Thompson Sampling for Unsupervised Sequential Selection

TL;DR

This paper introduces a Thompson Sampling algorithm for the Unsupervised Sequential Selection problem, a variant of multi-armed bandits where feedback is limited, achieving near-optimal regret under certain conditions.

Contribution

It proposes a novel Thompson Sampling approach for USS, demonstrating near-optimal regret and improved numerical performance over existing methods.

Findings

Achieves near-optimal regret in USS under Weak Dominance.

Outperforms existing algorithms in numerical experiments.

Provides theoretical analysis of Thompson Sampling in unsupervised settings.

Abstract

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.