4 research outputs found
Robust Dynamic Assortment Optimization in the Presence of Outlier Customers
We consider the dynamic assortment optimization problem under the multinomial
logit model (MNL) with unknown utility parameters. The main question
investigated in this paper is model mis-specification under the
-contamination model, which is a fundamental model in robust
statistics and machine learning. In particular, throughout a selling horizon of
length , we assume that customers make purchases according to a well
specified underlying multinomial logit choice model in a
()-fraction of the time periods, and make arbitrary purchasing
decisions instead in the remaining -fraction of the time periods.
In this model, we develop a new robust online assortment optimization policy
via an active elimination strategy. We establish both upper and lower bounds on
the regret, and show that our policy is optimal up to logarithmic factor in T
when the assortment capacity is constant. Furthermore, we develop a fully
adaptive policy that does not require any prior knowledge of the contamination
parameter . Our simulation study shows that our policy outperforms
the existing policies based on upper confidence bounds (UCB) and Thompson
sampling.Comment: 27 pages, 1 figur
Contextual Search in the Presence of Irrational Agents
We study contextual search, a generalization of binary search in higher
dimensions, which captures settings such as feature-based dynamic pricing.
Standard game-theoretic formulations of this problem assume that agents act in
accordance with a specific behavioral model. In practice, however, some agents
may not prescribe to the dominant behavioral model or may act in ways that are
seemingly arbitrarily irrational. Existing algorithms heavily depend on the
behavioral model being (approximately) accurate for all agents and have poor
performance in the presence of even a few such arbitrarily irrational agents.
We initiate the study of contextual search when some of the agents can behave
in ways inconsistent with the underlying behavioral model. In particular, we
provide two algorithms, one built on robustifying multidimensional binary
search methods and one on translating the setting to a proxy setting
appropriate for gradient descent. Our techniques draw inspiration from learning
theory, game theory, high-dimensional geometry, and convex analysis.Comment: Compared to the first version titled "Corrupted Multidimensional
Binary Search: Learning in the Presence of Irrational Agents", this version
provides a broader scope of behavioral models of irrationality, specifies how
the results apply to different loss functions, and discusses the power and
limitations of additional algorithmic approache