Combinatorial Blocking Bandits with Stochastic Delays
This work addresses a more realistic and complex variant of multi-armed bandits for sequential decision-making under uncertainty, with incremental contributions to the field.
The paper tackles the combinatorial blocking bandits problem with stochastic delays, extending prior deterministic models to allow multiple arms per round and random blocking times, and provides a tight analysis of a greedy heuristic with approximation guarantees and a UCB-based algorithm achieving sublinear regret matching lower bounds in delay-free cases.
Recent work has considered natural variations of the multi-armed bandit problem, where the reward distribution of each arm is a special function of the time passed since its last pulling. In this direction, a simple (yet widely applicable) model is that of blocking bandits, where an arm becomes unavailable for a deterministic number of rounds after each play. In this work, we extend the above model in two directions: (i) We consider the general combinatorial setting where more than one arms can be played at each round, subject to feasibility constraints. (ii) We allow the blocking time of each arm to be stochastic. We first study the computational/unconditional hardness of the above setting and identify the necessary conditions for the problem to become tractable (even in an approximate sense). Based on these conditions, we provide a tight analysis of the approximation guarantee of a natural greedy heuristic that always plays the maximum expected reward feasible subset among the available (non-blocked) arms. When the arms' expected rewards are unknown, we adapt the above heuristic into a bandit algorithm, based on UCB, for which we provide sublinear (approximate) regret guarantees, matching the theoretical lower bounds in the limiting case of absence of delays.