31 research outputs found
Ranking an Assortment of Products via Sequential Submodular Optimization
We study an optimization problem capturing a core operational question for
online retailing platforms. Given models for the users' preferences over
products as well as the number of items they are willing to observe before
clicking on one or abandoning the search, what is the best way to rank the
relevant products in response to a search query?
In order to capture both popularity and diversity effects, we model the
probability that a user clicks on an element from a subset of products as a
monotone submodular function of this set. We also assume that the patience
level of the users, or the number of items they are willing to observe before
clicking on one or abandoning the search, is a given random variable. Under
those assumptions, the objective functions capturing user engagement or
platform revenue can be written as a new family of submodular optimization
problems over a sequence of elements.
We call this family of natural optimization problems sequential submodular
optimization. By building on and extending the literature on submodular
maximization subject to matroid constraints, we derive a (1-1/e) optimal
approximation algorithm for maximizing user engagement and a bi-criteria
approximation algorithm for maximizing revenue subject to a lower bound on user
engagement
Beyond Submodularity: A Unified Framework of Randomized Set Selection with Group Fairness Constraints
Machine learning algorithms play an important role in a variety of important
decision-making processes, including targeted advertisement displays, home loan
approvals, and criminal behavior predictions. Given the far-reaching impact of
these algorithms, it is crucial that they operate fairly, free from bias or
prejudice towards certain groups in the population. Ensuring impartiality in
these algorithms is essential for promoting equality and avoiding
discrimination. To this end we introduce a unified framework for randomized
subset selection that incorporates group fairness constraints. Our problem
involves a global utility function and a set of group utility functions for
each group, here a group refers to a group of individuals (e.g., people)
sharing the same attributes (e.g., gender). Our aim is to generate a
distribution across feasible subsets, specifying the selection probability of
each feasible set, to maximize the global utility function while meeting a
predetermined quota for each group utility function in expectation. Note that
there may not necessarily be any direct connections between the global utility
function and each group utility function. We demonstrate that this framework
unifies and generalizes many significant applications in machine learning and
operations research. Our algorithmic results either improves the best known
result or provide the first approximation algorithms for new applications.Comment: This paper has been accepted for publication in the Journal on
Combinatorial Optimizatio
Non-monotone Sequential Submodular Maximization
In this paper, we study a fundamental problem in submodular optimization,
which is called sequential submodular maximization. Specifically, we aim to
select and rank a group of items from a ground set such that the
weighted summation of (possibly non-monotone) submodular functions is maximized, here each function
takes the first items from this sequence as input. The existing
research on sequential submodular maximization has predominantly concentrated
on the monotone setting, assuming that the submodular functions are
non-decreasing. However, in various real-world scenarios, like diversity-aware
recommendation systems, adding items to an existing set might negatively impact
the overall utility. In response, this paper pioneers the examination of the
aforementioned problem with non-monotone submodular functions and offers
effective solutions for both flexible and fixed length constraints, as well as
a special case with identical utility functions. The empirical evaluations
further validate the effectiveness of our proposed algorithms in the domain of
video recommendations. The results of this research have implications in
various fields, including recommendation systems and assortment optimization,
where the ordering of items significantly impacts the overall value obtained
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
SEQUENTIAL DECISION MAKING WITH LIMITED RESOURCES
One of the goals of Artificial Intelligence (AI) is to enable multiple agents to interact, co-ordinate and compete with each other to realize various goals. Typically, this is achieved via a system which acts as a mediator to control the agents' behavior via incentives. Such systems are ubiquitous and include online systems for shopping (e.g., Amazon), ride-sharing (e.g., Uber, Lyft) and Internet labor markets (e.g., Mechanical Turk). The main algorithmic challenge in such systems is to ensure that they can operate under a variety of informational constraints such as uncertainty in the input, committing to actions based on partial information or being unaffected by noisy input. The mathematical framework used to study such systems are broadly called \emph{sequential decision making} problems where the algorithm does not receive the entire input at once; it obtains parts of the input by interacting (also called "actions") with the environment.
In this thesis, we answer the question, under what informational constraints can we design efficient algorithms for sequential decision making problems.
The first part of the thesis deals with the Online Matching problem. Here, the algorithm deals with two prominent constraints: uncertainty in the input and choice of actions being restricted by a combinatorial constraint. We design several new algorithms for many variants of this problem and provide provable guarantees. We also show their efficacy on the ride-share application using a real-world dataset. In the second part of the thesis, we consider the Multi-armed bandit problem with additional informational constraints. In this setting, the algorithm does not receive the entire input and needs to make decisions based on partial observations. Additionally, the set of possible actions is controlled by global resource constraints that bind across time. We design new algorithms for multiple variants of this problem that are worst-case optimal. We provide a general reduction framework to the classic multi-armed bandits problem without any constraints. We complement some of the results with preliminary numerical experiments
Recommended from our members
Fundamental Tradeoffs for Modeling Customer Preferences in Revenue Management
Revenue management (RM) is the science of selling the right product, to the right person, at the right price. A key to the success of RM, which now spans a broad array of industries, is its grounding in mathematical modeling and analytics. This dissertation contributes to the development of new RM tools by: (1) exploring some fundamental tradeoffs underlying any RM problems, and (2) designing efficient algorithms for some RM applications. Another underlying theme of this dissertation is the modeling of customer preferences, a key component of any RM problem.
The first chapters of this dissertation focus on the model selection problem: many demand models are available but picking the right model is a challenging task. In particular, we explore the tension between the richness of a model and its tractability. To quantify this tradeoff, we focus on the assortment optimization problem, a very general and core RM problem. To capture customer preferences in this context, we use choice models, a particular type of demand model. In Chapters 1, 2, 3 and 4 we design efficient algorithms for the assortment optimization problem under different choice models. By assessing the strengths and weaknesses of different choice models, we can quantify the cost in tractability one has to pay for better predictive power. This in turn leads to a better understanding of the tradeoffs underlying the model selection problem.
In Chapter 5, we focus on a different question underlying any RM problem: choos- ing how to sell a given product. We illustrate this tradeoff by focusing on the problem of selling ad impressions via Internet display advertising platforms. In particular, we study how the presence of risk-averse buyers affects the desire for reservation con- tracts over real time buy via a second-price auction. In order to capture the risk aversion of buyers, we study different utility models
On the Correlation Gap of Matroids
A set function can be extended to the unit cube in various ways; the
correlation gap measures the ratio between two natural extensions. This
quantity has been identified as the performance guarantee in a range of
approximation algorithms and mechanism design settings. It is known that the
correlation gap of a monotone submodular function is , and this is tight
even for simple matroid rank functions.
We initiate a fine-grained study of correlation gaps of matroid rank
functions. In particular, we present improved lower bounds on the correlation
gap as parametrized by the rank and the girth of the matroid. We also show that
the worst correlation gap of a weighted matroid rank function is achieved under
uniform weights. Such improved lower bounds have direct applications for
submodular maximization under matroid constraints, mechanism design, and
contention resolution schemes. Previous work relied on implicit correlation gap
bounds for problems such as list decoding and approval voting
On Connections Between Machine Learning And Information Elicitation, Choice Modeling, And Theoretical Computer Science
Machine learning, which has its origins at the intersection of computer science and statistics, is now a rapidly growing area of research that is being integrated into almost every discipline in science and business such as economics, marketing and information retrieval. As a consequence of this integration, it is necessary to understand how machine learning interacts with these disciplines and to understand fundamental questions that arise at the resulting interfaces. The goal of my thesis research is to study these interdisciplinary questions at the interface of machine learning and other disciplines including mechanism design/information elicitation, preference/choice modeling, and theoretical computer science