Corpus ID: 211677262

# Budget-Constrained Bandits over General Cost and Reward Distributions

@inproceedings{Cayci2020BudgetConstrainedBO,
title={Budget-Constrained Bandits over General Cost and Reward Distributions},
author={Semih Cayci and Atilla Eryilmaz and Rayadurgam Srikant},
booktitle={AISTATS},
year={2020}
}
• Published in AISTATS 29 February 2020
• Computer Science, Mathematics
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… Expand
9 Citations

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#### References

SHOWING 1-10 OF 37 REFERENCES
Multi-Armed Bandit with Budget Constraint and Variable Costs
• Computer Science
• AAAI
• 2013
It is shown that when applying the proposed algorithms to a previous setting with fixed costs, one can improve the previously obtained regret bound, and results on real-time bidding in ad exchange verify the effectiveness of the algorithms and are consistent with the theoretical analysis. Expand
Bandits with Budgets: Regret Lower Bounds and Optimal Algorithms
• Computer Science
• SIGMETRICS 2015
• 2015
Numerical experiments suggest that B-KL-UCB has the same or better finite-time performance when compared to various previously proposed (UCB-like) algorithms, which is important when applying such algorithms to a real-world problem. Expand
Thompson Sampling for Budgeted Multi-Armed Bandits
• Computer Science, Mathematics
• IJCAI
• 2015
This paper extends the Thompson sampling to Budgeted MAB, where there is random cost for pulling an arm and the total cost is constrained by a budget, and proves that the distribution-dependent regret bound of this algorithm is O(lnB), where B denotes the budget. Expand
Linear Contextual Bandits with Knapsacks
• Computer Science, Mathematics
• NIPS
• 2016
This work combines techniques from the work on linContextual, BwK, and OSPP in a nontrivial manner while also tackling new difficulties that are not present in any of these special cases. Expand
Knapsack Based Optimal Policies for Budget-Limited Multi-Armed Bandits
• Computer Science
• AAAI
• 2012
Two pulling policies are developed, namely: (i) KUBE; and (ii) fractional KUBe, which are computationally less expensive and prove logarithmic upper bounds for the regret of both policies, and show that these bounds are asymptotically optimal. Expand
Budgeted Bandit Problems with Continuous Random Costs
• Computer Science
• ACML
• 2015
This work proposes an upper condence bound based algorithms for multi-armed bandits and a condence ball based algorithm for linear bandits, and proves logarithmic regret bounds for both algorithms. Expand
Bandits with concave rewards and convex knapsacks
• Mathematics, Computer Science
• EC
• 2014
A very general model for exploration-exploitation tradeoff which allows arbitrary concave rewards and convex constraints on the decisions across time, in addition to the customary limitation on the time horizon is considered. Expand
Multi-armed Bandits with Metric Switching Costs
• Mathematics, Computer Science
• ICALP
• 2009
A general duality-based framework is developed to provide the first O (1) approximation for metric switching costs; the actual constants being quite small. Expand
Multi-armed bandit problems with heavy-tailed reward distributions
• Computer Science, Mathematics
• 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
• 2011
An approach based on a Deterministic Sequencing of Exploration and Exploitation (DSEE) is developed for constructing sequential arm selection policies and it is shown that when the moment-generating functions of the arm reward distributions are properly bounded, the optimal logarithmic order of the regret can be achieved by DSEE. Expand
Exploration-exploitation tradeoff using variance estimates in multi-armed bandits
• Computer Science, Mathematics
• Theor. Comput. Sci.
• 2009
A variant of the basic algorithm for the stochastic, multi-armed bandit problem that takes into account the empirical variance of the different arms is considered, providing the first analysis of the expected regret for such algorithms. Expand