Arghya Roy Chaudhuri

Arghya Roy Chaudhuri, Pratik Jawanpuria, Bamdev Mishra · microsoft-research

In this work, we propose a multi-armed bandit-based framework for identifying a compact set of informative data instances (i.e., the prototypes) from a source dataset $S$ that best represents a given target set $T$. Prototypical examples of a given dataset offer interpretable insights into the underlying data distribution and assist in example-based reasoning, thereby influencing every sphere of human decision-making. Current state-of-the-art prototype selection approaches require $O(|S||T|)$ similarity comparisons between source and target data points, which becomes prohibitively expensive for large-scale settings. We propose to mitigate this limitation by employing stochastic greedy search in the space of prototypical examples and multi-armed bandits for reducing the number of similarity comparisons. Our randomized algorithm, ProtoBandit, identifies a set of $k$ prototypes incurring $O(k^3|S|)$ similarity comparisons, which is independent of the size of the target set. An interesting outcome of our analysis is for the $k$-medoids clustering problem $T = S$ setting) in which we show that our algorithm ProtoBandit approximates the BUILD step solution of the partitioning around medoids (PAM) method in $O(k^3|S|)$ complexity. Empirically, we observe that ProtoBandit reduces the number of similarity computation calls by several orders of magnitudes ($100-1000$ times) while obtaining solutions similar in quality to those from state-of-the-art approaches.

Arghya Roy Chaudhuri, Shivaram Kalyanakrishnan

In this paper, we propose a constant word (RAM model) algorithm for regret minimisation for both finite and infinite Stochastic Multi-Armed Bandit (MAB) instances. Most of the existing regret minimisation algorithms need to remember the statistics of all the arms they encounter. This may become a problem for the cases where the number of available words of memory is limited. Designing an efficient regret minimisation algorithm that uses a constant number of words has long been interesting to the community. Some early attempts consider the number of arms to be infinite, and require the reward distribution of the arms to belong to some particular family. Recently, for finitely many-armed bandits an explore-then-commit based algorithm~\citep{Liau+PSY:2018} seems to escape such assumption. However, due to the underlying PAC-based elimination their method incurs a high regret. We present a conceptually simple, and efficient algorithm that needs to remember statistics of at most $M$ arms, and for any $K$-armed finite bandit instance it enjoys a $O(KM +K^{1.5}\sqrt{T\log (T/MK)}/M)$ upper-bound on regret. We extend it to achieve sub-linear \textit{quantile-regret}~\citep{RoyChaudhuri+K:2018} and empirically verify the efficiency of our algorithm via experiments.

Arghya Roy Chaudhuri, Shivaram Kalyanakrishnan

We consider the problem of identifying any $k$ out of the best $m$ arms in an $n$-armed stochastic multi-armed bandit. Framed in the PAC setting, this particular problem generalises both the problem of `best subset selection' and that of selecting `one out of the best m' arms [arcsk 2017]. In applications such as crowd-sourcing and drug-designing, identifying a single good solution is often not sufficient. Moreover, finding the best subset might be hard due to the presence of many indistinguishably close solutions. Our generalisation of identifying exactly $k$ arms out of the best $m$, where $1 \leq k \leq m$, serves as a more effective alternative. We present a lower bound on the worst-case sample complexity for general $k$, and a fully sequential PAC algorithm, \GLUCB, which is more sample-efficient on easy instances. Also, extending our analysis to infinite-armed bandits, we present a PAC algorithm that is independent of $n$, which identifies an arm from the best $ρ$ fraction of arms using at most an additive poly-log number of samples than compared to the lower bound, thereby improving over [arcsk 2017] and [Aziz+AKA:2018]. The problem of identifying $k > 1$ distinct arms from the best $ρ$ fraction is not always well-defined; for a special class of this problem, we present lower and upper bounds. Finally, through a reduction, we establish a relation between upper bounds for the `one out of the best $ρ$' problem for infinite instances and the `one out of the best $m$' problem for finite instances. We conjecture that it is more efficient to solve `small' finite instances using the latter formulation, rather than going through the former.