Vishakha Patil

Vineet Nair, Vishakha Patil, Gaurav Sinha

Learning good interventions in a causal graph can be modelled as a stochastic multi-armed bandit problem with side-information. First, we study this problem when interventions are more expensive than observations and a budget is specified. If there are no backdoor paths from an intervenable node to the reward node then we propose an algorithm to minimize simple regret that optimally trades-off observations and interventions based on the cost of intervention. We also propose an algorithm that accounts for the cost of interventions, utilizes causal side-information, and minimizes the expected cumulative regret without exceeding the budget. Our cumulative-regret minimization algorithm performs better than standard algorithms that do not take side-information into account. Finally, we study the problem of learning best interventions without budget constraint in general graphs and give an algorithm that achieves constant expected cumulative regret in terms of the instance parameters when the parent distribution of the reward variable for each intervention is known. Our results are experimentally validated and compared to the best-known bounds in the current literature.

Arnab Maiti, Vishakha Patil, Arindam Khan

We study the Stochastic Multi-armed Bandit problem under bounded arm-memory. In this setting, the arms arrive in a stream, and the number of arms that can be stored in the memory at any time, is bounded. The decision-maker can only pull arms that are present in the memory. We address the problem from the perspective of two standard objectives: 1) regret minimization, and 2) best-arm identification. For regret minimization, we settle an important open question by showing an almost tight hardness. We show Ω(T^{2/3}) cumulative regret in expectation for arm-memory size of (n-1), where n is the number of arms. For best-arm identification, we study two algorithms. First, we present an O(r) arm-memory r-round adaptive streaming algorithm to find an ε-best arm. In r-round adaptive streaming algorithm for best-arm identification, the arm pulls in each round are decided based on the observed outcomes in the earlier rounds. The best-arm is the output at the end of r rounds. The upper bound on the sample complexity of our algorithm matches with the lower bound for any r-round adaptive streaming algorithm. Secondly, we present a heuristic to find the ε-best arm with optimal sample complexity, by storing only one extra arm in the memory.

Vishakha Patil, Ganesh Ghalme, Vineet Nair et al.

We study an interesting variant of the stochastic multi-armed bandit problem, called the Fair-SMAB problem, where each arm is required to be pulled for at least a given fraction of the total available rounds. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, called $r$-Regret, that takes into account the above fairness constraints and naturally extends the conventional notion of regret. Our primary contribution is characterizing a class of Fair-SMAB algorithms by two parameters: the unfairness tolerance and the learning algorithm used as a black-box. We provide a fairness guarantee for this class that holds uniformly over time irrespective of the choice of the learning algorithm. In particular, when the learning algorithm is UCB1, we show that our algorithm achieves $O(\ln T)$ $r$-Regret. Finally, we evaluate the cost of fairness in terms of the conventional notion of regret.

Vishakha Patil, Ganesh Ghalme, Vineet Nair et al.

We study an interesting variant of the stochastic multi-armed bandit problem, called the Fair-SMAB problem, where each arm is required to be pulled for at least a given fraction of the total available rounds. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, called r-Regret, that takes into account the above fairness constraints and naturally extends the conventional notion of regret. Our primary contribution is characterizing a class of Fair-SMAB algorithms by two parameters: the unfairness tolerance and learning algorithm used as a black-box. We provide a fairness guarantee for this class that holds uniformly over time irrespective of the choice of the learning algorithm. In particular, when the learning algorithm is UCB1, we show that our algorithm achieves O(log(T)) r-Regret. Finally, we evaluate the cost of fairness in terms of the conventional notion of regret.