The document presents a framework for optimizing query recommendations to gently guide users towards more rewarding queries or search sessions. It formulates the problem of recommending the next query as an optimization problem that aims to maximize the expected reward of the user's search path. It proposes greedy heuristics to solve the single-step and multi-step recommendation versions of this problem and evaluates their performance on query logs. The results show the heuristics can increase expected reward compared to baselines without decreasing relevance of recommendations.

1. An Optimization Framework for
Query Recommendation
Aris Anagnostopoulos, Luca Becchetti,
Carlos Castillo, Aristides Gionis

2. Source: B. Precourt at UWM.

5. As you set
out for Ithaca,
hope your road
is a long one,
full of adventure,
full of discovery.
K. Kavafis

6. Problem
Given a set of possible user histories
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7. Problem
Given a value for different states
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8. Problem
Given a value for different states
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9. Problem
“Nudge” the users in a certain direction
-
-
+
+
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10. Problem
“Nudge” the users in a certain direction
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11. Problem definition

Given a set of possible user sessions

Given a certain value for different states

“Nudge” the users in a certain direction
Objectives
– 1. collect a large reward along the way -or-
– 2. end the session at a rewarding action
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12. Constraints
• We are not almighty
Source: not-of-this-earth.com
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13. Constraints
• We are not almighty
– We can only suggest, not order
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14. Constraints
• We are not almighty
– We can only suggest, not order
• We are not all-knowing
Source: Wikimedia commons.
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15. Constraints
• We are not almighty
– We can only suggest, not order
• We are not all-knowing
– We do not know how the users will react
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16. Framework

17. Setting
• Talk: query recommendation
• Paper: general framework
– E.g.: optimizing links in web-sites
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20. Query recommendations
• Reformulation probabilities
– P(q,q') original
0.3 central park map
0.2 central park hotel
central park
0.2 central park new york
0.3
central park zoo
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21. Query recommendations
• Reformulation probabilities
– P(q,q') original
– P'(q,q') perturbed = P(q,q') + ρ(Q,q,q')
-0.1 0.3 central park map
-0.1 0.2 central park hotel
central park
+0.1 0.2 central park new york
+0.1 0.3
central park zoo
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22. Query recommendations
• Reformulation probabilities
– P(q,q') original
– P'(q,q') perturbed = P(q,q') + ρ(Q,q,q')
0.2 central park map
0.1 central park hotel
central park
0.3 central park new york
0.4
central park zoo
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23. Example values w(·)
• Search engine results page
– Quality of search results
• General page
– Dwell time
– User ratings
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24. Objective functions U(·)
Kavafian Machiavellian
“a road full of adventure” “ends justify means”
U(<q1,q2,...,qt>) = Σw(qi) U(<q1,q2,...,qt>) = w(qt)
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25. The Kavafian objective
Useful when users want to explore, or be entertained
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26. The Kavafian objective
Useful when users want to explore, or be entertained
+ “funny video”
-
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27. Optimization problem
• Given:
– Original transition probabilities P
– Starting node q
– Node values w
– Perturbation function ρ
• Add up to k links (per node), maximize
expected utility of paths starting at q
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28. Single-step recommendation
• Recommend now, leave user alone later
q t
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29. Single-step recommendation
• Recommend now, leave user alone later
+
q t
-
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30. Multi-step recommendation
• Recommend at each step in the future
q t
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31. Multi-step recommendation
• Recommend at each step in the future
-
- +
+
q - + t
-
+ -
+
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32. Multi-step case
• Multi- and Single-step
recommendation are NP-complete
– Reduction from MAXIMUM-COVER
• Heuristic for multi-step problem:
– at each node, assume rest of the graph is
unperturbed when computing utility of
adding an edge
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33. Single-step case
• Greedy heuristic for “Machiavellian”
objective: find (qi, qj) maximizing
ρij(E[U(path(qj))] – wi)
• Repeat k times
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34. Observation
• Greedy heuristic achieves utility at least (1-x) of
the optimum, with x << 1 in cases of practical
interest
– It is possible to construct pathological
instances s.t. that greedy performs poorly
– x depends on termination probability at qi
and probabilities of following
recommendations
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35. Application

36. Large-scale experiment
We observe perturbed probabilities P'(q,q'),
unless we disable search assist to see P(q,q')
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37. Empirical observations
• Notation:
– τq, τ'q session-end probabilities
• Recommendations decrease termination
probability:
• Average τq≈0.90
• Average τ'q≈0.84
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38. Termination probability

39. Empirical observations
• Recommendations decrease
termination probability, τq≈0.90 τ'q≈0.84
• Decrease is almost entirely due to
more clicks on recommendations
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41. Empirical observations
• Recommendations decrease
termination probability from ≈0.90 to
≈0.84
• Decrease is almost entirely due to
more clicks on recommendations
• ρ is difficult to estimate
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42. P'(q,q'): with recommendations
P(q,q'): without recommendations

43. P'(q,q'): with recommendations
There is an increase
P(q,q'): without recommendations

44. Many un-seen suggestions
P'(q,q'): with recommendations are clicked when shown
P(q,q'): without recommendations

45. The rest are in general
P'(q,q'): with recommendations difficult to predict
P(q,q'): without recommendations

46. So what do we do?
• We approximate ρ by a linear function on
– P(q,q')
– Textual similarity of q and q'
– Terminal probability of q
• We have a low accuracy on this prediction
– r ≈ 0.5
• We use as weights the CTR on results
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47. Evaluation

48. Evaluation results

Baselines:
– Prefer queries with large w
– Prefer queries with large ρ
– Prefer queries with large ρw

Greedy heuristic performs better for both
utility functions
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49. Expected utility
“Kavafian” objective “Machiavellian” objective

50. Evaluation results

Greedy heuristic performs well

What about relevance?

420 queries assessed by 3 judges

There were no significant changes in
relevance between systems
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51. Conclusions
• General framework for
“nudging” users in a
certain direction
• Open algorithmic and
practical questions
• In the paper: related work
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52. Q&A