# Multi-Objective Optimization for Sponsored Search

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6 Percentage of Covered Reult 100% 50% 0% Number of Iteration Figure 2. Iteration number in MOO and percentage of it covered ingle objective optimization reult (a) (c) Figure 1. MO O reult and reult from other algorithm Circle tand for reult from MOO and filled point tand for reult from ingle objective optimization or RnR optimization in CTR, which help it to be the mot balanced reult among thee optimization. In the following part, we will give more detailed analyi on the advantage of MOO from different apect Completene of MOO reult A decribed above, previou work, which aim to optimize ingle objective function, are all pecial cae of MOO framework. The Pareto Set from MOO contain all the reult found in ingle objective optimization. We how thi concluion from ome cae tudie in Figure 1, which how all the ranking reult in Pareto Set from MOO framework. In Figure 1(a) and Figure 1, filled point repreent the reult of ingle objective optimization for relevance, CTR and revenue repectively. Since triple are cattered on a 3D pace, we project it on Relevance-Revenue and CTR-Revenue 2D plane to how the complete view of thoe reult. We can oberve that the reult from ingle objective optimization are indeed contained in the Pareto Set. Generally, the ingle objective optimization earche in the feaible pace and chooe the maximum value of the pecific objective function it optimize for. They certainly belong to Pareto Set becaue they are not dominated by other rank reult. We alo compare the reult from MOO and a tradeoff optimization for revenue and relevance (RnR). Both of thee two algorithm return a et of the reult. In Figure 1(c), we ue filled Point to depict reult from RnR. Similar to above figure, RnR reult are alo contained in the Pareto Set from MOO. MOO alo provide u with ome reult inferior on Relevance-Revenue Plane but uperior in CTR core. In our experiment, with the ame complexity a ingle objective optimization, we manage to get the approximate Pareto Set, which cover 80% of the ingle objective optimization reult, within 50 iteration. The relationhip between the MOO iteration number and percentage of it covered ingle objective optimization reult are hown in Figure 2. Since the reult from MOO framework i a complete et of optimized reult, we can directly ue MOO to (a) Figure 3. Reult from MOO and other algorithm. Filled circle tand for balanced reult in all objective function. replace thoe ingle algorithm to reduce the duplicate computation when we try to run three different algorithm Potential balanced reult in MOO Beide covering the reult from ingle objective optimization, MOO alo bring u more promiing reult which cannot be found by previou work. From the decription of goal in ponored earch, we need a balance between different objective function. MOO i well uited for thi goal ince it provide u with a comprehenive view of the poible rank reult. We can find balanced reult in the Pareto Set baed on the MOO framework in almot every query in the experiment. Figure 3(a) i a cae tudy of the reult from a random picked query in experiment. Marker in Figure 3(a) are the ame a in previou ection, except for a filled circle. We can eaily oberve from thi projection that reult with maximum value in either revenue or relevance have low value in the other objective. However, the filled circle ha a more balanced value in thee two objective. Moreover, from another projection of thee reult which i drawn in Figure 3, we can undertand that thi reult alo ha a relatively high value in CTR core. The filled circle will never be found by ingle objective optimization becaue it doe not reach the maximum value in either of the objective function. But compared to thoe ingle objective optimized reult, thi reult i more likely to be competitive to atify all the three participant in the game of ponored earch. 5.3 Potential Application of MOO The MOO framework ha many more potential application. Thee application help u in different tak. In thi part, we how the powerfulne of MOO framework in variou field Lexicographic olution Different publiher may have different target for revenue, CTR and relevance. For a riing earch provider, the fame in uer i appreciated mot. In thi cae, advertier and the publiher own revenue hould be conidered after uer atifaction when thi earch engine i involved into the game of ponored earch. In another ituation, for a earch engine which ha already had a

7 (a) (a) (c) Figure 4. Lexicographic olution Filled point tand for reult from ingle objective optimization and filled circle tand for reult from Lexicographic olution (c) (d) table cutomer bae, how to attract more advertier may become it mot urgent tak. It hould concentrate on improving Clickthrough Rate to atify advertier and get more contract with other advertier. In either of the ituation, the ad ranking problem in ponored earch reduce to a major objective problem with ome other minor objective function. Under MOO framework, thi problem can be eaily olved by lexicographic method, which i introduced in Section 4.1. With the ame evolutionary method, we can equally olve thi problem and achieve the optimized reult. The only thing we need do i to redefine the le than relationhip between rank reult. We how a cae tudy of thi application in Figure 4(a). In thi cae, ingle objective optimization for relevance i depicted a filled point. We ee a filled circle in thi figure which tand for the reult from major objective olution. Single objective optimization only conider reaching the maximum of Relevance core. However, many rank reult can equally reach the maximum of Relevance core. In major objective olution, optimization for revenue i followed after we have optimized relevance, the major objective. A we can ee from the figure, it i obviouly a better reult if only relevance and revenue are conidered important. Figure 4 and 4(c) how other two cae of thi improvement. A a concluion, lexicographic olution i imilar to ingle objective optimization but with ucceive tep after major objective ha been optimized. Minor objective can be alo optimized, which will improve the total utility of all the participant. In our experiment, we find 32.2% cae of thi kind of improvement in MOO reult, which optimize the minor objective by 7.1 % on average. (e) (f) Figure 5. Solution with contraint Solution with contraint Sometime earch engine do not care much to get the optimized reult in ome pecific objective function. They imply et contraint on thee objective. After filtering olution which do not meet the contraint, they try to find optimized reult in other objective function. In that way, we can find more promiing reult compared to major objective olution. It i a imple method to find a good ad rank reult. However, the election of the con- Filled circle tand for the optimum reult with the certain contraint and traight line in the middle tand for contraint traint i not a imple a it eem to be. If the contraint i too weak, the filtering tep may be uele ince jut few reult are excluded from candidate in thi tep, which mean we totally give up to conider thi objective. On the contrary, if the contraint i too trong, many good reult in other objective may have been filtered before they are found. A good contraint hould keep the mot competitive reult while being effective to reduce the computation complexity after filtering tep. MOO framework can be efficiently ued to elect a proper contraint. To explain thi application, we firt how thi application in a cae tudy. The method for contraint election in one query by MOO framework can be generalized a follow. Firt, we can elect a ingle tet cae of data and depict all the reult olved from MOO framework in a graph. Then a proper contraint, which help u elect the mot propective reult, can be found in the graph. Further, we hould make a mall adjutment in thi contraint to ee if we can get a large improvement in other objective if the contraint i a little lower. Thu a proper contraint can be et on thi objective to help u find the olution we want. In the cae tudy hown in Figure 5(a) and 5, we chooe relevance a the contraint and revenue a the main objective that we want to optimize. If the contraint on relevance core i et a Figure 5(a), we can get only two candidate for further optimization, in which the optimized revenue core i In the other hand, we can eaily find in Figure 5 that if we only require relevance core to

8 Ratio of top rank reult in all tet cae Table 2. Empirical reult for acrifice and improvement among objective 1% 2% 3% 4% 5% 1% 2% 3% 4% 5% 1% 2% 3% 4% 5% Improve CTR Improve Revenue Improve either of the other two objective Reduce Rel Reduce CTR Reduce Rev 1% 67.6% 60.7% 54.0% 48.1% 42.7% 62.9% 54.8% 48.4% 43.0% 38.2% 88.3% 81.8% 75.2% 69.1% 63.3% 2% 74.2% 67.6% 61.6% 56.1% 50.7% 66.2% 58.5% 52.2% 46.5% 41.7% 90.2% 84.7% 79.2% 73.9% 68.6% Improve Relevance Improve Revenue Improve either of the other two objective 1% 68.6% 57.3% 45.1% 34.9% 28.0% 57.4% 48.8% 42.0% 36.2% 31.3% 89.0% 79.3% 68.2% 58.3% 50.0% 2% 71.4% 59.6% 47.5% 36.7% 29.8% 65.3% 57.1% 50.4% 44.5% 39.1% 91.2% 82.5% 72.8% 64.0% 56.3% Improve Relevance Improve CTR Improve either of the other two objective 1% 62.8% 49.8% 37.4% 29.1% 23.7% 55.3% 47.4% 40.8% 35.5% 30.8% 84.9% 73.6% 61.7% 53.0% 45.9% 2% 65.7% 52.8% 41.1% 32.3% 26.6% 62.4% 54.7% 48.0% 42.2% 36.9% 87.7% 77.8% 67.5% 58.9% 51.8% be larger than.95, which i jut a. % decreae, the publiher expectation of revenue increae from to 0.966, which experience a 5.5% improvement. It i a large profit to publiher. Figure 5(c), 5(d), 5(e) and 5(f) how other two example of contraint election. For application, a more general concluion hould be reached. From the maive tet cae, we conclude a tatitical reult, which how to u the relationhip between acrifice in one objective and the improvement in other objective. Thi can be regarded a an empirical reult o that whenever we want a quick adjutment of the relationhip between objective function, we can imply look up in thi table and modify the contraint a the data ay. Table 2 how to u the tatitical reult, where the firt column indicate the objective we want to acrifice and the econd column indicate the percentage of decreae on thi objective. The following part of the table how the poibility of expected improvement on other objective. Bolded reult indicate the improvement with at leat 40% poibility in ome pecific objective and at leat 60% poibility in either of the other two objective. Thi table i much more effective when we decreae the objective from optimized core Parameter election With the help of MOO framework, we can elect the tradeoff parameter for different participant in a fater and more intelligent way a decribed in Section 4.3. We firt how a cae tudy to find an optimal parameter et for one query. It i a viualized and parallel method o that both perception and computation of thi method are eay to reach. In Figure 6(a) and 6, all circle tand for reult in Pareto Set and each filled circle or other y m- bol tand for the optimized reult found by a different preet parameter configuration. We can compare thee reult and viually elect the parameter that meet our requirement. For example, if we want a balanced reult we may chooe the parameter repreented by the cro. Alo, if we want a higher revenue and relevance we may chooe the one correponding to the triangle. Similar to thi pecial cae, we generate large amount pair of requirement and their correponding parameter. Then we adopt neuron network on thee training data to train a model to predict parameter on new requirement. We evaluate the predicted p a- rameter together with everal fixed parameter configuration in tet data et of 27,926 querie. The evaluation metric in thi experiment i KL ditance [16] between the predicted reult and the requirement. In our experiment, we generate many tet cae with different requirement, in the competition with 176 parameter configuration, 19.7% of our predicted parameter perform the bet, and the other 80.3% are all ranked in the top 10 reult. The (a) # Rank Figure 7. Performance of predicted parameter in competition with 176 parameter configuration Figure 6. Parameter election Filled circle, triangle and croe all tand for optimum reult for different tradeoff parameter performance of thi prediction i hown in Figure 7. In the experiment we alo oberved that parameter do not have direct linear relationhip with requirement. For example, if the requirement i 1:0.6:0.6, the bet predicted parameter are 0.78:0.13:0.09. Thu, with the help of thi prediction work, whenever we have a requirement on the proportion of thee objective function, we can eaily predict a parameter configuration for it and find an optimized reult by thi weighted um global criterion. A decribed in Section 4.3, the training proce i much fater with MOO framework than the naïve enumeration method. Suppoe the training et can be contructed within 5 hour with MOO, it may take up to 4 day to get a ame cale training et by enumeration method. Thi i a great improvement in training peed. Since umming up weighted objective function i much fater than getting all the olution of MOO, thee parameter can be ued to replace MOO in ome pecific application like tated above. 6. CONCLUSIONS AND FUTURE WORK In thi paper, we propoed a Multi-Objective Optimization (MOO) framework to olve the ad rank problem in ponored earch. The

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