Optimal Keyword Bids in Search-Based Advertising with Stochastic Advertisement Positions

Dynamic bidding strategies in search-based advertising

“…3. Those include the dynamical versions of the optimal bidding strategy "BC" of Cholette et al (2011) under the "expected total cost not to exceed the budget" constraint and the optimal strategy that greedily bids the same amount until either time expires or the budget is depleted, whichever occurs first, so as to maximize the expected total net revenue. Because the latter two strategies have significantly less running-time and space requirements than those of the dynamic-programming approach, they can be considered as some viable alternatives as the numerical examples in the next section suggest.…”

“…In this paper, we consider a dynamic version of the keyword bid problem and attempt to determine the optimal bid price(s) subject to the budget constraint using dynamic programming. It is worth noting that a similar problem has been examined by Cholette et al (2011) who consider a static version of this problem, i.e., they find the constant optimal bid for each day which maximizes the expected profit under some soft budget constraint. They consider different versions of the problem, i.e., the problem (i) with no constraint, (ii) with a budget constraint where the expected cost of clicks must not exceed the available budget, (iii) with a budget constraint where the probability of exceeding the budget does not exceed a fraction, say, 0.10, and (iv) where the "ideal" bid amount is chosen after selecting a point on the efficient frontier of, (i) expected profit, and (ii) probability of exceeding the budget.…”

“…They consider different versions of the problem, i.e., the problem (i) with no constraint, (ii) with a budget constraint where the expected cost of clicks must not exceed the available budget, (iii) with a budget constraint where the probability of exceeding the budget does not exceed a fraction, say, 0.10, and (iv) where the "ideal" bid amount is chosen after selecting a point on the efficient frontier of, (i) expected profit, and (ii) probability of exceeding the budget. Our paper generalizes the Cholette et al (2011) models by allowing the possibility of dynamically selecting the bid prices after observing the remaining budget and the remaining time until the end of the period (usually a day) under hard budget constraint (namely, with probability one, the budget is never exceeded). Fruchter and Dou (2005) solve a different problem with dynamic programming: they find a dynamic strategy to optimally allocate a limited budget between a generic Web portal and a specialized Web portal using keyword-activated banner ads.…”

“…By solving a constrained nonlinear optimization problem, they find the optimal bidding amounts that maximize the expected total net revenue subject to a soft budget constraint: the expected total cost should not exceed the budget. Later Cholette et al (2011) enhanced the same model by explicitly modeling the stochastic ad positions, which we are adopting here as well, and by considering a probabilistic budget exceedance constraint, which is also a soft budget constraint.…”

“…We therefore propose and then examine two intuitive dynamic bidding strategies that can be calculated fast. The first strategy is the dynamical version of "budget-constrained" (BC) bidding strategy of Cholette et al (2011). S. Cholette and her colleagues proposed a static BC bidding strategy which bids all the time the same amount that initially maximizes the expected total net revenue subject to the constraint that the expected total cost should not exceed the budget.…”