John Maxwell, Data Scientist, Nordstrom at MLconf Seattle 2017

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John Maxwell, a data scientist at Nordstrom, did his graduate work in international development economics, focusing on field experiments. He has since led research projects in Indonesia and Ethiopia related to microenterprise, developed large mathematical simulation models used for investment decisions by WSDOT, built dynamic pricing algorithms at Thriftbooks.com, and led the development of Nordstrom’s open source a/b testing service: Elwin. He currently focuses on contextual multi-armed bandit problems and machine learning infrastructure at Nordstrom. Abstract summary Solving the Contextual Multi-Armed Bandit Problem at Nordstrom: The contextual multi-armed bandit problem, also known as associative reinforcement learning or bandits with side information, is a useful formulation of the multi-armed bandit problem that takes into account information about arms and users when deciding which arm to pull. The barrier to entry for both understanding and implementing contextual multi-armed bandits in production is high. The literature in this field pulls from disparate sources including (but not limited to) classical statistics, reinforcement learning, and information theory. Because of this, finding material that fills the gap between very basic explanations and academic journal articles is challenging. The goal of this talk is to provide those lacking intermediate materials as well as an example implementation. Specifically, I will explain key findings from some of the more cited papers in the contextual bandit literature, discuss the minimum requirements for implementation, and give an overview of a production system for solving contextual multi-armed bandit problems.

Technology

Solving the Contextual Multi-Armed Bandit
Problem at Nordstrom
John Maxwell
Nordstrom
2017/05/19

Motivating the Problem:
Limitations of A/B testing for product recommendations

Motivating the Problem:
Limitations of A/B testing for product recommendations
Need to balance exploration and exploitation intelligently

Motivating the Problem:
Limitations of A/B testing for product recommendations
Need to balance exploration and exploitation intelligently
People aren’t all the same, though maybe similar

Exploration vs Exploitation
Explore ﬁrst: explore then learn (like A/B testing)

Exploration vs Exploitation
-greedy: exploit–but also explore a little bit

Exploration vs Exploitation
Upper Conﬁdence Bound (UCB): optimistic when uncertain

UCB Illustrated
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UCB Illustrated
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UCB Illustrated
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UCB Illustrated
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Including Context
How can we use things we know about people and products
(context) along with UCB?

Including Context
How can we use things we know about people and products
(context) along with UCB?
Train a ridge regression for each arm (regress rewards on
contexts)

Including Context
This seems hard to implement

Including Context
This seems hard to implement
Have to invert a potentially large matrix on every call

Including Context
This seems hard to implement
Have to invert a potentially large matrix on every call
How do you deal with delayed rewards?

Including Context
Notice how similar this is to classiﬁcation
arm 1 arm 2 arm 3
1 . .
. .5 .
. . 2
.8 . .

Including Context
Notice how similar this is to classiﬁcation
arm 1 arm 2 arm 3
1 . .
. .5 .
. . 2
.8 . .
We have partial feedback. . . how can we get full feedback?

Including Context
Inverse propensity scoring:
ci,t = −
ri,t(ai ) · I{π(xi,t) = ai }
pi,t(ai )
arm 1 arm 2 arm 3
c1,1 0 0
0 c2,2 0
0 0 c3,3
c1,4 0 0
Agarwal et al. (2014)

Including Context
If you think about IPS transformed rewards as costs, you can
reduce this to cost-sensitive classiﬁcation

Including Context
If you think about IPS transformed rewards as costs, you can
reduce this to cost-sensitive classiﬁcation
Can use any cost-sensitive multi-class classiﬁcation algorithm

Implementation
Dora: a node app that explores using -greedy

Implementation
Dora: a node app that explores using -greedy
Logging, delayed joins

Implementation
Dora: a node app that explores using -greedy
Logging, delayed joins
TensorFlow + TensorFlow Serving: Consistent way to train and
serve cost-sensitive classiﬁer

Questions?
twitter: @jhnmxwll
github: jmmaxwell
site: john-maxwell.com
email: john [at] john-maxwell.com

References
Agarwal, Alekh, Daniel J. Hsu, Satyen Kale, John Langford, Lihong
Li, and Robert E. Schapire. 2014. “Taming the Monster: A Fast
and Simple Algorithm for Contextual Bandits.” CoRR
abs/1402.0555. http://arxiv.org/abs/1402.0555.
Li, Lihong, Wei Chu, John Langford, and Robert E Schapire. 2010.
“A Contextual-Bandit Approach to Personalized News Article
Recommendation.” In Proceedings of the 19th International
Conference on World Wide Web, 661–70. ACM.

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