2,659 research outputs found
Bandit Problems
We survey the literature on multi-armed bandit models and their applications in economics. The multi-armed bandit problem is a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. This classic problem has received much attention in economics as it concisely models the trade-off between exploration (trying out each arm to find the best one) and exploitation (playing the arm believed to give the best payoff).One-Armed Bandit, Multi-Armed Bandit, Bayesian Learning, Experimentation, Index Policy, Matching, Experience Goods
An Incentive Compatible Multi-Armed-Bandit Crowdsourcing Mechanism with Quality Assurance
Consider a requester who wishes to crowdsource a series of identical binary
labeling tasks to a pool of workers so as to achieve an assured accuracy for
each task, in a cost optimal way. The workers are heterogeneous with unknown
but fixed qualities and their costs are private. The problem is to select for
each task an optimal subset of workers so that the outcome obtained from the
selected workers guarantees a target accuracy level. The problem is a
challenging one even in a non strategic setting since the accuracy of
aggregated label depends on unknown qualities. We develop a novel multi-armed
bandit (MAB) mechanism for solving this problem. First, we propose a framework,
Assured Accuracy Bandit (AAB), which leads to an MAB algorithm, Constrained
Confidence Bound for a Non Strategic setting (CCB-NS). We derive an upper bound
on the number of time steps the algorithm chooses a sub-optimal set that
depends on the target accuracy level and true qualities. A more challenging
situation arises when the requester not only has to learn the qualities of the
workers but also elicit their true costs. We modify the CCB-NS algorithm to
obtain an adaptive exploration separated algorithm which we call { \em
Constrained Confidence Bound for a Strategic setting (CCB-S)}. CCB-S algorithm
produces an ex-post monotone allocation rule and thus can be transformed into
an ex-post incentive compatible and ex-post individually rational mechanism
that learns the qualities of the workers and guarantees a given target accuracy
level in a cost optimal way. We provide a lower bound on the number of times
any algorithm should select a sub-optimal set and we see that the lower bound
matches our upper bound upto a constant factor. We provide insights on the
practical implementation of this framework through an illustrative example and
we show the efficacy of our algorithms through simulations
On the Optimal Amount of Experimentation in Sequential Decision Problems
We provide a tight bound on the amount of experimentation under the optimal
strategy in sequential decision problems. We show the applicability of the
result by providing a bound on the cut-off in a one-arm bandit problem
Dynamic Ad Allocation: Bandits with Budgets
We consider an application of multi-armed bandits to internet advertising
(specifically, to dynamic ad allocation in the pay-per-click model, with
uncertainty on the click probabilities). We focus on an important practical
issue that advertisers are constrained in how much money they can spend on
their ad campaigns. This issue has not been considered in the prior work on
bandit-based approaches for ad allocation, to the best of our knowledge.
We define a simple, stylized model where an algorithm picks one ad to display
in each round, and each ad has a \emph{budget}: the maximal amount of money
that can be spent on this ad. This model admits a natural variant of UCB1, a
well-known algorithm for multi-armed bandits with stochastic rewards. We derive
strong provable guarantees for this algorithm
Satisficing in multi-armed bandit problems
Satisficing is a relaxation of maximizing and allows for less risky decision
making in the face of uncertainty. We propose two sets of satisficing
objectives for the multi-armed bandit problem, where the objective is to
achieve reward-based decision-making performance above a given threshold. We
show that these new problems are equivalent to various standard multi-armed
bandit problems with maximizing objectives and use the equivalence to find
bounds on performance. The different objectives can result in qualitatively
different behavior; for example, agents explore their options continually in
one case and only a finite number of times in another. For the case of Gaussian
rewards we show an additional equivalence between the two sets of satisficing
objectives that allows algorithms developed for one set to be applied to the
other. We then develop variants of the Upper Credible Limit (UCL) algorithm
that solve the problems with satisficing objectives and show that these
modified UCL algorithms achieve efficient satisficing performance.Comment: To appear in IEEE Transactions on Automatic Contro
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