Speeding up the Metabolism in E-commerce by Reinforcement Mechanism Design Hua-Lin He Chun-Xiang Pan Alibaba Inc. Alibaba Inc. Hangzhou, China Hangzhou, China hualin.hhl@alibaba-inc.com xuanran@taobao.com Qing Da An-Xiang Zeng Alibaba Inc. Alibaba Inc. Hangzhou, China Hangzhou, China daqing.dq@alibaba-inc.com renzhong@taobao.com ABSTRACT customers, enterprises and start-ups, and hundreds of thousands of In a large E-commerce platform, all the participants compete for service providers, making it a new type of economic entity rather impressions under the allocation mechanism of the platform. Exist- than enterprise platform. In such a economic entity, a major re- ing methods mainly focus on the short-term return based on the sponsibility of the platform is to design economic institutions to current observations instead of the long-term return. In this paper, achieve various business goals, which is the exact field of Mecha- we formally establish the lifecycle model for products, by defining nism Design [1]. Among all the affairs of the E-commerce platform, the introduction, growth, maturity and decline stages and their tran- impression allocation is one of the key strategies to achieve its busi- sitions throughout the whole life period. Based on such model, we ness goal, while products are players competing for the resources further propose a reinforcement learning based mechanism design under the allocation mechanism of the platform, and the platform framework for impression allocation, which incorporates the first is the game designer aiming to design game whose outcome will principal component based permutation and the novel experiences be as the platform desires. generation method, to maximize short-term as well as long-term Existing work of impression allocation in literature are mainly return of the platform. With the power of trial-and-error, it is pos- motivated and modeled from a perspective view of supervised learn- sible to optimize impression allocation strategies globally which ing, roughly falling into the fields of information retrieval [2, 3] and is contribute to the healthy development of participants and the recommendation [4, 5]. For these methods, a Click-Through-Rate platform itself. We evaluate our algorithm on a simulated environ- (CTR) model is usually built based on either a ranking function ment built based on one of the largest E-commerce platforms, and or a collaborative filtering system, then impressions are allocated a significant improvement has been achieved in comparison with according to the CTR scores. However, these methods usually op- the baseline solutions. timize the short-term clicks, by assuming that the properties of products is independent of the decisions of the platform, which CCS CONCEPTS may hardly hold in the real E-commerce environment. There are also a few work trying to apply the mechanism design to the al- • Computing methodologies → Reinforcement learning; Policy location problem from an economic theory point of view such iteration; • Applied computing → Online shopping; as [6–8]. Nevertheless, these methods only work in very limited KEYWORDS cases, such as the participants play only once, and their properties is statistically known or does not change over time, etc., making Reinforcement Learning, Mechanism Design, E-commerce them far from practical use in our scenario. A recent pioneer work ACM Reference Format: named Reinforcement Mechanism Design [9] attempts to get rid of Hua-Lin He, Chun-Xiang Pan, Qing Da, and An-Xiang Zeng. 2018. Speeding nonrealistic modeling assumptions of the classic economic theory up the Metabolism in E-commerce by Reinforcement Mechanism Design . and to make automated optimization possible, by incorporating the In Proceedings of ACM SIGIR Workshop on eCommerce (SIGIR 2018 eCom). Reinforcement Learning (RL) techniques. It is a general framework ACM, New York, NY, USA, 7 pages. which models the resource allocation problem over a sequence of 1 INTRODUCTION rounds as a Markov decision process (MDP) [10], and solves the MDP with the state-of-the-art RL methods. However, by defining Nowadays, E-commerce platform like Amazon or Taobao has de- the impression allocation over products as the action, it can hardly veloped into a large business ecosystem consisting of millions of scale with the number of products/sellers as shown in [11, 12]. Permission to make digital or hard copies of part or all of this work for personal or Copyright © 2018 by the paper’s authors. Copying permitted for private and academic purposes. Besides, it depends on an accurate behavioral model for the prod- classroom In: use is granted J. Degenhardt, withoutS.feeKallumadi, G. Di Fabbrizio, providedM. that copies Kumar, are Lin, Y.-C. not A. made or distributed Trotman, H. Zhao ucts/sellers, which is also unfeasible due to the uncertainty of the (eds.): Proceedings for profit of the SIGIR or commercial 2018 eCom advantage and workshop, 12 bear that copies July, this 2018,notice Ann Arbor, Michigan, and the USA, full citation published at http://ceur-ws.org on the first page. Copyrights for third-party components of this work must be honored. real world. For all other uses, contact the owner/author(s). Although the properties of products can not be fully observed SIGIR 2018 eCom, July 2018, Ann Arbor, Michigan, USA or accurately predicted, they do share a similar pattern in terms © 2018 Copyright held by the owner/author(s). SIGIR 2018 eCom, July 2018, Ann Arbor, Michigan, USA Hua-Lin He et al. of development trend, as summarized in the product lifecycle the- of these research suffer from low accuracy of click-through rate ory [13, 14]. The life story of most products is a history of their estimation for the lack of exposure historical data of start-ups. passing through certain recognizable stages including introduction, One of the most related topics in user impressions allocation is growth, maturity and decline stages. item cold-start problem [17], which has been extensively studied • Introduction: Also known as market development - this is over past decades. Researches can be classified into three cate- when a new product is first brought to market. Sales are low gories: hybrid algorithms combining CF with content-based tech- and creep along slowly. niques [18, 19], bandit algorithms [20–22] and data supplement • Growth: Demand begins to accelerate and the size of the total algorithms [23]. Among these researches, the hybrid algorithms market expands rapidly. exploit items’ properties, the bandit algorithms are designed for • Maturaty: Demand levels off and grows. no item content setting and gathering interactions from user effec- • Decline: The product begins to lose consumer appeal and tively, and the data supplement algorithms view cold-start as data sales drift downward. missing problem. Both of these research did not take the whole prod- uct lifecycle of items into account for the weakness of traditional During the lifecycle, new products arrive continuously and outdated prediction based machine learning model, resulting in long-term products wither away every day, leading to a natural metabolism imbalance between global efficiency and lifecycle optimization. in the E-commerce platform. Due to the insufficient statistics, new The application of reinforcement learning in commercial system products usually attract few attention from conventional supervised such as web recommendations and e-commerce search engines has learning methods, making the metabolism a very long period. not yet been well developed. Some attempts are made to model Inspired by the product lifecycle theory as well the reinforcement the user impression allocation problem in e-commerce platform mechanism design framework, we consider to develop reinforce- such as Tabao.com and Amazon.com. By regarding the platforms ment mechanism design while taking advantage of the product life- with millions of users as environment and treating the engines cycle theory. The key insight is, with the power of trial-and-error, allocating user impressions as agents, an Markov Decision Process it is possible to recognize in advance the potentially hot products or at least Partially Observable Markov Decision Process can be in the introduction stage as well as the potentially slow-selling established. For example, an reinforcement learning capable model products in the decline stage, so the metabolism can be speeded is established on each page status by limit the page visit sequences up and the long-term efficiency can be increased with an optimal to a constant number in a recommendation scene [24]. And another impression allocation strategy. proposed model is established on global status by combining all We formally establish the lifecycle model and formulate the the item historical representations in platform [11]. However, both impression allocation problem by regarding the global status of of these approaches struggled to manage an fixed dimensionality products as the state and the parameter adjustment of a scoring of state observation, low-dimensional action outputs and suffered function as the action. Besides, we develop a novel framework from partially observation issues. which incorporates a first principal component based algorithm Recently, mechanism design has been applied in impression and a repeated sampling based experiences generation method, allocation, providing a new approach for better allocating user im- as well as a shared convolutional neural network to further en- pressions [9, 25]. However, the former researches are not suitable hance the expressiveness and robustness. Moreover, we compare for real-world scenes because of the output action space is too large the feasibility and efficiency between baselines and the improved to be practical. In this paper, a reinforcement learning based mech- algorithms in a simulated environment built based on one of the anism design is established for the impression allocation problem largest E-commerce platforms. to maximize both short-term as well as long-term return of prod- The rest of the paper is organized as follows. The product lifecy- ucts in the platform with a new approach to extract states from all cle model and reinforcement learning algorithms are introduced in products and to reduce action space into practical level. section 3. Then a reinforcement learning mechanism design frame- work is proposed in section 4. Further more, experimental results are analyzed in section 5. Finally, conclusions and future work are discussed in section 6. 3 PRELIMINARIES 2 RELATED WORK 3.1 Product Lifecycle Model Many researches have been conducted on impression allocation In this subsection, we establish a mathematical model of product and dominated by supervised learning. In ranking phase, search lifecycle with noises. At step t, each product has an observable engine aims to find out good candidates and brought them in front attribute vector x t ∈ Rd and an unobservable latent lifecycle state so that products with better performance will gain more impres- zt ∈ L, where d is the dimension of the attribute space, and L = sions. Among which click-through rate is one of the most common {0, 1, 2, 3} is the set of lifecycle stages indicating the the introduction, representation of products performance. Some research presents an growth, maturity and decline stages respectively. Let pt ∈ R be the approach to automatically optimize the retrieval quality with well- CTR and qt ∈ R be the accumulated user impressions of the product. founded retrieval functions under risk minimization frame-work Without loss of generality, we assume pt and qt are observable, by historical click-through data [15]. Some other research proposed pt , qt are two observable components of x t , the platform allocates an unbiased estimation of document relevance by estimating the the impressions ut ∈ R to the product. The dynamics of the system presentation probability of each document [16]. Nevertheless, both Speeding up the Metabolism in E-commerce by Reinforcement Mechanism DesignSIGIR 2018 eCom, July 2018, Ann Arbor, Michigan, USA can be written as 0.14 Typical Lifecycle    qt +1 = qt + ut pt +1 = pt + f (zt , qt )   (1) zt +1 = д(x t , zt , t)  0.11 CTR   where f can be seen as the derivative of the p, and д is the state Maturity 0.08 transition function over L. th De ow clin According to the product lifecycle theory and online statistics, Introduction Gr e the derivative of the CTR can be formulated as 0.05 0 20 40 60 80 100 120 140 160  (ch − cl )e −δ (qt ) Time Step + ξ , z ∈ {1, 3}   f (zt , qt ) = (2 − z)(1 + e −δ (qt ) )2   (2) ξ , z    ∈ {0, 2} Figure 2: CTR evolution with the proposed lifecycle model. where ξ ∼ N (0, σ 2 ) is a gaussian noise with zero mean and vari- ance σ 2 , δ (qt ) = (qt − q˜t z − δ µ )/δ σ is the normalized impressions space S, action space A, a conditional probability distribution accumulated from stage z , q˜t z is the initial impressions when the p(·) and a scalar reward function r = R(s, a), R : S × A → R. product is firstly evolved to the life stage z, δ µ , δ σ are two unobserv- For states st , st +1 ∈ S and action at ∈ A, distribution function able parameters for normalization, and ch , cl ∈ R are the highest p(st +1 |st , at ) denotes the transition probability from state st to st +1 CTR and the lowest CTR during whole product lifecycle, inferred when action at is adopted in time step t, and the Markov property from two neural networks, respectively: p(st +1 |st , at ) = p(st +1 |s 1 , a 1 , · · · , st , at ) holds for any historical tra- cl = h(x t |θl ), ch = h(x t |θh ), (3) jectories s 1 , a 1 , · · · , st to arrive at status st . A future discounted γ return at time step t is defined as R t = k∞=t γ k−t R(sk , ak ), where Í where h(·|θ ) is a neural network with the fixed parameter θ , indi- γ is a scalar factor representing the discount. A policy is denoted cating that cl , ch are unobservable but relevant to attribute vector as πθ (at |st ) which is a probability distribution mapping from S to x t . Intuitively, when the product stays in introduction or maturity A , where different policies are distinguished by parameter θ . stage, the CTR can be only influenced by the noise. When the prod- The target of agent in reinforcement learning is to maximize the uct in the growth stage, f will be a positive increment, making the expected discounted return, and the performance objective can be CTR increased up to the upper bound ch . Similar analysis can be denoted as obtained for the product in the decline stage.  γ max J = E R 1 π ] t > t2 , q < q2 π = Es∼d π ,a∼πθ [R(s, a)] (4) t > t1 q > q2 t > t3 g: z=0 z=1 z=2 z=3 where d π (s) is a discounted state distribution indicating the possi- bility to encounter a state s under the policy of π . An action-value function is then obtained iteratively as Figure 1: State transition during product lifecycle Q(st , at ) = E R(st , at ) + γ Ea∼πθ [Q(st +1 , at +1 )]   (5) Then we define the state transition function of product lifecycle In order to avoid calculating the gradients of the changing state as a finite state machine as illustrated in Fig. 1. The product starts distribution in continuous action space, the Deterministic Policy with the initial stage z = 0, and enters the growth stage when the Gradient(DPG) method [26, 27] and the Deep Deterministic Policy time exceeds t 1 . During the growth stage, a product can either step Gradient [28] are brought forward. Gradients of the deterministic in to the maturity stage if its accumulated impressions q reaches q 2 , policy π is or the decline stage if the time exceeds t 2 while q is less than q 2 . A ∇θ µ J = Es∼d µ ∇θ µ Q w (s, a)   product in the maturity stage will finally enter the last decline stage = Es∼d µ ∇θ µ µ(s)∇a Q w (s, a)|a=µ(s)   (6) if the time exceeds t 3 . Otherwise, the product will stay in current stage. Here, t 1 , t 2 , t 3 , q 2 are the latent thresholds of products. where µ is the deep actor network to approximate policy function. We simulate several product during the whole lifecycle with And the parameters of actor network can be updated as different latent parameters (the details can be found in the experi- θ µ ← θ µ + αE ∇θ µ µ(st )∇a Q w (st , at )|a=µ(s)   (7) mental settings), the CTR curves follow the exact trend described in Fig. 2. where Q w is an obtained approximation of action-value function called critic network. Its parameter vector w is updated according 3.2 Reinforcement Learning and DDPG to objective methods min L = Es∼d µ yt − Q w (st , at ))2   (8) w Reinforcement learning maximizes accumulated rewards by trial- where yt = R(st , at ) + γQ w (st +1 , µ ′ (st +1 )), µ ′ is the target actor ′ and-error approach in a sequential decision problem. The sequen- network to approximate policy π , Q w is the target critic network ′ tial decision problem is formulated by MDP as a tuple of state SIGIR 2018 eCom, July 2018, Ann Arbor, Michigan, USA Hua-Lin He et al. to approximate action-value function. The parameters w ′, θ µ are ′ meaning of this formulation is the mathematical expect over all updated softly as products in platform for the average click amount of an product w ′ ← τw ′ + (1 − τ )w during its lifecycle, indicating the efficiency of products in the platform and it can be calculated accumulatively in the online θ µ ← τθ µ + (1 − τ )θ µ ′ ′ (9) environment, which can be approximately obtained by n i t 4 A SCALABLE REINFORCEMENT R(s, a) ≈ 1Õ 1 Õ pi ui (15) MECHANISM DESIGN FRAMEWORK n i ti τ =0 τ τ In our scenario, at each step, the platform observes the global infor- A major issue in the above model is that, in practices there will mation of all the products, and then allocates impressions according be millions or even billions of products, making combinations of to the observation and some certain strategy, after which the prod- all attribute vectors to form a complete system state with size n × d ucts get their impressions and update itself with the attributes as computationally unaffordable as referred in essays [11]. A straight- well as the lifecycle stages. Then the platform is able to get a feed- forward solution is to applying feature engineering technique to back to judge how good its action is, and adjust its strategy based generate a low dimension representation of the state as sl = G(s), on all the feedbacks. The above procedures leads to a standard where G is a pre-designed aggregator function to generate a low di- sequential decision making problem. mensional representation of the status. However, the pre-designed However, application of reinforcement learning to this problem aggregator function is a completely subjective and highly depends encounters sever computational issues, due to high dimensionality on the the hand-craft features. Alternatively, we attempt to tackle of both action space and state space, especially with a large n. this problem using a simple sampling based method. Specifically, Thus, we model the impression allocation problem as a standard the state is approximated by ns products uniformly sampled from reinforcement learning problem formally, by regarding the global all products information of the platform as the state ŝ = [x 1 , x 2 , · · · , x ns ]T ∈ Rns ×d (16) s = [x 1 , x 2 , ..., x n ]T ∈ Rn×d (10) where ŝ is the approximated state. Then, two issues arise with such where n is the number of the product in the platform, d is the dimen- sampling method: sion of the attribute space, and regarding the parameter adjustion • In which order should the sampled ns products permutated of a score function as the action, in ŝ, to implement the permutation invariance? a = π (s |θ µ ) ∈ Rd (11) • How to reduce the bias brought by the sampling procedure, especially when ns is much smaller than n? where π is the policy to learn parameterize by θ µ , and the action a To solve these two problem, we further propose the first principal can be further used to calculate scores of all products component based permutation and the repeated sampling based 1 experiences generation, which are described in the following sub- oi = , ∀i ∈ {1, 2, ..., n} (12) 1 + e −a x i T sections in details. After which the result of impression allocation over all n products can be obtained by 4.1 First Principal Component based e oi Permutation ui = Ín o , ∀i ∈ {1, 2, ..., n} (13) i e i The order of each sampled product in the state vector has to be Without loss of generosity, we assume at each step the summation proper arranged, since the unsorted state matrix vibrates severely of impressions allocated is 1, i.e., ni ui = 1. As is well known, during training process, making the parameters in network hard to Í products number n(billions) is far bigger than products attributes converge. To avoid it, a simple way for permutation is to make order dimensions d(thousands) in large scale E-commerce platforms. By according to a single dimension, such as the brought time ti , or the such definition, the dimension of the action space is reduced to d, sig- accumulated impressions qi . However, such ad-hoc method may nificantly alleviating the computational issue in previous work [12], lose information due to the lack of general principles. For example, where the the dimension of the action space is n. if we sort according to a feature that is almost the same among The goal of policy is to speeded up the metabolism by scoring all products, state matrix will keep vibrating severely between ob- and ranking products under the consideration of product lifecycle, servations. A suitable solution is to sort the products in an order making the new products grow into maturity stage as quickly as that keep most information of all features, where the first principal possible and keeping the the global efficiency from dropping down components are introduced [29]. We design a first principal compo- during a long term period. Thus, we define the reward related to s nent based permutation algorithm, to project each x i into a scalar and a as vi and sort all the products according to vi n  ∫t i dq(t)     R(s, a) = 1 Õ  1 p(t) dt (14) et = arg max e Tst Tst e (17) n i  ti dt  ∥e ∥=1  t =0 β ê + (1 − β) (et − ê)  ê =  where ti is the time step of the i-th product after being brought (18) ∥β ê + (1 − β) (et − ê)∥ to the platform, p(t), q(t) is the click through rate function and accumulated impressions of a product respectively. The physical vi = ê Tx i , i = 1, 2, · · · , ns (19) Speeding up the Metabolism in E-commerce by Reinforcement Mechanism DesignSIGIR 2018 eCom, July 2018, Ann Arbor, Michigan, USA where et is the first principal component of system states in current Algorithm 1: The Scalable Reinforcement Mechanism Design step t obtained by the classic PCA method as in Eq. 17. ê is the Framework projection vector softly updated by et in Eq. 18, with which we Initialize the parameters of the actor-critic network calculate the projected score of each products in Eq. 19. Here 0 < θ µ , w, θ µ , w ′ ′ β < 1 is a scalar indicating the decay rate of ê. Finally, the state Initialize the replay buffer M vector is denoted as j Initialize m observations ŝ 0 ŝ = [x k1 , x k2 , · · · , x kns ]T (20) Initialize the first principal component p̂ by ŝ 0 foreach training step t do where k 1 , k 2 , · · · , kns is the order of products, sorted by vi . Select action at = µ(ŝt1 |θ µ ) Execute action at and observe reward r t 4.2 Repeated Sampling based Experiences foreach j ∈ 1, 2, · · · , m do Generation Sample a random subset of ns products We adopt the classic experience replay technique [30, 31] to enrich Combine an observation in the order of x kTê T j  experiences during the training phase just as other reinforcement ŝt ← x k1 , x k2 , · · · , x kns learning applications. In the traditional experience replay tech- nique, the experience is formulated as (st , at , r t , st +1 ). However, Update first principal component  jT j  as what we describe above, there are Cnns observations each step et ← arg max e Tŝt ŝt e ∥e ∥=1 theoretically, since we need to sample ns products from all the n ê ← norm (β ê + (1 − β) (et − ê)) products to approximate the global statistics. If ns is much smaller end than n, such approximation will be inaccurate. foreach i, j ∈ 1, 2, · · · , m do To reduce the above bias, we propose the repeated sampling j based experiences generation. For each original experience, we do M ← M ∪ {(ŝti , at , r t , ŝt +1 )} repeated sampling st and st +1 for m times, to obtain m 2 experiences end of Sample nk transitions from M: (ŝk , ak , r k , ŝk +1 ) j (ŝti , at , r t , ŝt +1 ), i, j ∈ 1, 2, · · · , m (21) Update critic and actor networks αw Õ as illustrated in Fig. 3. This approach improves the stability of ob- w ←w + (yk − Q w (ŝk , ak ))∇w Q w (ŝk , ak ) nk k (oi,t , at , Rt , oj,t+1 ) µ µ αµ Õ ∇θ µ µ(ŝk )∇ak Q w (ŝk , ak ) (st , at , Rt , st+1 ) θ ←θ + nk k t t Update the target networks at+1 at+1 Sliding Pool Sampling Batch agent Sliding Pool Sampling Batch agent w ′ ← τw ′ + (1 − τ )w θ µ ← τθ µ + (1 − τ )θ µ ′ ′ Figure 3: Classical experiences generation(left): One experi- end ence is obtained each step by pair(st , at , r t , st +1 ); Repeated sampling based experiences generation(right): m2 experi- j ences are obtained each step by pair(ŝti , at , r t , ŝt +1 ) Finally, the agent observes system repeatedly and train the actor- critic network to learn an optimized policy gradually. servation in noise environment. It is also helpful to generate plenty of experiences in the situation that millions of times repetition is 5 EXPERIMENTAL RESULTS unavailable. To demonstrate how the proposed approach can help improve the It is worth noting that, the repeated sampling is conducted in long-term efficiency by speeding up the metabolism, we apply the the training phase. When to play in the environment, the action proposed reinforcement learning based mechanism design, as well at is obtained through a randomly selected approximated state as other comparison methods, to a simulated E-commerce platform ŝt , i.e., at = π (ŝt1 ). Actually, since at does not necessarily equal built based on the proposed product lifecycle model. to π (ŝti ), ∀i ∈ 1, 2, · · · , m, it can further help learning a invariant presentation of the approximated state observations. 5.1 The Configuration The overall procedure of the algorithm is described in Algo- The simulation is built up based on product lifecycle model pro- rithm 1. Firstly, a random sampling is utilized to get a sample of posed in section 3.1. Among all of the parameters, q 2 is uniformly system states. And then the sample is permutated by the projection sampled from [104 , 106 ], t 1 , t 2 , t 3 , δ µ , δ σ are uniformly sampled of the first principal components. After that, a one step action and from [5, 30], [35, 120], [60, 180], [104 , 106 ], [2.5 × 103 , 2.5 × 105 ] re- multiple observations are introduced to enrich experiences in expe- spectively, and parameter σ is set as 0.016 . The parameters cl , ch rience pool. Moreover, a shared convolutional neural network is are generated by a fixed neural network whose parameter is uni- applied within the actor-critic networks and target actor-critic net- formly sampled from [−0.5, 0.5] to model online environments, with works to extract features from the ordered state observation [32, 33]. the outputs scaled into the intervals of [0.01, 0.05] and [0.1, 0.15] SIGIR 2018 eCom, July 2018, Ann Arbor, Michigan, USA Hua-Lin He et al. Table 1: Parameters in learning phase 160 discounted return Param Value Reference 140 ns 103 Number of products in each sample β 0.999 First principal component decay rate 120 FPC-CNN-EXP γ 0.99 Rewards discount factor FPC-CNN τ 0.99 Target network decay rate FPC 100 T-Perm m 5 Repeated observation times 200 400 600 800 1000 1200 1400 1600 1800 step respectively. Apart from the normalized dynamic CTR p and the accumulated impressions q, the attribute vector x is uniformly sam- Figure 4: Performance Comparison between algorithms pled from [0, 1] element-wisely with the dimension d = 15. All the latent parameters in the lifecycle model are assumed unobservable improvement in speeding up the converging process. Both the three during the learning phase. FCP based algorithms converge to same final accumulated rewards The DDPG algorithm is adopted as the learning algorithm. The for their state inputs have the same observation representation. learning rates for the actor network and the critic network are 10−4 and 10−3 respectively, with the optimizer ADAM [34]. The replay buffer is limit by 2.5 × 104 . The most relevant parameters evolved 0.6 in the learning procedure are set as table 1. 0.5 Comparisons are made within the proposed reinforcement learn- percentage 0.4 ing based methods as 0.3 • CTR-A: The impressions are allocated in proportion to the Introduction CTR score. 0.2 Growth • T-Perm: The basic DDPG algorithm, with brought time 0.1 Maturity based permutation and a fully connected network to process Decline 0.0 the state 200 400 600 800 1000 1200 1400 1600 1800 • FPC: The basic DDPG algorithm, with first principal com- step ponent based permutation and a fully connected network to process the state. Figure 5: Percentage of impressions allocated to different • FPC-CNN: FPC with a shared two-layers convolutional neu- stages. ral network in actor-critic networks. • FPC-CNN-EXP: FPC-CNN with the improved experiences generation method. Then we investigate the distribution shift of the impression allocation over the 4 lifecycle stages after the training procedure where CTR-A is the classic supervised learning method and the of the FPC-CNN-EXP method, as shown in Fig. 5. It can be seen others are the proposed methods in this paper. For all the experi- that the percentage of decline stage is decreased and percentage ments, CTR-A is firstly applied for the first 360 steps to initialize of introduction and maturity stages are increased. By giving up system into a stable status, i.e., the distribution over different life- the products in the decline stage, it helps the platform to avoid the cycle stages are stable, then other methods are engaged to run for waste of the impressions since these products are always with a another 2k steps and the actor-critic networks are trained for 12.8k low CTR. By encouraging the products in the introduction stage, times. it gives the changes of exploring more potential hot products. By supporting the products in the maturity stage, it maximizes the 5.2 The Results short-term efficiency since the they are with the almost highest We firstly show the discounted accumulated rewards of different CTRs during their lifecycle. methods at every step in Fig. 4. After the initialization with the We finally demonstrate the change of the global clicks, rewards CTR-A, we find that the discounted accumulated reward of CTR-A as well as the averaged time durations for a product to grow up itself almost converges to almost 100 after 360 steps (actually that into maturity stage from its brought time at each step, in terms why 360 steps is selected for the initialization), while that of other of relative change rate compared with the CTR-A method, as is methods can further increase with more learning steps. It is showed shown in Fig. 6. The global average click increases by 6% when the that all FPC based algorithms beat the T-Perm algorithm, indicating rewards is improved by 30%. The gap here is probably caused by the that the FPC based algorithm can find a more proper permutation inconsistency of the reward definition and the global average click to arrange items while the brought time based permutation leads metric. In fact, the designed reward contains some other implicit to a loss of information, making a drop of the final accumulated objectives related to the metabolism. To further verify the guess, we rewards. Moreover, CNN and EXP algorithms perform better in ex- show that the average time for items to growth into maturity stage tracting feature from observations automatically, causing a slightly has dropped by 26%, indicating that the metabolism is significantly Speeding up the Metabolism in E-commerce by Reinforcement Mechanism DesignSIGIR 2018 eCom, July 2018, Ann Arbor, Michigan, USA speeded up. Thus, we empirically prove that, through the proposed [11] Qingpeng Cai, Aris Filos-Ratsikas, Pingzhong Tang, and Yiwei Zhang. Reinforce- reinforcement learning based mechanism design which utilizes ment mechanism design for fraudulent behaviour in e-commerce. 2018. [12] Qingpeng Cai, Aris Filos-Ratsikas, Pingzhong Tang, and Yiwei Zhang. 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