indices cannot be computed. One can then resort to reinforcement learning (RL) algorithms that explore the state space to learn these indices while exploiting to maximize the reward collected. In this work, we propose tabular (QGI) and Deep RL (DGN) algorithms for learning the Gittins index that are based on the retirement formulation for the multi-armed bandit problem. When compared with existing RL algorithms that learn the Gittins index, our algorithms have a lower run time, require less storage space (small Q-table size in QGI and smaller replay buffer in DGN), and illustrate better empirical convergence to the Gittins index. This makes our algorithm well suited for problems with large state spaces and is a viable alternative to existing methods. As a key application, we demonstrate the use of our algorithms in minimizing the mean flowtime in a job scheduling problem when jobs are available in batches and have an unknown service time distribution.

We consider a distributed storage system which stores several hot (popular) and cold (less popular) data files across multiple nodes or servers. Hot files are stored using repetition codes while cold files are stored using erasure codes. The nodes are prone to failure and hence at any given time, we assume that only a fraction of the nodes are available. Using a cavity process based mean field framework, we analyze the download time for users accessing hot or cold data in the presence of failed nodes. Our work also illustrates the impact of the choice of the storage code on the download time performance of users in the system.

In distributed machine learning (DML), the training data is distributed across multiple worker nodes to perform the underlying training in parallel. One major problem affecting the performance of DML algorithms is presence of stragglers. These are nodes that are terribly slow in performing their task which results in under-utilization of the training data that is stored in them. Towards this, gradient coding mitigates the impact of stragglers by adding sufficient redundancy in the data. Gradient coding and other straggler mitigation schemes assume that the straggler behavior of the worker nodes is identical. Our experiments on the Amazon AWS cluster however suggest otherwise and we see that there is a correlation in the straggler behavior across iterations. To model this, we introduce a heterogeneous straggler model where nodes are categorized into two classes, slow and active. To better utilize training data stored with slow nodes, we modify the existing gradient coding schemes with shuffling of the training data among workers. Our results (both simulation and cloud experiments) suggest remarkable improvement with shuffling over existing schemes. We perform theoretical analysis for the proposed models justifying their utility.

Based on the covert communication framework, we consider a covert queueing problem that has a Markovian statistic. Willie jobs arrive according to a Poisson process and require service from server Bob. Bob does not have a queue for jobs to wait and hence when the server is busy, arriving Willie jobs are lost. Willie and Bob enter a contract under which Bob should only serve Willie jobs. As part of the usage statistic, for a sequence of N consecutive jobs that arrived, Bob informs Willie whether each job was served or lost (this is the Markovian statistic). Bob is assumed to be violating the contract and admitting non-Willie (Nillie) jobs according to a Poisson process. For such a setting, we identify the hypothesis testing to be performed (given the Markovian data) by Willie to detect the presence or absence of Nillie jobs. We also characterize the upper bound on arrival rate of Nillie jobs such that the error in the hypothesis testing of Willie is arbitrarily large, ensuring covertness in admitting Nillie jobs.