Download presentation

Presentation is loading. Please wait.

Published byEliseo Pallett Modified over 2 years ago

1
TFG - MARA, Budapest, September 20051 Modeling Complex Multi-Issue Negotiations Using Utility Graphs Valentin Robu, Koye Somefun, Han La Poutré CWI, Center for Mathematics and Computer Science, Amsterdam, The Netherlands

2
TFG - MARA, Budapest, September 20052 Multi-issue (multi-item) negotiation Negotiation = method of competitive (or partially cooperative) allocation of goods, resources, tasks between agents Applications: E-commerce: Bundling can be an effective method to increase sales (use in recommender systems) High degree of customization – possible through negotiations Logistics: mechanism for task allocation Many deals are negotiated bilaterally or in closed groups of companies (e.g. transportation contracts) Utility functions are not (or partially) revealed => indirect revelation mechanism Search with incomplete information

3
TFG - MARA, Budapest, September 20053 Utility functions for multi-issue negotiations Linearly additive: Linear combination of issue utilities: Search space is structured -> more accesible to heuristics [Faratin Sierra & Jennings. 2002], [Jonker & Robu 2004], [Coehoorn & Jennings 2004] [Gerding & La Poutre, 2004] “Auction-type”: XOR of ANDs K-additive: Captures local substitutability/complementarity effects between k issues Finding optimal allocation can become hard even for the 2- additive case Exiting solutions: assume a trusted mediator, computationally expensive (3000-5000 bids for 50 issues) [Klein, Faratin, Sayama & Bar-Yam, 2003] [Lin 2004]

4
TFG - MARA, Budapest, September 20054 Utility graphs: basic ideas Inspiration: probabilistic graphical models Each node = one issue under negotiation (or item in a bundle) Nodes grouped into clusters of connected nodes Cost of representation Exponential in size of the cluster Linear in the number of clusters Use in negotiation Opponent modelling: seller maintains & updates a model of buyer’s preferences

5
TFG - MARA, Budapest, September 20055 Utility graphs: an example Global utility is a sum of utility over clusters, rather than individual issues Buyer - cluster potentials: u(I1) = $7, u(I2) = $5, u(I3) = $0 u(I4) = $0, u(I1, I2)= - $5, u(I2, I3)=$4,u(I2, I4)=$4 Seller - all items have cost $2. u BUYER (I1=1, I2=0, I3=1, I4=0) = $7 Gains from Trade = Buyer_utility – Seller_Cost Optimal combination? GT(I1=0, I2=1, I3=1, I4=1)=$13 - 3*$2 = $7

6
TFG - MARA, Budapest, September 20056 Utility graphs: Use in negotiation Bundles with maximal G.T. Pareto-optimal bundles [Somefun, Klos & La Poutré 2004] Seller keeps a model of the utility graph of the buyer and aims for a bundle with maximal GT After each counter-offer, he updates this model (true graph of the buyer remains hidden) Seller knows a super-graph of possible buyer utility graphs (qualitative assumption)

7
TFG - MARA, Budapest, September 20057 Partitioning a utility graph Q: How to select the bundle with a maximal GT, with respect to a utility graph learned so far? A1 (Brute force answer): generate all possible bundles and select the best one. Complexity for 50 issues: 2 50 > 10 15 bundles A2: Partition the graph into sub-graphs Nodes belonging to more than 1 subgraph = cutset nodes For all possible instantiations of cutset nodes, compute local sub-bundle combination Merge them, such that a local optimum is achieved

8
TFG - MARA, Budapest, September 20058 Partitioning a utility graph (2) Complexity of exploring all bundles: 2 c * (2 p + 2 q ) Partitions can be found in polynomial time (always for graphs of tree-width 2)

9
TFG - MARA, Budapest, September 20059 Learning in utility graphs (1) Seller has a super-graph for possible inter- dependencies in the buyer population This graph contains tables for each cluster, with size 2 at the power of size of the cluster Initial values = proportional to the Hamming distance Values are adjusted as follows:, for the combination induced from buyer’s bid, for all other combinations

10
TFG - MARA, Budapest, September 200510 Learning: a simple example Two complementary issues: I1 and I2 I1I2time t t+1t+2 00000 01$7$8.4$10 10$5$4$3.2 11$17$13.6$10.9 Buyer asks, for several rounds: I1=0, I2=1 This combination gets updated with (1+α), the others with (1-α) Supposing costs are c(I1)=c(I2)=$3, α=0.2 the bundle with maximal GT changes from (1,1) to (0,1) after 2 steps

11
TFG - MARA, Budapest, September 200511 Learning in utility graphs (2) The cluster update factor is clique-specific: |C| = total number of cliques; α, β = learning parameters Where the clique Gains from Trade Ratio is defined as ratio of “local” (per clique) vs. total (bundle-wide) GT: We adjust the model more towards the other’s value for clusters which are less important, and less for the others

12
TFG - MARA, Budapest, September 200512 Experimental validation: set-up Graph with 50 issues, 28 clusters: 3 of size 4, 16 of size 3, 6 of size 2, 3 of size 1 Costs and strength of interdependencies: drawn from a independent, normal distributions (i.i.d-s): Means around 1*(Hamming Distance) Spreads between 0 and 5 => highly non-linear search space Results averaged for 100 tests/configuration

13
TFG - MARA, Budapest, September 200513 Experimental results

14
TFG - MARA, Budapest, September 200514 Negotiation part: Conclusions It is possible to reach Pareto-efficient outcomes reasonably fast, by exploiting the decomposable structure of utility functions Consequence: We can handle complex negotiations even in time constrained domains / with buyer impatience Assumption: A structure of the super-graph for the population of likely buyers Solution: collaborative filtering past negotiation data

15
TFG - MARA, Budapest, September 200515 Structure of the initial utility graph Preferences of buyers are in some way clustered Class (population) of buyers with similar preference structures => largely overlapping utility graphs Can we estimate which items can be potentially complementary/substitutable by looking at previous buying patterns? Collaborative filtering asks the same questions ! Not all relationships hold for all users – only a super-graph of these relationships is required

16
TFG - MARA, Budapest, September 200516 Architecture & simulation model view

17
TFG - MARA, Budapest, September 200517 Collaborative filtering: Overview Output recommendations to buyers, based on previous buy instances User-based: for each user, select a neighbourhood of users with a similar preferences Item-based: identify relationships between items, based on previous buying patterns In our case, recommendation step is completely replaced by negotiation => more customization possible

18
TFG - MARA, Budapest, September 200518 Step 1: Data preparation Items Previous negotiations I1I1 I2I2 I K...I 50 Neg. 10110 Neg. 2 … 1…1… 1…1… 0…0… 1…1… Neg. N (eg. N=2000) 1100 Negotiation outcomes matrix Item pairs I1I1 I2I2 I K...I 50 I1I1 N134…220 I2I2 134N…… IKIK ………… I 50 220……N 1-1 pairs: N i,j (1,1) 1-0 pairs: N i,j (0,1) 0-1 pairs: N i,j (1,0) 0-0 pairs: N i,j (0,0) Total no. buys (out of N) N 1 (1)N 2 (1)N K (1)..N 50 (1) 260130…50 4 Item-item matrixes

19
TFG - MARA, Budapest, September 200519 Step 2: Data analysis (1) Compute item-item similarity, based on the appearance data ItemI1I1 I K...I 50 I1I1 N…220 IKIK ……… I 50 220…N ItemI1I1 I K...I 50 I1I1 1…0.84 IKIK 0.23…… I 50 0.84…1 Number Buys / item N 1 (1)…N 50 (1) 26050 4 Item-item matrixes Total number buys/item Cosine / correlation matrix 2 matrixes for cosine- based similarity 1 matrix for correlation- based similarity

20
TFG - MARA, Budapest, September 200520 Criteria 1: Cosine-based similarity Measure of distance between the buying vectors for two items i, j Intuitive, but not so precise Complementarity effect: Substitutability effect:

21
TFG - MARA, Budapest, September 200521 Criteria 2: Correlation-based similarity Average buys per item: Similarity between items i and j:

22
TFG - MARA, Budapest, September 200522 Results: Correlation-based similarity

23
TFG - MARA, Budapest, September 200523 Conclusions & discussion Utility graphs efficient way to guide online learning of buyer preferences in electronic negotiations Learning a starting structure of these graphs – possible through collaborative filtering By combining the two techniques => relatively short negotiations (around 20 steps/50 issues) Intuition: we explicitly utilize the clustering effect between utility functions of typical buyers Personalization techniques used in collaborative filtering can be successfully combined with personalization through agent-mediated negotiation

24
TFG - MARA, Budapest, September 200524 Questions Thank you very much for your attention! Full paper(s) available from: homepages.cwi.nl/~robu

Similar presentations

OK

1 Information Filtering & Recommender Systems (Lecture for CS410 Text Info Systems) ChengXiang Zhai Department of Computer Science University of Illinois,

1 Information Filtering & Recommender Systems (Lecture for CS410 Text Info Systems) ChengXiang Zhai Department of Computer Science University of Illinois,

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on ice cream industry Ppt on word association test pdf Ppt on java swing components Ppt on power generation by speed breaker games Ppt on diode as rectifier bridge Free ppt on rocks and minerals Ppt on latest gadgets used at home Ppt on group life insurance Ppt on endangered species in india Ppt on acid bases and salts for class 10