Risk-aware dynamic reserve prices of programmatic guarantee in display advertising

Transcription

1 Risk-aware dynamic reserve prices of programmatic guarantee in display advertising Bowei Chen University of Lincoln United Kingdom Data Mining for Service (DMS) Workshop

2 Background What is display advertising? Display banner ads

3 Background Who are the participants? Online user expresses information need by web surfing or searching. Media buyer Advertiser wants to deliver marking messages to online users. Demand-side platform (DSP) helps advertisers to purchase ad services. Media seller Publisher provides advertising services/inventories. Supply-side platform (SSP) help publishers to sell their ad services.

4 Background How are display banner ads are sold? RTB Traditional Direct Sales Media buyer Ad exchange Private negotiation Media seller Media buyer Online user Media seller Passive PG Active PG Posted guaranteed prices Media seller Media buyer Media seller Media buyer

5 Price Model Schematic illustration Buy request Accepted request Reserve price Bid in RTB T T J 1 J 2 J 3 J 4 J 5 Time

6 Model Decision making at time t At time t, if an advertiser submits a buy request and proposes the guaranteed price G (t) for an impression, the publisher s decision making can be expressed as { max R(t)x(t) + V ( t + δt, s x(t) )}. x(t) {,1} x(t) is the decision variable R(t) is the expected revenue if accepting the buy request V (t, s) is the publisher s value function at time t, representing the expected total value of s remaining impressions which will be created in [T, T ]

7 Model Lower bound of reserve price Given time t and remaining impressions s, if there is a guaranteed price that makes the publisher s two decisions indifferent, this price is the lower bound of reserve price for the guaranteed impression, denoted by r(t, s), then r(t, s) = ( ) 1 V (t + δt, s) V (t + δt, s 1). 1 ωγ Hence, the decision variable x(t) = I {G (t) r(t,s)}. ω is the probability that the publisher fails to deliver a guaranteed impression γ is the size of penalty

8 Model Time-independent properties By employing the Bellman s Principle of Optimality, we have [ { } ] V (t, s) = E max r(t, s)(1 γω)x(t) + V (t + δt, s x(t)) x(t) {,1} ( ) = P[G (t) r(t, s)] r(t, s)(1 γω) + V (t + δt, s 1) ( ) + 1 P[G (t) r(t, s)] V (t + δt, s). Time-independent properties V (t, s) = V (k, s), k [t, T ], r(t, s) = r(k, s), k [t, T ]. For detailed simple derivation, see paper III A.

9 Model Risk-aware terminal value The publisher s value function at time T can be expressed as { s ( φ(ξ) + λψ(ξ) ), if π(ξ) φ(ξ) + λψ(ξ), V (T, s) = sπ(ξ), if π(ξ) < φ(ξ) + λψ(ξ), ξ is the per-impression demand in RTB. φ( ) computes the expected per-impression payment in RTB for the given ξ. ψ( ) computes the standard deviation of payments in RTB for the given ξ. π( ) computes the expected winning bid in RTB for the given ξ. λ is the level of risk aversion of the publisher.

10 Model Static supply and demand, and estimation of ξ The total supply of and demand for impressions that will be created in the period [T, T ] are assumed to be static, denoted by S and Q, respectively. If there are s remaining impressions, then there are Q (S s) remaining demand, therefore ξ = (Q S)/s + 1.

11 Model Estimation of φ(ξ) Probabilistic method: ( )( ξ 2dx. φ(ξ) = xξ(ξ 1)g(x) 1 F(x) F(x)) x Ω If X U[, v], φ(ξ) = v(ξ 1)/(ξ + 1). If X LN(µ, σ 2 ), φ(ξ) can be obtained via numerical integration. Empirical method: robust locally weighted regression (RLWR) method. x is an advertiser s bid in RTB g( ) is the density function F( ) is the cumulative distribution function.

12 Model Revenue analysis Expected total revenue of selling all S impressions in RTB: R RTB = Sφ(Q/S), Expected total revenue of selling some impressions in advance through PG and selling the remaining impressions in RTB: R PG+RTB = where ξ = Q T t= x(t) S T t= x(t). T ( R(t)x(t) + t= T S t= ) x(t) φ(ξ ), Increased Revenue R PG+RTB R RTB. For detailed derivation, see the paper III. C

13 Experiments Data Dataset SSP-1 SSP-2 DSP Market UK UK China From 8 Jan Jan Oct 213 To 14 Feb Jan Oct 213 # of ad slots # of user tags NA # of publishers NA 5932 NA # of advertisers 374 NA 4 # of impressions # of bids Bid quote GBP/CPM GBP/CPM CNY/CPM Bids of each campaign NA NA Reserve price NA NA Winning bid Winning payment

14 Price (normalised) Supply and demand Experiments Periodical patterns in hourly data Upper and lower bounds Average payment Demand Supply Time (hourly scaled)

15 Experiments Surface regressions for S and Q Num of total advertisers (demand) Fit surface Training data Prediction (b) (a) (c) Hour 2 Day Empirical example of demand regressions: (a) PNR(5,5); (b) PNR(2,3); (c) LQR 2

16 Experiments Surface regressions for S and Q Demand Supply Model L 2 norm avg. L 2 norm std. L 2 norm avg. L 2 norm std. PNR(5,5) PNR(4,5) PNR(3,5) PNR(2,5) PNR(1,5) PNR(5,4) PNR(4,4) PNR(3,4) PNR(2,4) PNR(1,4) PNR(5,3) PNR(4,3) PNR(3,3) PNR(2,3) PNR(1,3) PNR(5,2) PNR(4,2) PNR(3,2) PNR(2,2) PNR(1,2) PNR(5,1) PNR(4,1) PNR(3,1) PNR(2,1) PNR(1,1) LQR

17 Payment per auction (normalised) Experiments Estimating φ(ξ) using the RLWR method Resampling data Real data?(9) Demand per auction Chen et al. A dynamic pricing model for unifying programmatic guarantee and real-time bidding in display advertising. In ADKDD, 214. Algorithm 1.

18 Experiments Buy request Reserve price Accepted request.4 Price (normalised) 1.8 Price (normalised) Price (normalised) Risk-aware dynamic reserve prices.6.4 Buy request Reserve price Accepted request Time (hourly normalised and logarithmic) Time (hourly normalised and logarithmic) 1-2 Buy request Reserve price Accepted request Time (hourly normalised and logarithmic) The arrival of guaranteed buy requests follows a homogeneous Poisson process with the intensity rate QT where T is expressed in terms of year (i.e., #days/365). The proposed guaranteed buy prices are randomly sampled from RTB. 1-2

19 Experiments Revenue results Number of Ratio of payment Ratio of reserve Dataset advertisers to winning bid price to payment SSP % NA SSP-2 NA 77.9%.1% DSP % NA Using data in the Learning data in delivery period the training period R Predict PG+RTB RPredict RTB 1% 1% R Predict PG+RTB RReal RTB 8.77% 1% (R Predict RTB RReal RTB )/RReal RTB

20 Conclusion Contributions and future work This paper discusses a simple framework for passive PG, which Considers risk into reserve prices Has less limitations on buyer s purchase behaviour Generates increased revenue compared to only RTB Future directions include: Uncertain total supply and demand Optimal passive PG Comparison of active PG and passive PG

21 Thank you and welcome questions (??)