2,964 research outputs found
Dynamic Assortment Optimization with Changing Contextual Information
In this paper, we study the dynamic assortment optimization problem under a
finite selling season of length . At each time period, the seller offers an
arriving customer an assortment of substitutable products under a cardinality
constraint, and the customer makes the purchase among offered products
according to a discrete choice model. Most existing work associates each
product with a real-valued fixed mean utility and assumes a multinomial logit
choice (MNL) model. In many practical applications, feature/contexutal
information of products is readily available. In this paper, we incorporate the
feature information by assuming a linear relationship between the mean utility
and the feature. In addition, we allow the feature information of products to
change over time so that the underlying choice model can also be
non-stationary. To solve the dynamic assortment optimization under this
changing contextual MNL model, we need to simultaneously learn the underlying
unknown coefficient and makes the decision on the assortment. To this end, we
develop an upper confidence bound (UCB) based policy and establish the regret
bound on the order of , where is the dimension of
the feature and suppresses logarithmic dependence. We further
established the lower bound where is the cardinality
constraint of an offered assortment, which is usually small. When is a
constant, our policy is optimal up to logarithmic factors. In the exploitation
phase of the UCB algorithm, we need to solve a combinatorial optimization for
assortment optimization based on the learned information. We further develop an
approximation algorithm and an efficient greedy heuristic. The effectiveness of
the proposed policy is further demonstrated by our numerical studies.Comment: 4 pages, 4 figures. Minor revision and polishing of presentatio
A Tractable Online Learning Algorithm for the Multinomial Logit Contextual Bandit
In this paper, we consider the contextual variant of the MNL-Bandit problem.
More specifically, we consider a dynamic set optimization problem, where a
decision-maker offers a subset (assortment) of products to a consumer and
observes their response in every round. Consumers purchase products to maximize
their utility. We assume that a set of attributes describes the products, and
the mean utility of a product is linear in the values of these attributes. We
model consumer choice behavior using the widely used Multinomial Logit (MNL)
model and consider the decision maker problem of dynamically learning the model
parameters while optimizing cumulative revenue over the selling horizon .
Though this problem has attracted considerable attention in recent times, many
existing methods often involve solving an intractable non-convex optimization
problem. Their theoretical performance guarantees depend on a problem-dependent
parameter which could be prohibitively large. In particular, existing
algorithms for this problem have regret bounded by ,
where is a problem-dependent constant that can have an exponential
dependency on the number of attributes. In this paper, we propose an optimistic
algorithm and show that the regret is bounded by ,
significantly improving the performance over existing methods. Further, we
propose a convex relaxation of the optimization step, which allows for
tractable decision-making while retaining the favourable regret guarantee.Comment: updated version, under revie
Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing
Key challenges in running a retail business include how to select products to
present to consumers (the assortment problem), and how to price products (the
pricing problem) to maximize revenue or profit. Instead of considering these
problems in isolation, we propose a joint approach to assortment-pricing based
on contextual bandits. Our model is doubly high-dimensional, in that both
context vectors and actions are allowed to take values in high-dimensional
spaces. In order to circumvent the curse of dimensionality, we propose a simple
yet flexible model that captures the interactions between covariates and
actions via a (near) low-rank representation matrix. The resulting class of
models is reasonably expressive while remaining interpretable through latent
factors, and includes various structured linear bandit and pricing models as
particular cases. We propose a computationally tractable procedure that
combines an exploration/exploitation protocol with an efficient low-rank matrix
estimator, and we prove bounds on its regret. Simulation results show that this
method has lower regret than state-of-the-art methods applied to various
standard bandit and pricing models. Real-world case studies on the
assortment-pricing problem, from an industry-leading instant noodles company to
an emerging beauty start-up, underscore the gains achievable using our method.
In each case, we show at least three-fold gains in revenue or profit by our
bandit method, as well as the interpretability of the latent factor models that
are learned
Revenue Maximization and Learning in Products Ranking
We consider the revenue maximization problem for an online retailer who plans
to display a set of products differing in their prices and qualities and rank
them in order. The consumers have random attention spans and view the products
sequentially before purchasing a ``satisficing'' product or leaving the
platform empty-handed when the attention span gets exhausted. Our framework
extends the cascade model in two directions: the consumers have random
attention spans instead of fixed ones and the firm maximizes revenues instead
of clicking probabilities. We show a nested structure of the optimal product
ranking as a function of the attention span when the attention span is fixed
and design a -approximation algorithm accordingly for the random attention
spans. When the conditional purchase probabilities are not known and may depend
on consumer and product features, we devise an online learning algorithm that
achieves regret relative to the approximation
algorithm, despite of the censoring of information: the attention span of a
customer who purchases an item is not observable. Numerical experiments
demonstrate the outstanding performance of the approximation and online
learning algorithms
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
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