Abstract

In this work we study the safe sequential decision making problem under the setting of adversarial contextual bandits with sequential risk constraints. At each round, nature prepares a context a cost for each arm, and additionally a risk for each arm. The learner leverages the context to pull an arm and receives the corresponding cost and risk associated with the pulled arm. In addition to minimizing the cumulative cost, for safety purposes, the learner needs to make safe decisions such that the average of the cumulative risk from all pulled arms should not be larger than a pre-defined threshold. To address this problem, we first study online convex programming in the full information setting where in each round the learner receives an adversarial convex loss and a convex constraint. We develop a meta algorithm leveraging online mirror descent for the full information setting and then extend it to contextual bandit with sequential risk constraints setting us ing expert advice. Our algorithms can achieve near-optimal regret in terms of minimizing the total cost, while successfully maintaining a sublinear growth of accumulative risk constraint violation. We support our theoretical results by demonstrating our algorithm on a simple simulated robotics reactive control task.