Combinatorial Cascading Bandits
This work addresses a partial monitoring problem in network routing and similar domains, offering a novel algorithm for scenarios with non-linear rewards and partial observability, though it is incremental as it builds on existing stochastic combinatorial semi-bandits.
The paper tackles the problem of combinatorial cascading bandits, where an agent selects constrained tuples of items with stochastic binary weights and receives a reward only if all weights are one, observing only the first failing item. The result is the CombCascade algorithm, which achieves gap-dependent and gap-free regret bounds and performs well on real-world problems even when assumptions are violated.
We propose combinatorial cascading bandits, a class of partial monitoring problems where at each step a learning agent chooses a tuple of ground items subject to constraints and receives a reward if and only if the weights of all chosen items are one. The weights of the items are binary, stochastic, and drawn independently of each other. The agent observes the index of the first chosen item whose weight is zero. This observation model arises in network routing, for instance, where the learning agent may only observe the first link in the routing path which is down, and blocks the path. We propose a UCB-like algorithm for solving our problems, CombCascade; and prove gap-dependent and gap-free upper bounds on its $n$-step regret. Our proofs build on recent work in stochastic combinatorial semi-bandits but also address two novel challenges of our setting, a non-linear reward function and partial observability. We evaluate CombCascade on two real-world problems and show that it performs well even when our modeling assumptions are violated. We also demonstrate that our setting requires a new learning algorithm.