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The Stepwise Tutorial to Bid Abstract Form

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Comprehend How to Fulfill the Bid Abstract Form

okay yeah thank you joan kim for the.transaction and thanks everyone to.attend my.talk so i'm enjoying from stanford.double e and today i'm.going to talk about my recent work on.how to be in repeated first press.auctions.this is a joint work with my advisor.sergey weissman at the stanford double e.and my collaborator the jung angel from.omaha stern who is also here today.aaron floss and eric edently both from.yahoo research.so yep recent years has witnessed acute.success of digital ads.for example in 2019 the digital ad.spending in the united states.has surpassed for the first time the.combined spending of traditional ad.channels.including tv radio and newspapers and is.also.projected in to increase in upcoming.years.a core element of ad digital ads.is the online auctions where the bidder.or the advertiser or the bid would like.to buy advertising spaces or impressions.from the publisher or for the seller.through an.ad exchange well typically some type of.auction will be hosted.in reality the model is more complicated.than this there could be some demand.side platform between the advertiser and.the exchange.which will be on behalf of the.advertiser and similarly also.some supply side platform between ad.exchange and the publisher.so there are some popular auction.designs for the ad exchange.including the second price sales bit.auction and the first price create.auction.and you may be familiar with these type.of auctions.so in both auctions the bidder will.submit a bid.to the ad exchange and the bidder with.the highest.bid wins the auction the only difference.is that.in second price auctions the winner pays.the price equal to the second highest.speed.however in the first price auction the.bidder will pay the price equal to the.highest bid.several years ago the second price.auction was a.predominant auction design in.most online ad exchanges however in.recent years there is an industrial.shift from second price to first price.auctions.for example several ad exchanges.including app nexus.index exchange and open x started to.draw out first price auctions in 2017.and the last year google also started to.switch from second price to first price.auctions.there are multiple reasons to ship to.first price auctions.for example first first price auction.provides greater transparency to the.bidders as.the price leaders pay at exactly the.price they beat.in contrast in second price auctions.bidders typically do not know whether.the price they pay is the true second.price as.there could be several practical tricks.by the seller or.by the supply chain platform to pay to.squeeze.out some revenue from the bid the second.reason is that.first price auction often leads to.enhanced monetization or revenue for the.sellers.though yeah as some of you may be.familiar with auction theory.there is a celebrated crm called the.revenue equivalence theorem.claiming that okay in both the second.price or the.and the first price auctions the.expected revenue for the seller should.be the same.in theory however this is not the case.in practice.and most practitioners just observe and.enhance the revenue for sellers after.switching to first price.auction partially because the bidders.are.over bidding in this scenario and the.final reason is that the first price.auction is a preferable model for header.reading.which is a new technology in online.advertising which was very popular in.the recent few years.to see a real example let's cut yeah.this.chart does show that just from december.2017 to march 2018.the fraction of first price auctions it.just.increases from six percent to around.about 43 percent.yeah meanwhile we see the fraction of a.second price after the job.by a significant amount here the grid.area just represents.second price auction with anomalies or.just called the unfair second price.auction.which essentially played some types of a.trick i just mentioned before.just to squeeze out the revenue from the.bidder and sometimes.also from the seller this is just an.illustration of the unfairness.issue in the previous second price.auction platforms and.a motivation to shift to first price.options.this industrial shift has brought forth.important challenges for the bidder.that is how to beat inverse price.auctions.note that in secondary price auctions we.do not have such a problem because it is.a weekly dominant strategy.to just be the true valuation of the.item because we are paying the second.price.however the inverse price functions.things are different and we need to pay.strictly.less than we ran our private evaluation.on the item.a form called the bead shading now the.question is that what is the optimal.base gb shading we should perform here.know that when we know the others the.distribution.of other speeds then we are in a good.shape and all we need to do is to solve.an explicit optimization problem to find.the optimal b.however in practice we hardly know the.distribution of.other speeds so this means that we need.to learn other distribution.or even assume that other bits that do.not follow any distribution assumptions.on top of that there could be even.possibly censored feedback.for the auction which prevents us from.donating.to illustrate those factors let's.consider a sequential decision.model for the bidder in repeated first.price auctions.note that repeated first press auctions.happen a lot in practice.because builders or demand side.platforms typically submit a lot of bid.requests.every day so at the beginning of each.round key.the target beater just sees the item and.computes a private value on that item.and based on his preference value and.his own knowledge.he will submit a bid bt to the ad.exchange.and meanwhile other bidders will also.submit their bids.and let mt be the maximum of them.then finally the ad exchange just.compiled the.numbers mt and bte make the decision on.this round.and also give feedback information id to.the target builder.which the specific form of the feedback.information will be specified later.and the target reader just puts the.information he observed to his.knowledge class and.yeah before we move to other stuff let's.record some important notations.here capital t just denotes the time.horizon.that is the number of total runs of.actions.and that vt bt and mt be the private.value be the speed and the maximum.competing b at time t.respectively and by a simple scaling we.assume that all of them.belong to the unit interval the r01 in.first price auctions.it is also clear that the instantaneous.reward for the single bidder at time t.is exactly the difference between the.private value.and the bidder speed conditioning on the.fact that let's be the windsor option.that is.bt greater than empty so the little r.function.denotes the easterner's reward at time t.now the beta score as standard in online.learning.is to devise a bidding policy pi which.is a collection of.beasts at each round to minimize the.regret.which is which is defined to be the.difference between the expected security.reward achieved by the bidder.and that of an oracle who could beat.the best bidding policy strategy in a.reasonable and.rich family f in hindsight that being.said.the oracle will know the perfect.information about all.these and oms and could choose the best.one in hindsight.however as for our b as the leaders.we only know the knowledge we constantly.know so we are operating in a fully.online fashion.so our main target is to characterize.what is the minimum regret we can.achieve.as well as the policy that achieves that.and in particular we will be interested.in the case.where the regret rp is a lot much less.than t.meaning that at each round on average.the.resulting policy adopted by a bidder is.essentially the best one.with only a dignitable gap.now here is a business goal and we still.need to specify.what is the feedback structures we.consider three different feedback.structures in practice.from the weakest to the strongest so the.weakest one is that the.observable beats or the patch or the.binary feedback.that is the bidder only knows whether he.or she wins or not at the end of each.round.but cannot observe any other beat this.scenario.as the subset of this scenario was.studied in a recent paper by berserio.at all in 2019 which shows that.in that scenario but in that scenario.the resulting regret will be very high.which means that okay this feedback.might be.two scores and the next.feedback structure is the winner only of.the four beats.that is the beatle will know the winner.speed.at the end of each round that is the.auctioneer just announces.the winner speed at the end of each.round so this may.happen in some practice in practice such.as the original touch option with.descending beats or with some reported.auction types called that for example.such as the master's action in.netherlands.so basically in this scenario we still.remark that we will have a sense of.feedback here because.when the beetle wins the auction he or.she will lose the information of this.round.so we are still have a partial feedback.here.and the last feedback structure will be.the fully observable bids.while the bidder will know the perfect.number of others the highest other.competing bid.this could happen in open bid auctions.where.everyone just calls out his feeds or in.some online.ad platform such as the google adventure.where.the minimum b2 win for each bidder at.each round will be returned to the beta.in our in this talk we will consider.yeah the winner only obviously is at.our setting one and the abdominal will.be at our setting too.and to have a more detailed description.of setting one.also known as the stochastic operations.we will assume that.the private value follows either an id.or another stereo registry.or id distribution of the adversarial.sequence.that is any arbitrary individual.sequence.so we do not have a real uh we do not.really have an assumption on vt.so the crucial assumption is that we.assume that.the other's maximum beat is as follows.an id.but an unknown distribution so.essentially.this is yeah the weakest assumption we.need to assume.in order for us to learn about the other.distributions.and this might happen when competition.is very high meaning that okay.my strategy have little impact on others.also.my own private evaluation also have a.little impact on others competition.other value or specific advertising.space.and we assume a feedback structure that.is only the.meaning beat will be revealed and in.this scenario.the regret in stochastic options will be.defined as the.difference between the cumulative reward.achieved by the bidder.and the best article in the world.meaning that.the yeah means that the oracle knows.that.unknown cdf the distribution g and it.could make.the optimal decision at the every round.so not.know that the the price the.oracle b could depend on vt at the d.at a different different t meaning that.we are actually competing with a very.strong oracle.the key features of this problem.includes that.well whenever the bid with the option he.or she loses the information.this is just a sense of feedback we.talked about.and us can also be treated as a.information version of the winner's.curse that if we win they will lose.something and the main question we would.like to ask in this scenario is that.what is the optimal way to learn g in.view of a sensor.feedback in this value okay.and in the second setting which we'll.call the adversary options.the main diff assumption will be a.difference in sets now we'll assume.both vt and mp could be adversarial so.we drop.any distribution assumptions on them.however we assume a stronger feedback.structure that is empty is always.revealed.and the reward here is defined to be the.difference between a cumulatively.expected reward achieved by the reader.and the best one leap shift bidding.strategy is a word.yeah in hindsight so here.yeah we restrict the oracle to use our.one leaflet's bidding strategy.meaning that okay his strength beating.his the priority b is must be at this.dismissive function.of the private value and whenever the.oracle sees two.items with similar private value he is.required to be the similar reprices for.them.know that this constraint is somehow is.natural and also somehow.necessary because the best article in.the world would be.just the b to be the mt at each round.however it is impossible for a beater to.predict an adversarial sequence based on.path history so some constraint on the.oracle class should is necessary here.the key feature in this setting is that.we impose no distribution assumptions on.other speeds.so a good policy must be robust to other.strategic.or even adversarial moves and the main.question.we would like to ask in this scenario is.to propose a robust.strategy to any distribution assumptions.and the main result of this talk is that.in both settings.there actually uses efficiently computer.bb strategy.such that a regressed bound of root t.times a vector polybag.could be attained since the juice t law.of.regret is a standard law about the.online learning this simply shows that.we could achieve the optimal regret both.in view of the extensive feedback.or the robustness constraint.okay i'd like to pause here to create.any questions if you have.yeah okay so yeah no.no questions let me move on to part one.on stochastic.auctions the materials could be found in.the paper optimal request learning.repeated first price options available.on.archive so.let's start from a simplest bidding.strategy for this scenario to appreciate.this problem.recall that the key difficulty in this.scenario is the sense of feedback.that is if we win then we lose the.information but if we lose we have the.ability to learn.so perhaps the simplest strategy one.could think of is just to.okay let's how about we first learn and.then utilize that.that is we just beat zero in the first.keynote rounds so that we could observe.t.not four observations and then we.based on which we could find a good.estimate g hat of the unknown.distribution g.and in phase two we just plug in this.estimator g hat to the operating program.and work out.and find out what is our optimal bid.based on g hat.okay then how should we analyze this.scheme.okay in the first phase at each round we.may incur.a regret at the moment are constant.so the total regret bound in the first.phase will be t naught.and for the second phase we know that.the estimation area between g hat and g.based on k9 observations is typically.one by.root t naught so the total regret.incurred as the fifth two.will be of the order t by root t naught.then yeah then using the optimal.tradeoff between those two terms we.arrive at a regret.of the order t to the two thirds and.however which is still.far from the t and the question is that.how should we improve this regret bound.to of.the order root t before.before answering that we first remark.that the theta two third.regret is actually optimal when the.feedback is binary.and we are seeking a better performance.within our research feedback.and a challenge or a subtle p of this.problem is that.actually we have some selection buyers.for example.let's bt with the price weight beat at.some ground.and if it turns out that mp is smaller.than bt.then we cannot observe mt but only know.that.mt is at most pt so this observation.will only give us about the information.about the.probability of mt smaller than bt.it might be attempting to think okay.maybe things get better.when mt is greater than bt yes.however even when mp is greater than bt.that that observation does not give.directly give us the distribution of mp.it only gives us a distribution of the.condition conditional distribution of.mp given the fact that mt is greater.than pt.while the probability of the condition.event.yeah it's real unknown i need to be.estimated.which complicates this problem so this.is a selection bias in this problem.and to overcome this difficulty we.introduce a concept.of a monotone group contextual bandit.well first we record what is a.multi-armored bending problem.it is nothing but a sequential.decision-making problem with time.horizon key and.different actions and there is a learner.who aims to maximize the cumulative.reward.the key feature in multiple benefit.problems is that there is abandoned.feedback.that is only the reward of each chosen.action will be revealed at each time.for example yet consider the following.reward table.and suppose that at time 1 the learner.chooses to take action 3.and then at the end of time 1 the.learner will observe the reward for.action 3.and based on which he may decide to.choose action 2 at the second round.and similarly on the second round the.learner knows observation.observes the reward for action 2 and.proceed with the process and it is well.known that the optimal regret relative.to the best fixed action in multi-album.bandits will be of the order.root k times t where k is the number of.actions and the t is the time horizon.okay the multi-hour balance problem.could be generalized to another setting.called the contextual multi-outband.that is simply a multi-underbended.problem with several contexts.where each context will correspond to a.different environment on the rewards.so in other words instead of working on.a single reward table.in this scenario where we'll have.several rubric tables where each table.corresponds to.one context so yeah.no yeah also we know that the contacts.will be observed but bid.by the learner at the very beginning so.consider the scenario that.okay at time one the learner observed a.contact of c1 so.he knows that yeah he's not operating on.this.reward table and let's say he chooses.action three and again.the crucial feedback structure here is.that.only the reward of each chosen action.under the given environment will be.revealed in contextual amount of banded.problem.so he can only observe this entry of.this particular table.and similarly at round two the.contact may become c2 and the learner of.the truth would like to choose actions.two on the other table and in this.scenario it could be shown that the.optimal regress relative to the best.contact specific action will be of the.order root c.times k times t where c is a total.number of contexts.so here the best contact specific action.just means that the article can choose.different actions.on different tables now the.now the question is that how is the.contextual.multi-armored bandit problem related to.us.actually the correspondence is as.follows actually we.could treat the bitter speed as the.action.actions and also the private value at.the context.so basically at it at the beginning of.each round.the bidder will observe a price value.for that so.he would like to work on the specific.reward table.and up and the action he can choose.could be just a quantized set of the.prices.of the unit interval from 0 to 1 and.he could choose a price to beat and then.after that he could observe the reward.achieved by that price.and if we apply the previous regret.analysis to this problem.the total regret for contextual.multi-armored bandit will be of the.order root c times k times t e.however we also have some quantization.error by quantizing.the private values as well as the bit.prices.so here are the quantitation areas so.finally using optimal trade-off it gives.us a key to the four.three-fourths regret to us which is even.worse than the simplest strategy we.talked about in the beginning.so this is so this suggests that.there must be something we miss here and.in fact.the crucial question is that does the.bandit feedback really hold.in first price auctions the answer is.actually no.not so actually each bid.will provide amount of feedback in the.sense that.beating a low price will give us a full.information.about the reward of building a high.price.to see that just consider two different.scenarios the first scenario will be.that.okay what will be the price b and.it turns out that the other speed are.lower than me.then in this scenario we'll definitely.know that if we beat a higher price.with we still win in that scenario.so we could observe the rewards of all.larger beats in that case and conversely.if we lose that action auction then our.feedback structure tells us that.we could observe the other speed so in.that scenario actually we can observe.the reward of.all given speeds and and also all.contacts because we are essentially as a.full information model.so yeah so actually so this is called a.mountain feedback that is the.information about.information of a kid will reveal the.full information of the rewards of.all larger actions given all contexts.this is also reflected in this table.that is.at the first round let's say the price.value is v1 and.we choose the action b3 here so b3 is.actually choose but it also reflects the.inform.the reward information of all logical.actions.and also under all contexts so this is a.new table we are operating.in in this study another interesting.property for first price auctions is.that we also have a monotone optimal.action property.that is also we don't know the.optimal action taken by the oracle under.each context.but we definitely know that that unknown.optimal action under each context.must be non-decreasing in the context so.translating to.yeah auction to the auction setting.it just means that as long as the oracle.sees another item with a higher private.valuation.then he will be willing to pay a prior.price for that.this is just the intuitive explanation.for that so.for example in this table let's assume.that the b3 is the optimal.that's the optimal action of the oracle.on the private value v1 then for a.larger.private value v2 we know that okay it.could be the case that the optimal.action for the article is b4 but it will.never be the case that the optimal.action will be b2 is that a scenario.okay now using those two properties in.hand we.are ready to define what is called a.monotone group contextual bandit.so we propose this definition that is.just a contextual bandit problem.satisfying both the monotone feedback.and multiple optimal action properties.and the main reason why we introduce.this notion is that.in for this problem actually uh expected.regret of.duty times the rhythmic factors could be.achieved.given the fact that the contexts are id.across time or just use chamber across.time.so translating to the auction scenario.in stochastic first price auctions we.conclude that there is a bidding policy.achieving and duty time the box reality.expected regret.when the private values are id or.exchangeable.so here note that the results just hold.when the.price when the private values are id but.but it imposes no assumptions on which.common distribution they have.and also we remember also we won't.elaborate it.here we remark that the mountain group.contextual bandit structure or.it also holds in some other problems.involving some sensor observation.for example the news vendor problem with.the sensor demand but we will not.have the time to elaborate it here okay.now it's a we are your position to.describe.what is the policy to achieve such a.regress bond.and the policy is actually quite simple.the high level description is that.okay suppose we have a subroutine which.could successfully eliminate.probably bad actions from our past.observations under each context.and now the previous two properties come.into play.in the sense that okay the monotone.optimal action property.tells us that okay we can eliminate more.actions if necessary but just ensure.that the smallest active action.under each contest will be not.decreasing over the contest.and the the modern feedback property.just suggests us to choose the smallest.active action.under the current contact at every round.so as to give the full feedback for all.possible active actions.for example at the first round let's.assume.let's assume that the private value is.v1 and currently we know nothing so we.just.choose the smallest beads and tools and.way of receiving the feedback of.all possible actions and based on.this observation under each context we.may just eliminate some probably.fairly bad actions oh wow to fl2.okay maybe some animation spark here.okay okay let me just give that part.and let me talk about what is the key.inside behind the algorithm.the key answer is that the number of.available observations at time t.is actually about the number of past.private values.which is smaller than or equal to vt.here.so this number is the effective number.of effector effective sample sizes.and in the best scenario where which is.increasing.then this value will be of the order t.and in the worst scenario where which is.decreasing.this value will be only a constant.and the crux is that for any id.distribution.this value the number of effective.number of observations will.be linear in expectation and this is the.key.why our previous algorithm work for any.id distribution because we have.sufficiently many observations for that.however now our natural question will be.that.okay what about a non-stochastic contest.or even a worst case contest so will.that algorithm still.give the same answer for any possible.context.actually we prove a much stronger lower.bound that is.there actually will exist an instance of.a mountain group contextual vendor.problem.and an adversarially chosen sequence of.contexts such that.any policy yeah not limited to the.policy i just.described will incur a worst case regret.at the list of the order k to the two.thirds so this means that actually there.is a string of separation between the.performances.on the stochastic case and the other.serial case.so basically yeah we will have a root t.regret on average.but i have a regret of the other typical.two-thirds again for worst case contest.meaning that this framework does not.directly extend to other serial price.values.and at least for general monotone group.contextual bandit.the title ii cellular graph bound is.optimal yeah for adversarial contexts.however this does not mean that for.first press options.this lower bound also holds the key here.is that.we still have some interesting.properties of first price options.which motivates the following interval.splitting scheme for that.so what is the additional observation.here recall that.the previously in mountain group bandit.the main of the the main message is that.beating a low price.will give a full information for the.reward of a beating a high price.actually in first-place auctions the.partial converse is also true.that is beating a high price will also.give the partial information for the.reward of beating a low price.so basically yeah this could be seen.where a very trivial identity that is.for.b smaller than b prime we could express.the probability of m t.greater than b into the sum of two terms.while beating up price b.prime will give one more observation for.the first term so the estimation error.will be smaller.however for the second term we still.have the same.sample size yeah the crucial observation.is that.the second term has a smaller target.quantity.so this this term will also enjoy a.smaller estimation error because the.target quantity is smaller and.yeah the everything is as follows let's.assume that b1 to b5 are the bidding.prices the other.other beads will make for the first five.rounds and m1 and 5 are the first.minimum b2b.yeah you know that it is scenario yeah.only.m1 and m3 are greater than the.respective b's so we could observe m1.and ms3 in four.however we cannot locate the precise.locations of m2 m4 and m5 because of the.cannot.we do not observe the exact speeds only.but only know that.m2 m4 and m5 lie in some respective.interval.now in this specific example what is.what.how should we estimate the probability.of mt.greater than b the idea is just.to split into several small intervals.that is.to split the interval b to 1 into.several small intervals from b to b 5 b.5 to b 4 before to b 2 and b 2 to 1.and ask me the probabilities of this.small subset.separately and how should we estimate is.the probability.of each small subset so here to estimate.the probability from b to b5.we conclude that we only have two.observations.that we are certain that which we are.certain to.belong to this small interval or not for.example here.we know that m1 is not m3 is not but we.are uncertain of.m4 2 m4 or m5 so estimation for that.will be 0 divided by 2..and how about the interval from b5 to b4.here we are sure that m1 is inside m3 is.not inside.and we also know that m5 is not in this.interval although we don't know.what what what is the exact value of m5.and for m2 and m4 was still uncertain so.here the effective symbol size will be.three.and one of which we arrived in this.interval so.one third will be the estimate for this.small interval and.so on and so forth and we finally we add.them together.so in this scenario we will have.different sample sizes in different.intervals.and similarly in addition to the single.point estimate we could also estimate.the.standard deviation for that estimate.okay assuming the independence across.the estimate in different.small intervals the standard deviation.at the point b.will be looking like this where the.probability here is the true probability.of the mt of course yeah in practice we.don't know what is the true probability.so we need to replace it by the.estimated probability to obtain an.estimate.estimated quantity for the standard.deviation and.as long as we both have the single.estimate and the standard deviation.we could you we could run up ucb policy.that is we could find an upper complex.bound.a good other function for the ground for.the.for each action and the final policy is.just.okay we just choose the bidding price to.maximize uppercase bounds.yeah this is the main idea in the new.scheme.although there will be some other.characters including.okay we need to handle the different.dependence across different intervals.and we also need to handle the.dependence across time because bt.depends on the previous observations and.there is also some estimation area of.the standard deviation.and to handle the dependence we we.propose a multi-state.algorithm of the of the usb algorithm to.do that and we refer to our full paper.for details the main result is that.the usb algorithm achieves a regret of.the other rule t.times log cube t are within logarithmic.factors.even for adversarially chosen private.values showing that a root t.of a regress bound could still be.attained for.first price auctions even on the other.series chosen private values.so this is a special property different.from the general.monotone group contextual bandit and.yeah the sum yeah to summary part one.first.input in stochastic auctions we showed.that the sensory feedback could be.modeled as a monotone group catastrophic.bandit.which leads to a root breath in average.by the title two-thirds regret in worst.case.and for first price auctions an.additional nature of our correlative.rewards could.lead to a routine regret even for worst.case private values.and yeah and any questions for this part.okay let's move on to the last part.maybe we can take.questions yeah or questioning the end.and okay the second part is about other.series auctions.and your the materials or is also.containing the following paper of.available archive and record the setting.of the.adversary auctions that is we assume.that both private values and the minimum.b2b to be out of stereo.and to account for strategic or even.adversarial moves of the environment.however we assume a stronger feedback.structure.that is empty is always revealed at each.time and the regret in this case.is defined to be the difference of our.performance and the best one difficult.bidding strategy.in this scenario and the main result.may be surprising is that okay even in.this adversarial.scenario there still exists a billion.strategy such that the regret of root t.times logic.is attained furthermore this request can.be.obtained by an efficient algorithm.requiring a space linear in t and time.polynomial t.so this means that okay we could achieve.some robustness in this scenario.this part will be decomposed into three.steps the first step is that.we propose a statistically optimal.policy for in this scenario.which could be computationally e.efficient.and in our second step we modify the.algorithm to make it computationally.efficient.and finally we implement our algorithm.on the real some real data sets provided.by various media which shows.the superior performance of our.algorithm relative to.the existing ones okay the.first step is to propose a certificate.optimal policy.and to do that we need to introduce a.problem of prediction with expert advice.so similar to the multi-argument problem.this is also a sequential.decision-making problem.where the learner aims to maximize the.chemistry rewards.the only difference is that now we.assume a full information feedback.that is the rewards of all actions no.matter whether i choose it or not.will be revealed in this at this time so.for.example the learner would may choose.action three or expert three at time one.and then.he will observe the rewards of all.experts and similarly.proceed to round two and observe all.rewards and so on and so forth.and here the optimal regret relative to.the best fixed.export will be of the order like root p.times the.k so compared to the multi-armored.banded case we see that the dependence.on the number of expert k.improves from root k to root 1 k in this.value.and how is that scenario related to us.so we need to specify what is the advice.of each expert.of course each expert is not selecting.us to be the constant price.but instead of bidding strategy.represented by our one lipids function.in the class of all such functions.so each one liberties function is an.expert.however the clinicality of that class is.infinite.so we need to discretize in some way.motivated by the mathematical.carbonyl gamma due to common graph and t.homidov in 1959.saying that okay the space of all one.lipstick functions could be discretized.to a discrete set.of carnality.the absolute so now.we have this a final set of candidates.in this scenario.and at each step yeah approximating.the entire set by this final set will.incur an approximate.area of epsilon so the total opposite.error error will be t times epsilon.and for this discrete set of experts.yeah though using the previous result.the regret against the best candidate.will be of the order root t.times log calculator which will give us.root t.by epsilon in this scenario so by.balancing these two terms we are.we conclude that the best achievable.regret is t.to the two thirds still another root t.now what is where what are we missing.here.so here actually i'm missing the.similarity.between different candidates the.different experts to illustrate that.okay we actually we can consider the.following scenario.let f1 to fk3 be all possible.when somehow all possible experts that.is each function is just a one degree.speeding strategy.and with if we call this expert.employees.then actually we could also find out.some managers such that each manager.just manages some of his employees.so basically each manager aims to manage.a similar group of employees.and the strategy used by the oracle or.used by the manager.is simply uh to follow or render.expert he manages and on top of that.similarly for similar managers we could.just.also assign vps to manage those managers.or essentially we finally will have the.box that manages all vps.and the final target of the boss is to.find or find out a learning algorithm.which comes close.to the best of the experts so the.performance gap could be decomposed into.several stages and for each stage.yeah one could just use the prediction.with expert otherwise algorithm to.arrive at some regret.the only remaining issue here is that.okay if we apply the nail idea.or id a nail regression.in prediction with export otherwise we.see that okay the last.regret the regret bound on the last.layer is sphere of the order root t.times dot k3 which is still very large.yeah essentially.the same regress bond we obtained in our.last page.so the only so we so.to overcome this we still need to make.use of the similarity between different.experts yeah this is some property we.haven't used yet.and this motivates us to for.motivate the definition of a good expert.that is in prediction research effort.otherwise.we call an expert is delta good if at.each time.the reward of that expert it will be.better close to the best one.so if data is small maybe a good.strategy is just to follow that that's a.good expert.so which will give us a nail regression.like t times delta.however this bond is not that good when.delta is of the.or is essentially a constant because we.know that our root cube.actually is attainable in that scenario.and the main result for this sub problem.is that actually in view in the presence.of a.delta good expert actually we can.achieve a regress bound.like root t times delta times log k.an improvement from just till the.template okay to.root t times the delta times log so we.have an additional parameter delta here.and in this and so in this scenario.okay actually we can introduce.additional terms delta here.in the regress incurred at each stage.and note that the similarity level will.increase yeah when we move to the from.the root to the leaf.that is f1 and f2 are more similar than.the similarity between p21 and p22 so.we'll conclude that.delta delta 1 will be smaller will be.larger than delta 2.and which is larger than delta 3. so.delta i i.is shrinking however k is growing.and obtaining a careful tradeoff between.those two terms.just give us an output policy which we.call the chain exponential rating policy.or just the true policy.yeah which satisfy was satisfying the.regret bound of the order due to t.times not t so this training idea will.lead to a statistically optimal policy.here.now some of you may have noticed that.yeah this algorithm.can can cannot be computationally.efficient.because at the bottom level we have lots.of.uh lots of oh it's mainly many experts.here.and to draw exponential rating algorithm.among those gives then v.many exports will take an exponential.many extent.of an exponential time so it is not.efficient.so the next step is that we would like.to modify the algorithm to make it.computationally efficient yeah i'm.afraid that i don't have enough i don't.have time.to talk about that in detail yeah.because.because i believe you guys are more.interested in the empirical results.at the end so let me let me just.skip this part but to emphasize that the.main idea from this part is that.we slightly enlarge the set of the.experts.so that they will form a product.structure.and the main observation is that the.product structure.will lead to efficient computation in.that scenario.okay let me skip this part yeah we.that involves the definition of lots of.managers and employees and the resulting.algorithm is called the co algorithm.yeah we'll take the space linear in t.and time polynomial in t.and the regress bound will be of of the.order just t.of two log vectors and finally.yeah let me move on to the real data.experiments.so we obtain three real data sets from.various media.here each of which consists of two.sequences that is the private value of.vt.and the minimum between mt so here the.minimum b2b is.returned yeah it is returned by us by.the analyst.by the google by the end exchange and vt.here.is computed by the variable media people.using an independent algorithm yeah.which is the independent of the bidding.process and the time duration of the.data set is around one month.yes this year and the sample sizes range.from half a million to two million.we also consider two three computing.policies.the first one may be the simplest one is.a linear bit shading.that is we assume that our base is.linear in the private value with.parameter theta.and we learn this data in an online.fashion that is we.just look at the past the data in the.past one day window and.then we obtain we find out what is the.optimal.theta for that window and the second.approach is.a state-of-the-art approach yeah some.lamellar bit shading approach.where bt is some non-linear function of.vt permutates by theta with some.non-linear for function f and we.learn the parameter theta using the.exactly the same way as the linear bit.shading.the last pompedian policy has somehow.different ideas from the.previous ones yeah yes basically.rather than modeling the bs by a.function.of vt the distribution learning is a.non-parametric approach.that would like to estimate the.distribution.of the minimum between and plug in that.distribution to find out what is the.optimal.price to bid in this scenario so those.are the competing policies.and the experimental results that show.that.the cumulative reward achieved by our.policy.uniformly our imp up journey for me.improves.over all possible baselines.here the x-axis is the time and the.y-axis.is accumulating reward normalized to 0 1.and here the blue curve is the.cumulative.the curve of cumulative reward as a.function of time for our algorithm.and the other curves are just for other.bidding algorithms.so here we see that okay for all data.sets our blue the blue curve.is always on top of that and sometimes.it could outperform the.non-linear shading one yeah or very.mature.strategy by a large percent by large.percent.and sometimes yeah the gap is narrower.but we still have an improvement here.in both beta set b and data cell c.and also a closer inspection of the data.also reveals that.our co algorithm our algorithm also is.theoretically robust.empirically also shown to be adaptive to.different.natures of the data for example let's.take a look at the visualization of data.set a.here is just the huge screen of the.private values and the maximum competing.b's.we see that the distribution of private.value.looks very continuous it's maybe except.for this spike.however the distribution for continuous.competing b is actually quite.uh discrete yeah only maybe only.supported on those four points.and it turns out that if we also plot.the histogram.of our the prices we beat well the blue.bar represents the total.number of bees we make at this price and.the red bar represents the fraction of.that beast.those beasts where we win and we will.observe that.okay i'll see always actually.find out what the support the location.of this product fairly well.and knows how to win it at this auction.at each time.so however as a comparison the.non-linear big shading.method is still adapts.essentially adapt to the private value.so the performance is not so great.for them for for data set a so this is a.performance for data set a.and also for the data c with a different.nature of data.in the private values and competing b's.well perhaps the competing bees.looks very continuous except for this.spike.and the price values also maybe it looks.more discreet but possibly with more.two main strikes and in this scenario.we see that our co algorithm has three.stacks.actually one will crisp will correspond.to the spike in the measurement.completing these.and the other two correspond to the.spike's impact values.so basically the algorithm actually.adapts to different.natures of the data including the.measures for private values and the.complete bs.and it's not aiming to to somehow fit.the nature of of either specific.it was your specific data source.and so to summarize in part two we.obtained a statistical optimal policy.by hierarchical changing and we could.eventually implement it.by utilizing its product structure.and on offline real data we also show a.superior and.empirical performances on all data sets.and to conclude.in this talk we mainly figure out the.optimal regret efficiently are treatable.for a single bidder in various scenarios.with different assumptions on.either the characteristics of the other.beta speed or the bidder's private.evaluation.or the feedback structure or the.reference policies with which our.computer competes.i also would i'd also like to point out.some future directions.the first direction is to incorporate.additional site information in our model.so in practice.there are typically plenty of style.information available for us.to let's say to estimate the to predict.what is the minimum between at each.round so it will be very interesting to.incorporate the system information into.this framework.actually we are currently pursuing this.direction and we have some.very amazing results and the second the.second part.the second free objection is that in.this talk we mostly focus on a single.beat.however it will be very interesting to.establish what is the equilibrium theory.involving multiple beta sellers for.example.if all of them figured out a practical.strategy to perform in.for in the auction then what will be the.resulting equilibrium of the market.will that market be efficient that would.be interesting question to ask.and finally we will also we.also are interested in the case.where the utility function or the payout.function is non-additive.meaning that okay the payoff for.two rounds may not be the sum of the.payout for each round.this may happen when the last e.economics.when the goods are kind of complementary.or alternative to each other.then the utility function will not be.additive.it could be super additive or sub.attitude so what we are.what happens in this kind of scenarios.will also be very interesting to us.okay so thank you for your attention and.i'm happy to take your questions.

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How can I fill out Google's intern host matching form to optimize my chances of receiving a match?

I was selected for a summer internship 2016. I tried to be very open while filling the preference form: I choose many products as my favorite products and I said I'm open about the team I want to join. I even was very open in the location and start date to get host matching interviews (I negotiated the start date in the interview until both me and my host were happy.) You could ask your recruiter to review your form (there are very cool and could help you a lot since they have a bigger experience). Do a search on the potential team. Before the interviews, try to find smart question that you are Continue Reading

Do military members have to pay any fee for leave or fiancee forms?

First off there are no fees for leaves or requests for leave in any branch of the United States military. Second there is no such thing as a fiancée form in the U.S. military. There is however a form for applying for a fiancée visa (K-1 Visa)that is available from the Immigration and Customs Service (Fiancé(e) Visas ) which would be processed by the U.S. State Department at a U.S. Consulate or Embassy overseas. However these fiancée visas are for foreigners wishing to enter the United States for the purpose of marriage and are valid for 90 days. They have nothing to do with the military and are Continue Reading

How do I fill out the form of DU CIC? I couldn't find the link to fill out the form.

Just register on the admission portal and during registration you will get an option for the entrance based course. Just register there. There is no separate form for DU CIC.

How can I make it easier for users to fill out a form on mobile apps?

Make it fast. Ask them as few questions as possible (don't collect unnecessary information) and pre-populate as many fields as possible. Don't ask offputting questions where the respondent might have to enter sensitive personal information. If some users see you collecting sensitive information, they might not be ready to share that with you yet based on what you are offering, and they will think twice about completing the form.

How do you know if you need to fill out a 1099 form?

It can also be that he used the wrong form and will still be deducting taxes as he should be. Using the wrong form and doing the right thing isnt exactly a federal offense

How much do Government contractors make?

A MASSIVE amount of cash for a short period of time doing jobs that Soldiers do for a fraction of the money. If we paid them less, we could make more. A friend of mine was making upwards of 75k per rotation performing a security detail for some dude. Rotations were 3 months long. I also knew a dude that worked at a rec center making 30K every 3 months. He handed out basketballs and towels... The money is disgusting. I know plenty of Soldiers who would do better for less. :(

Who qualifies as a federal contractor?

The point is that the U.S. may need people of their experience and expertise. When confronted with perennial problems, like North Korea and Iran, serving professionals often turn to former officials for their experience, advise, contacts, and counsel. They know that they can discuss classified information with these trusted people. Also, many employees of defense contractors and other sensitive industries were government employees and bring their clearances into private industry. They can do valuable work if they have permission to see classified documents in the course of their work. It is crit Continue Reading

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