Online Ad Allocation: Theory and Practice

Transcription

1 Online Ad Allocation: Theory and Practice Vahab Mirrokni December 19, 2014 Based on recent papers in collaboration with my colleagues at Google, Columbia Univ., Cornell, MIT, and Stanford. [S. Balseiro, A. Bhalgat, J. Feldman, G. Goel, N. Korula, S. Muthukrishnan, S. OveisGharan, M. Pal, R. Paes Leme, C. Stein, Q. Yan, M. ZadiMoghaddam]

2 Budget Constraints in Online Advertising

3 Budget Constraints in Online Advertising

4 Capacity Constraints in Display Advertising Publishers sell contracts to advertisers for a number of impressions per day, e.g., 1M Pepsi ads per day.

5 Capacity Constraints in Display Advertising Publishers sell contracts to advertisers for a number of impressions per day, e.g., 1M Pepsi ads per day. Different impressions have different values

6 Capacity Constraints in Display Advertising Publishers sell contracts to advertisers for a number of impressions per day, e.g., 1M Pepsi ads per day. Different impressions have different values Goal: Respect capacity/budget; maximize(advertiser) value. Challenge: Allocation is done Online. Do not know future.

7 Online Ad Allocation When a page arrives, assign an eligible ad. value of assigning page i to ad a: via

8 Online Ad Allocation When a page arrives, assign an eligible ad. value of assigning page i to ad a: via Online Weighted Matching with Free Disposal [Display Ads (DA)] problem: Maximize value of ads served: max i,a v iax ia Capacity of ad a: i A(a) x ia C a

9 Online Ad Allocation When a page arrives, assign an eligible ad. revenue from assigning page i to ad a: b ia Budgeted Allocation [ AdWords (AW)] problem: Maximize revenue of ads served: max i,a b iax ia Budget of ad a: i A(a) b iax ia B a

10 General Form of LP max i,a v ia x ia x ia 1 ( i) a s ia x ia C a ( a) i x ia 0 ( i, a) Online Matching: v ia = s ia = 1 Weighted Matching s ia = 1 Disp. Ads (DA): Budgeted Allocation s ia = v ia AdWords (AW):

11 Outline Survey on Online Stochastic Assignment Problems Adversarial Arrival Model: Primal-Dual Algorithms Random Order: Dual Algorithms IID with known Distribution: Primal Algorithms Experimental Results Five Problems/Results: 1. Robust Approximation: Simultaneous Adversarial & Stochastic 2. Small Capacity: Beat 1/2 even for SWM? 3. Bicriteria Online Approximation? 4. PTAS in iid with known distribution? 5. Dealing with incentive issues: Clinching Auctions

12 Arrival Models Adversarial Arrival Model: ALG is α-competitive? if for each H, ALG(H) OPT(H) α

13 Arrival Models Adversarial Arrival Model: ALG is α-competitive? if for each H, ALG(H) OPT(H) α Random Order or IID with unknown dist.: ALG is α-approximation? if w.h.p., ALG(H) OPT(H) α or ALG is α-approximation? if E[ALG(H)] E[OPT(H)] α

14 Arrival Models Adversarial Arrival Model: ALG is α-competitive? if for each H, ALG(H) OPT(H) α Random Order or IID with unknown dist.: ALG is α-approximation? if w.h.p., ALG(H) OPT(H) α or ALG is α-approximation? if E[ALG(H)] E[OPT(H)] α iid with known distributions:

15 Greedy Algorithm Assign impression to an advertiser maximizing Marginal Gain

16 Greedy Algorithm Assign impression to an advertiser maximizing Marginal Gain Competitive Ratio: Tight 1/2. [NWF78] Follows from submodularity of the value function.

17 Greedy Algorithm Assign impression to an advertiser maximizing Marginal Gain Competitive Ratio: Tight 1/2. [NWF78] Follows from submodularity of the value function. n copies 1 Ad 1: C 1 = n 1 + ɛ Ad 2: C 2 = n

18 Greedy Algorithm Assign impression to an advertiser maximizing Marginal Gain Competitive Ratio: Tight 1/2. [NWF78] Follows from submodularity of the value function. n copies 1 Ad 1: C 1 = n 1 + ɛ n copies 1 Ad 2: C 2 = n

19 Greedy Algorithm Assign impression to an advertiser maximizing Marginal Gain Competitive Ratio: Tight 1/2. [NWF78] Follows from submodularity of the value function. n copies 1 Ad 1: C 1 = n 1 + ɛ n copies 1 Ad 2: C 2 = n

20 Arrival Models Adversarial Arrival Model: Primal-dual Approach Unweighted: 1-1/e-competitive algorithm [KarpVV] Weighted (Large Capacity): 1-1/e-competitive algorithm [MehtaSVV,FeldmanKMMP]

21 Primal-dual Algorithms AdWords Problem: [MSVV05] The following is a 1 1 e -aprx: Assign impression i to an advertiser a: maximizing b ia (1 e spent a Ba 1 ),

22 Primal-dual Algorithms AdWords Problem: [MSVV05] The following is a 1 1 e -aprx: Assign impression i to an advertiser a: maximizing b ia (1 e spent a Ba 1 ), Display Ads problem: Assign impression to an advertiser a: maximizing (imp. value - β a ), Greedy: βa = min. impression assigned to a. Better (pd-avg): β a = average value of top C a impressions assigned to a. Optimal (pd-exp): order value of edges assigned to a: v(1) v(2)... v(c a ): β a = 1 C a (e 1) C a j=1 v(j)(1 + 1 C a ) j 1. Thm: pd-exp achieves optimal competitive Ratio: 1 1 e ɛ if C a > O( 1 ɛ ). [FeldmanKMMP09]

23 Arrival Models Adversarial Arrival Model: Primal-dual Approach Unweighted: 1-1/e-competitive algorithm [KarpVV] Weighted (Large Capacity): 1-1/e-competitive algorithm [MehtaSVV,FeldmanKMMP] Random Order or IID with unknown dist.: Dual Approach Unweighted: 0.69-competitive algorithm [MahdianY] Weighted (Large Capacity): 1 ɛ-competitive by applying a Dual Approach: learn dual variables and use them later [DevanurH,AWY,FHKMS,VJV]

24 Arrival Models Adversarial Arrival Model: Primal-dual Approach Unweighted: 1-1/e-competitive algorithm [KarpVV] Weighted (Large Capacity): 1-1/e-competitive algorithm [MehtaSVV,FeldmanKMMP] Random Order or IID with unknown dist.: Dual Approach Unweighted: 0.69-competitive algorithm [MahdianY] Weighted (Large Capacity): 1 ɛ-competitive by applying a Dual Approach: learn dual variables and use them later [DevanurH,AWY,FHKMS,VJV] iid with known distributions: Primal Approach Unweighted: 0.72-competitive [FeldmanMMM & ManshadiOS] Weighted: 0.66-competitive [HaeuplerMZ]

25 Dual-base Algorithm For Random Order max v ia x ia i,a x ia 1 ( i) a x ia C a ( a) i x ia 0 ( i, a) min C a β a + z i a i z i v ia β a ( i, a) β a, z i 0 ( i, a)

26 Dual-base Algorithm For Random Order max v ia x ia i,a x ia 1 ( i) a x ia C a ( a) i x ia 0 ( i, a) min C a β a + z i a i z i v ia β a ( i, a) β a, z i 0 ( i, a) Fact: If opt. β a are known, assigning i to argmax(v ia β a) is opt. Proof: Comp. slackness. Given β a, compute x as follows: x ia = 1 if a = argmax(v ia β a).

27 Dual-base Algorithm For Random Order max v ia x ia i,a x ia 1 ( i) a x ia C a ( a) i Algorithm: x ia 0 ( i, a) min a C a β a + z i i z i v ia β a ( i, a) β a, z i 0 ( i, a) Solve the dual program on a sample. Assign each impression i to ad a that maximizes v ia β a.

28 Experiments: setup Real ad impression data from several large publishers 200k - 1.5M impressions in simulation period advertisers Edge weights = predicted click probability Algorithms: greedy: maximum marginal value pd-avg, pd-exp: pure online primal-dual from [FKMMP09]. dualbase: training-based primal-dual [FHKMS10] hybrid: convex combo of training based, pure online. lp-weight: optimum efficiency

29 Experimental Evaluation: Summary Algorithm Avg Efficiency% Provable Ratio opt 100% 1 greedy 69% 1/2 pd-avg 77% 1/2 pd-exp 82% 1-1/e dualbase 87% 1 ɛ hybrid 89%? pd-exp & pd-avg outperform greedy by 9% and 14% (with more improvements in tight competition.) With good prediction (of size 1%), dualbase outperforms pure online algorithms by 6% to 12%. By Feldman, Henzinger, Korula, M., Stein 11.

30 In Production Algorithms inspired by these techniques are in use at Google DoubleClick display ad serving system, delivering billions of ads per day.

31 In Production Algorithms inspired by these techniques are in use at Google DoubleClick display ad serving system, delivering billions of ads per day. Smooth Delivery of Display Ads (Bhalgat, Feldman, M. - KDD) Model this with multiple nested capacity constraints. Whole-page Ad Allocation (Korula, M., Yan - EC) Assign multiple ads with configuration constraints. Display Ad Allocation with Ad Exchange (Balseiro, Feldman, M., Muthukrishnan - EC) Maximize quality of reservation ads and revenue of Ad Exchange. Bicriteria online matching (Korula, M., ZadiMoghaddam - WINE) maximize both clicks and delivery

32 In Production Algorithms inspired by these techniques are in use at Google DoubleClick display ad serving system, delivering billions of ads per day. Smooth Delivery of Display Ads (Bhalgat, Feldman, M. - KDD) Model this with multiple nested capacity constraints. Whole-page Ad Allocation (Korula, M., Yan - EC) Assign multiple ads with configuration constraints. Display Ad Allocation with Ad Exchange (Balseiro, Feldman, M., Muthukrishnan - EC) Maximize quality of reservation ads and revenue of Ad Exchange. Bicriteria online matching (Korula, M., ZadiMoghaddam - WINE) maximize both clicks and delivery Final Algorithm: Adversarial or Stochastic? hybrid.

33 In practice: Adversarial or Stochastic? Stochastic? No. Traffic spikes contradict with the simple random arrival assumption. Adversarial? No. Too pessimistic. Some forecasts are useful.

34 In practice: Adversarial or Stochastic? Stochastic? No. Traffic spikes contradict with the simple random arrival assumption. Adversarial? No. Too pessimistic. Some forecasts are useful. Simultaneous Approximation: Adversarial algorithms that are robust against traffic spikes and perform better when the stochastic information is valid. (a,b)-approximation: a-competitive for random order. b-competitive for adversarial. Problem 1: Assuming C a max s ia, can we achieve the best of both worlds?

35 Simultaneous adversarial & stochastic optimization (a,b)-approximation: a-competitive for random order. b-competitive for adversarial. Problem 1: Assuming C a max s ia, can we achieve the best of both worlds i.e. a (1 ɛ, 1 1 e )-approximation?

36 Simultaneous adversarial & stochastic optimization (a,b)-approximation: a-competitive for random order. b-competitive for adversarial. Problem 1: Assuming C a max s ia, can we achieve the best of both worlds i.e. a (1 ɛ, 1 1 e )-approximation? Yes for unweighted edges!(m.,oveisgharan, ZadiMoghaddam) PD-EXP algorithm achieves (1 ɛ, 1 1 e )-approximation.

37 Simultaneous adversarial & stochastic optimization (a,b)-approximation: a-competitive for random order. b-competitive for adversarial. Problem 1: Assuming C a max s ia, can we achieve the best of both worlds i.e. a (1 ɛ, 1 1 e )-approximation? Yes for unweighted edges!(m.,oveisgharan, ZadiMoghaddam) PD-EXP algorithm achieves (1 ɛ, 1 1 e )-approximation. No for the weighted case! (M.,OveisGharan,ZadiMoghaddam) Achieving (0.97, 1 1 e )-approximation is impossible. PD-EXP achieves (0.76, 1 1 e )-approximation.

38 Hardness Result Any 1 ɛ-competitive algorithm for stochastic input can not have a competitive ratio better than 4 ɛ in the adversarial model. Achieving (4 ɛ, 1 ɛ)-approximation is impossible. In particular, any 1 1/e competitive algorithm in the adversarial case has competitive ratio at most 97.6% for the random order.

39 Factor-revealing Mathematical Program We have n balls, so t is in [n]. F is the antiderivative of f, and o j is how much value is assigned to bin j in the optimum solution. 1 MP : minimize OPT j r j(n)c j j c jf (r j (t)) = φ(t) t [n], ɛ j o jf (r j ((k + 1)nɛ)) φ((k + 1)nɛ) φ(knɛ) k [ 1 ɛ 1], o j c j j [m], j o j = OPT, r j (t) r j (t + 1) j, t [n 1], r j (n) 1 j [m].

40 Converting Factor-revealing MP to Poly-size LP We discretize time and spent budget ratios into k parts, so we have k variables for values of potential function at different time intervals. We have variable c[r, t] that denotes the sum of capacities of bins with rations in range [r, r + 1/k] at time t. Similarly we define o[r, t]. { LP minimize 1 φ( 1 1 1/e ɛ ) } 1/ɛ 1 ρ=0 c ρ,k (ρɛ/e e ρɛ 1 ) 1/ɛ 1 ρ=0 c ρ,k (ρɛ e ρɛ 1 ) φ(k) k [ ɛ 1 ] 1/ɛ 1 ρ=0 ɛo ρ,k+1 (1 e (ρ+1)ɛ 1 ) φ(k + 1) φ(k) k [ ɛ 1 1] o ρ,k c ρ,k ρ [ ɛ 1 1], k [ ɛ 1 ] 1/ɛ 1 i=0 1/ɛ 1 l=i o ρ,k = 1 k [ ɛ 1 ] : c l,k 1/ɛ 1 c l=i l,k+1 i [ ɛ 1 1], k [ ɛ 1 1]

41 Summary: Robust Models Summary: Simultaneous Approximations Unweighted: (1 1/e, 0.70) (1 1/e, 1 ɛ). Weighted: (1 1/e, 1 1/e) (1 1/e, 0.76). Impossible to get (1 1/e, 0.97) for weighted. Other robust stochastic models? Approximation factor as a function of accuracy of prediction?

42 Summary: Robust Models Summary: Simultaneous Approximations Unweighted: (1 1/e, 0.70) (1 1/e, 1 ɛ). Weighted: (1 1/e, 1 1/e) (1 1/e, 0.76). Impossible to get (1 1/e, 0.97) for weighted. Other robust stochastic models? Approximation factor as a function of accuracy of prediction? Adaptively increase/decrease β s using a controller. Tan and Srikant show asymptotic optimality in an iid model. Handling bursty random arrival models: Periodic re-optimization achieves constant-factor approximation even in a bursty random arrival model [Ciacon and Farias] Mixed adversarial & stochastic models[esfandiari, Korula, M.] Modeling traffic spikes as an adversarial model inside the stochastic model.

43 Outline Survey on Online Stochastic Assignment Problems Adversarial Arrival Model: Primal-Dual Algorithms Random Order: Dual Algorithms IID with known Distribution: Primal Algorithms Experimental Results Five Problems/Results: 1. Robust Approximation: Simultaneous Adversarial & Stochastic 2. Small Capacity: Beat 1/2 even for SWM? 3. Bicriteria Online Approximation? 4. PTAS in iid with known distribution? 5. Dealing with incentive issues: Clinching Auctions

44 Problem 2: Improve Greedy for Small Capacities? Greedy gives a 1/2-approximation for adversarial model.

45 Problem 2: Improve Greedy for Small Capacities? Greedy gives a 1/2-approximation for adversarial model. Open Problem: Beat 1/2-approximation for online budgeted allocation or online weighted matching (even for random order)?

46 Problem 2: Improve Greedy for Small Capacities? Greedy gives a 1/2-approximation for adversarial model. Open Problem: Beat 1/2-approximation for online budgeted allocation or online weighted matching (even for random order)? I will present a recent progress for a generalization: Online Submodular Welfare Maximization.

47 Online Submodular Welfare Maximization(SWM) m buyers and n items. S 1 S 5 S 6 S 2 S 3 S 4 Buyers f 1 (S 1 ) f 2 (S 2 ) f 3 (S 3 ) f 4 (S 4 ) f 5 (S 5 ) f 6 (S 6 ) Goal: Assign items to buyers and maximize social welfare, i.e, i f i(s i ). Offline SWM Special case of submodular maximization subject to matroid constraint 1 1/e-approximation by Vondrak /e is tight with subexponential #queries (MirrokniSV 08)

48 Online Submodular Welfare Maximization(SWM) m buyers and n items. S 1 S 5 S 6 S 2 S 3 S 4 Buyers f 1 (S 1 ) f 2 (S 2 ) f 3 (S 3 ) f 4 (S 4 ) f 5 (S 5 ) f 6 (S 6 ) Goal: Assign items to buyers and maximize social welfare, i.e, i f i(s i ). Offline SWM Special case of submodular maximization subject to matroid constraint 1 1/e-approximation by Vondrak /e is tight with subexponential #queries (MirrokniSV 08) Online SWM Greedy is a 1/2-approximation algorithm (NWF) Adversarial: Unless P = NP 1/2 is tight (KaprakovPV 13).

49 Online Submodular Welfare Maximization(SWM) m buyers and n items. S 1 S 5 S 6 S 2 S 3 S 4 Buyers f 1 (S 1 ) f 2 (S 2 ) f 3 (S 3 ) f 4 (S 4 ) f 5 (S 5 ) f 6 (S 6 ) Goal: Assign items to buyers and maximize social welfare, i.e, i f i(s i ). Offline SWM Special case of submodular maximization subject to matroid constraint 1 1/e-approximation by Vondrak /e is tight with subexponential #queries (MirrokniSV 08) Online SWM Greedy is a 1/2-approximation algorithm (NWF) Adversarial: Unless P = NP 1/2 is tight (KaprakovPV 13). How about random order? Can we get 1/2 + Ω(1)?

50 Online SWM for random order Thm (KorulaM.ZadiMoghaddam): Greedy is a approximation for online SWM in the random order model.

51 Online SWM for random order Thm (KorulaM.ZadiMoghaddam): Greedy is a approximation for online SWM in the random order model. Proof Idea: Descritize the time horizon to 1 ɛ intervals and Consider marginal gains of assigning items to each buyer in each interval and Assuming that we run the greedy algorithm find variants and write a factor-revealing mathematical program... Next: Rough Idea via differential equations

52 Greedy beats 1/2 in random order: Rough Idea Assume opt = 1 and consider the allocation of items to buyers on average over the time horizon [0, 1]. Let g(t) = E[Greedy s gain at timet] g(1) is approximation factor.

53 Greedy beats 1/2 in random order: Rough Idea Assume opt = 1 and consider the allocation of items to buyers on average over the time horizon [0, 1]. Let g(t) = E[Greedy s gain at timet] g(1) is approximation factor. g(0) = 0 and 0 g(t) 1. g(t) is monotone and non-decreasing. g (t) is non-increasing (since f is submodular).

54 Greedy beats 1/2 in random order: Rough Idea Assume opt = 1 and consider the allocation of items to buyers on average over the time horizon [0, 1]. Let g(t) = E[Greedy s gain at timet] g(1) is approximation factor. g(0) = 0 and 0 g(t) 1. g(t) is monotone and non-decreasing. g (t) is non-increasing (since f is submodular). dg(t) (1 t g(t))dt/(1 t) g (t) 1 g(t)/(1 t).

55 Greedy beats 1/2 in random order: Rough Idea Assume opt = 1 and consider the allocation of items to buyers on average over the time horizon [0, 1]. Let g(t) = E[Greedy s gain at timet] g(1) is approximation factor. g(0) = 0 and 0 g(t) 1. g(t) is monotone and non-decreasing. g (t) is non-increasing (since f is submodular). dg(t) (1 t g(t))dt/(1 t) g (t) 1 g(t)/(1 t). g(t) = (1 t) ln 1 1 t thus g(1) 1/e.

56 Greedy beats 1/2 in random order: Rough Idea 2 Let g(t) = E[Greedy s gain at timet] g(1) is approximation factor. g(0) = 0 and 0 g(t) 1. g(t) is non-decreasing. g (t) is non-increasing (since f is submodular). g (t) = 1 t t 0 g (s) 1 t 1 s ds 1 t

57 Greedy beats 1/2 in random order: Rough Idea 2 Let g(t) = E[Greedy s gain at timet] g(1) is approximation factor. g(0) = 0 and 0 g(t) 1. g(t) is non-decreasing. g (t) is non-increasing (since f is submodular). g (t) = 1 t t 0 g (s) 1 t 1 s ds 1 t g(t) = t t2 2 and g (t) = 1 t thus g(1) 1/2.

58 Greedy beats 1/2 in random order: Rough Idea 2 Let g(t) = E[Greedy s gain at timet] g(1) is approximation factor. g(0) = 0 and 0 g(t) 1. g(t) is non-decreasing. g (t) is non-increasing (since f is submodular). g (t) = 1 t t 0 g (s) 1 t 1 s ds 1 t g(t) = t t2 2 and g (t) = 1 t thus g(1) 1/2. As t 1 the marginal gain according to the above argument tends to zero. Can we use the random order to put another bound the loss in optimum from the first half of the assignment?

59 Greedy beats 1/2 in random order: Rough Idea 3 Assignment of an item can reduce the expected gains from future items, but this reduction in future gains is bounded, and random order evenly spreads it out among future items Bound the total loss in opt in the first half of items (HM). For k = 500 intervals the solution to this program is Minimize α Subject to: α = k i=1 w i w i w i+1 1 i k 1 w i b i + s i + a i 1 i k w i 1/k s i i 1 i =1 a i /(k i ) 1 i k s i a i /(k i) 1 i k 1 HM k/2 i=1 a i (k/2)/(k i) X HM k/2 i=1 (s i + b i + a i (k/2 i)/(k i)) w i ( X (k + 1 i)/(k/2) i i =k/2+1 b i ) /(k + 1 i) k/2 < i k

60 Online SWM for random order[kmz 14] Thm (KorulaM.ZadiMoghaddam): Greedy is a approximation for online SWM in the random order model. Thm (KorulaM.ZadiMoghaddam): Greedy is a 0.51-approximation for online SWM in the random order model when the submodular function is second-order submodular. Conjecture (KorulaM.ZadiMoghaddam): Greedy is a 0.57-approximation for online SWM in the random order model. Some of the techniques are used to get improved distributed algorithms for submodular maximization (e.g., in MapReduce, or streaming models).

61 Problem 4: Online Stochastic Matching i.i.d. with known distributions Power of Two Choices: Offline: Find two matchings offline in a sampled instance. Online: implement these two matchings in an order. Online Stochastic Matching: 0.67-approximation (whp) [FMMM09] Improved to approximation (in expectation) [MOS11] Improved to 0.73-approximation (in expectation) [JX14] One cannot achieve better than 0.82-approximation [MOS11].

62 Problem 4: Online Stochastic Matching i.i.d. with known distributions Power of Two Choices: Offline: Find two matchings offline in a sampled instance. Online: implement these two matchings in an order. Online Stochastic Matching: 0.67-approximation (whp) [FMMM09] Improved to approximation (in expectation) [MOS11] Improved to 0.73-approximation (in expectation) [JX14] One cannot achieve better than 0.82-approximation [MOS11]. Online Stochastic Weighted Matching: [HMZ11] 0.66-approximation.

63 Problem 4: Online Stochastic Matching i.i.d. with known distributions Power of Two Choices: Offline: Find two matchings offline in a sampled instance. Online: implement these two matchings in an order. Online Stochastic Matching: 0.67-approximation (whp) [FMMM09] Improved to approximation (in expectation) [MOS11] Improved to 0.73-approximation (in expectation) [JX14] One cannot achieve better than 0.82-approximation [MOS11]. Online Stochastic Weighted Matching: [HMZ11] 0.66-approximation. OPEN: PTAS compared to the optimal optimal dynamic program?

64 Outline Survey on Online Stochastic Assignment Problems Adversarial Arrival Model: Primal-Dual Algorithms Random Order: Dual Algorithms IID with known Distribution: Primal Algorithms Experimental Results Five Problems/Results: 1. Robust Approximation: Simultaneous Adversarial & Stochastic 2. Small Capacity: Beat 1/2 even for SWM? 3. Bicriteria Online Approximation? 4. PTAS in iid with known distribution? 5. Dealing with incentive issues: Clinching Auctions

65 Problem 5: Incentive Issues in repeated allocations Game theoretic challenges in repeated 2nd price auctions: If budget of some ads is exhausted early on, competition/price decreases for others! This results in unstable outcomes.

66 Problem 5: Incentive Issues in repeated allocations Game theoretic challenges in repeated 2nd price auctions: If budget of some ads is exhausted early on, competition/price decreases for others! This results in unstable outcomes. Practical approaches: Spend budget smoothly Bid throttling: let ads participate in auctions probabilistically Bid lowering: lower bids by a factor

67 Problem 5: Incentive Issues in repeated allocations Game theoretic challenges in repeated 2nd price auctions: If budget of some ads is exhausted early on, competition/price decreases for others! This results in unstable outcomes. Practical approaches: Spend budget smoothly Bid throttling: let ads participate in auctions probabilistically Bid lowering: lower bids by a factor Mechanism design approach: Design for (mean-field) equilibria? See paper by Balseiro, Besbes, and Weintraub 14 Incentive-compatibility: Clinching Ascending Auctions (Goel, M., Paes Leme, STOC12, SODA13, EC 14)

68 Research Directions More theoretical open problems: Small budgets and small degrees: Improve 1/2-approximation. Compete with online DP in the iid model: PTAS? Other robust stochastic models? Improve simultaneous approximations (1 1/e, 0.76). Approximation factor as a function of accuracy of prediction? Incentive issues, e.g., in AdWords repeated 2nd-price auctions Incentive-compatibility: Clinching Auctions (Goel, M., Paes Leme, STOC12, SODA13, EC 14) (mean-field) equilibria? extensive-form or Nash equilibria? Thank You