Budget-Constrained Bandits over General Cost and Reward Distributions

• URL: http://arxiv.org/abs/2003.00365v1
• Date: Sat, 29 Feb 2020 23:50:08 GMT
• Title: Budget-Constrained Bandits over General Cost and Reward Distributions
• Authors: Semih Cayci, Atilla Eryilmaz, R. Srikant
• Abstract summary: We consider a budget-constrained bandit problem where each arm pull incurs a random cost, and yields a random reward in return. We show that if moments of order $(2+gamma)$ for some $gamma > 0$ exist for all cost-reward pairs, $O(log B)$ regret is achievable for a budget $B>0$.
• Score: 32.63624728528415
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a budget-constrained bandit problem where each arm pull incurs a random cost, and yields a random reward in return. The objective is to maximize the total expected reward under a budget constraint on the total cost. The model is general in the sense that it allows correlated and potentially heavy-tailed cost-reward pairs that can take on negative values as required by many applications. We show that if moments of order $(2+\gamma)$ for some $\gamma > 0$ exist for all cost-reward pairs, $O(\log B)$ regret is achievable for a budget $B>0$. In order to achieve tight regret bounds, we propose algorithms that exploit the correlation between the cost and reward of each arm by extracting the common information via linear minimum mean-square error estimation. We prove a regret lower bound for this problem, and show that the proposed algorithms achieve tight problem-dependent regret bounds, which are optimal up to a universal constant factor in the case of jointly Gaussian cost and reward pairs.

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