  Thompson Sampling has generated significant interest due to its better
empirical performance than upper confidence bound based algorithms. In this
paper, we study Thompson Sampling based algorithm for Unsupervised Sequential
Selection (USS) problem. The USS problem is a variant of the stochastic
multi-armed bandits problem, where the loss of an arm can not be inferred from
the observed feedback. In the USS setup, arms are associated with fixed costs
and are ordered, forming a cascade. In each round, the learner selects an arm
and observes the feedback from arms up to the selected arm. The learner's goal
is to find the arm that minimizes the expected total loss. The total loss is
the sum of the cost incurred for selecting the arm and the stochastic loss
associated with the selected arm. The problem is challenging because, without
knowing the mean loss, one cannot compute the total loss for the selected arm.
Clearly, learning is feasible only if the optimal arm can be inferred from the
problem structure. As shown in the prior work, learning is possible when the
problem instance satisfies the so-called `Weak Dominance' (WD) property. Under
WD, we show that our Thompson Sampling based algorithm for the USS problem
achieves near optimal regret and has better numerical performance than existing
algorithms.
