A Dominant Strategy Truthful, Deterministic Multi-Armed Bandit Mechanism with Logarithmic Regret
نویسندگان
چکیده
Stochastic multi-armed bandit (MAB) mechanisms are widely used in sponsored search auctions, crowdsourcing, online procurement, etc. Existing stochastic MAB mechanisms with a deterministic payment rule, proposed in the literature, necessarily suffer a regret of Ω(T ), where T is the number of time steps. This happens because the existing mechanisms consider the worst case scenario where the means of the agents’ stochastic rewards are separated by a very small amount that depends on T . We make, and, exploit the crucial observation that in most scenarios, the separation between the agents’ rewards is rarely a function of T . Moreover, in the case that the rewards of the arms are arbitrarily close, the regret contributed by such sub-optimal arms is minimal. Our idea is to allow the center to indicate the resolution, ∆, with which the agents must be distinguished. This immediately leads us to introduce the notion of ∆-Regret. Using sponsored search auctions as a concrete example (the same idea applies for other applications as well), we propose a dominant strategy incentive compatible (DSIC) and individually rational (IR), deterministic MAB mechanism, based on ideas from the Upper Confidence Bound (UCB) family of MAB algorithms. Remarkably, the proposed mechanism ∆-UCB achieves a ∆-regret of O(log T ) for the case of sponsored search auctions. We first establish the results for single slot sponsored search auctions and then non-trivially extend the results to the case where multiple slots are to be allocated.
منابع مشابه
Characterizing Truthful Multi-armed Bandit Mechanisms
We consider a multi-round auction setting motivated by payper-click auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of...
متن کاملA Truthful Budget Feasible Multi-Armed Bandit Mechanism for Crowdsourcing Time Critical Tasks
Motivated by allocation and pricing problems faced by service requesters on modern crowdsourcing platforms, we study a multi-armed bandit (MAB) problem with several realworld features: (a) the requester wishes to crowdsource a number of tasks but has a fixed budget which leads to a trade-off between cost and quality while allocating tasks to workers; (b) each task has a fixed deadline and a wor...
متن کاملA novel ex-post truthful mechanism for multi-slot sponsored search auctions
In this paper, we advance the state-of-the-art in designing ex-post truthful multi-armed bandit (MAB) mechanisms for multi-slot sponsored search auctions (SSA) through two different contributions. First, we prove two important impossibility results which rule out the possibility of an expost monotone MAB allocation rule having sublinear regret with time when the click through rates (CTR) of the...
متن کاملOnline Regret Bounds for Markov Decision Processes with Deterministic Transitions
We consider an upper confidence bound algorithm for Markov decision processes (MDPs) with deterministic transitions. For this algorithm we derive upper bounds on the online regret (with respect to an (ε-)optimal policy) that are logarithmic in the number of steps taken. These bounds also match known asymptotic bounds for the general MDP setting. We also present corresponding lower bounds. As an...
متن کاملTruthful multi-armed bandit mechanisms for multi-slot sponsored search auctions
In pay-per-click sponsored search auctions which are currently extensively used by search engines, the auction for a keyword involves a certain number of advertisers (say k) competing for available slots (say m) to display their advertisements (ads for short). A sponsored search auction for a keyword is typically conducted for a number of rounds (say T). There are click probabilities μij associ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017