Many online learning problems require choosing policies when the environment's distributions are unknown. This paper considers stochastic optimization problems in that setting, where each period the algorithm plays a policy and observes feedback. The feedback model is semi-bandit: it reveals more than a simple reward but less than the full state of the problem.
The authors focus on monotone stochastic problems and propose an algorithm that achieves near-optimal regret. Regret compares the learner's cumulative performance with that of the best policy in hindsight. A near-optimal guarantee means the algorithm's loss is close to the theoretical minimum, making it an efficient choice for this class of problems.
Because only the abstract is available, the specific algorithm and proof details are not described here. Still, the result is a useful theoretical benchmark for semi-bandit learning in monotone settings.