Knapsack based Optimal Policies for Budget-Limited Multi-Armed Bandits
This addresses the problem of optimizing sequential decisions under budget constraints for learners in scenarios like resource allocation, though it appears incremental as it builds on existing MAB frameworks.
The paper tackles the budget-limited multi-armed bandit problem, where actions have costs and a fixed budget, by developing two policies (KUBE and fractional KUBE) that achieve up to 40% better performance and prove asymptotically optimal logarithmic regret bounds.
In budget-limited multi-armed bandit (MAB) problems, the learner's actions are costly and constrained by a fixed budget. Consequently, an optimal exploitation policy may not be to pull the optimal arm repeatedly, as is the case in other variants of MAB, but rather to pull the sequence of different arms that maximises the agent's total reward within the budget. This difference from existing MABs means that new approaches to maximising the total reward are required. Given this, we develop two pulling policies, namely: (i) KUBE; and (ii) fractional KUBE. Whereas the former provides better performance up to 40% in our experimental settings, the latter is computationally less expensive. We also prove logarithmic upper bounds for the regret of both policies, and show that these bounds are asymptotically optimal (i.e. they only differ from the best possible regret by a constant factor).