Subhashini Krishnasamy

Subhashini Krishnasamy, Rajat Sen, Ramesh Johari et al. · stanford

Consider a queueing system consisting of multiple servers. Jobs arrive over time and enter a queue for service; the goal is to minimize the size of this queue. At each opportunity for service, at most one server can be chosen, and at most one job can be served. Service is successful with a probability (the service probability) that is a priori unknown for each server. An algorithm that knows the service probabilities (the "genie") can always choose the server of highest service probability. We study algorithms that learn the unknown service probabilities. Our goal is to minimize queue-regret: the (expected) difference between the queue-lengths obtained by the algorithm, and those obtained by the "genie." Since queue-regret cannot be larger than classical regret, results for the standard multi-armed bandit problem give algorithms for which queue-regret increases no more than logarithmically in time. Our paper shows surprisingly more complex behavior. In particular, as long as the bandit algorithm's queues have relatively long regenerative cycles, queue-regret is similar to cumulative regret, and scales (essentially) logarithmically. However, we show that this "early stage" of the queueing bandit eventually gives way to a "late stage", where the optimal queue-regret scaling is $O(1/t)$. We demonstrate an algorithm that (order-wise) achieves this asymptotic queue-regret in the late stage. Our results are developed in a more general model that allows for multiple job classes as well.

Subhashini Krishnasamy, Akhil P T, Ari Arapostathis et al.

In small-cell wireless networks where users are connected to multiple base stations (BSs), it is often advantageous to switch off dynamically a subset of BSs to minimize energy costs. We consider two types of energy cost: (i) the cost of maintaining a BS in the active state, and (ii) the cost of switching a BS from the active state to inactive state. The problem is to operate the network at the lowest possible energy cost (sum of activation and switching costs) subject to queue stability. In this setting, the traditional approach -- a Max-Weight algorithm along with a Lyapunov-based stability argument -- does not suffice to show queue stability, essentially due to the temporal co-evolution between channel scheduling and the BS activation decisions induced by the switching cost. Instead, we develop a learning and BS activation algorithm with slow temporal dynamics, and a Max-Weight based channel scheduler that has fast temporal dynamics. We show using convergence of time-inhomogeneous Markov chains, that the co-evolving dynamics of learning, BS activation and queue lengths lead to near optimal average energy costs along with queue stability.

Sandeep Juneja, Subhashini Krishnasamy

Given a vector of probability distributions, or arms, each of which can be sampled independently, we consider the problem of identifying the partition to which this vector belongs from a finitely partitioned universe of such vector of distributions. We study this as a pure exploration problem in multi armed bandit settings and develop sample complexity bounds on the total mean number of samples required for identifying the correct partition with high probability. This framework subsumes well studied problems such as finding the best arm or the best few arms. We consider distributions belonging to the single parameter exponential family and primarily consider partitions where the vector of means of arms lie either in a given set or its complement. The sets considered correspond to distributions where there exists a mean above a specified threshold, where the set is a half space and where either the set or its complement is a polytope, or more generally, a convex set. In these settings, we characterize the lower bounds on mean number of samples for each arm highlighting their dependence on the problem geometry. Further, inspired by the lower bounds, we propose algorithms that can match these bounds asymptotically with decreasing probability of error. Applications of this framework may be diverse. We briefly discuss one associated with finance.

Subhashini Krishnasamy, Rajat Sen, Sewoong Oh et al.

With a vast number of items, web-pages, and news to choose from, online services and the customers both benefit tremendously from personalized recommender systems. Such systems however provide great opportunities for targeted advertisements, by displaying ads alongside genuine recommendations. We consider a biased recommendation system where such ads are displayed without any tags (disguised as genuine recommendations), rendering them indistinguishable to a single user. We ask whether it is possible for a small subset of collaborating users to detect such a bias. We propose an algorithm that can detect such a bias through statistical analysis on the collaborating users' feedback. The algorithm requires only binary information indicating whether a user was satisfied with each of the recommended item or not. This makes the algorithm widely appealing to real world issues such as identification of search engine bias and pharmaceutical lobbying. We prove that the proposed algorithm detects the bias with high probability for a broad class of recommendation systems when sufficient number of users provide feedback on sufficient number of recommendations. We provide extensive simulations with real data sets and practical recommender systems, which confirm the trade offs in the theoretical guarantees.