Yonatan Gur

Non-Stationary Stochastic Optimization

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget , that controls the extent of said change, and study how restrictions on this budget impact achievable performance. We identify sharp conditions under which it is possible to achieve long-run average optimality and more refined performance measures such as rate optimality that fully characterize the complexity of such problems. In doing so, we also establish a strong connection between two rather disparate strands of literature: (1) adversarial online convex optimization and (2) the more traditional stochastic approximation paradigm (couched in a non-stationary setting). This connection is the key to deriving well-performing policies in the latter, by leveraging structure of optimal policies in the former. Finally, tight bounds on the minimax regret allow us to quantify the “price of non-stationarity,” which mathematically captures the added complexity embedded in a temporally changing environment versus a stationary one.

Optimization in Online Content Recommendation Services: Beyond Click-Through Rates

A new class of online services allows publishers to direct readers from articles they are currently reading to other web-based content they may be interested in. A key feature of such a dynamic recommendation service is that users interact with the provider along their browsing path. While the click-through rate of articles (a myopic performance indicator) is often the key metric accounted for in the recommendation process, we quantify the performance improvement that one may capture by accounting for the potential future path of users. To that end, using a large data set of user path history at major media sites, we develop a representation of content along two key dimensions: clickability, the likelihood to click to an article when it is recommended; and engageability, the likelihood to click from an article when it hosts a recommendation. We introduce a class of path-focused heuristics that leverages engageability values, quantify its performance and then test its impact when integrated into the operating system of a worldwide leading provider of content recommendations. We conduct a live experiment to compare the performance of these heuristics (adjusting for the limitations of real-time information flow) to that of current algorithms used by the service provider. The experiment documents the improvement relative to current practice, which is attributable to accounting for the future path of users through the engageability parameters when optimizing recommendations.

Technical Note—The Competitive Facility Location Problem in a Duopoly: Advances Beyond Trees

We consider a competitive facility location problem on a network where consumers located on vertices wish to connect to the nearest facility. Knowing this, each competitor locates a facility on a vertex, trying to maximize market share. We focus on the two-player case and study conditions that guarantee the existence of a pure-strategy Nash equilibrium for progressively more complicated classes of networks. For general graphs, we show that attention can be restricted to a subset of vertices referred to as the central block. By constructing trees of maximal bi-connected components, we obtain sufficient conditions for equilibrium existence. Moreover, when the central block is a vertex or a cycle (for example, in cactus graphs), this provides a complete and efficient characterization of equilibria. In that case, we show that both competitors locate their facilities in a solution to the 1-median problem, generalizing a well-known insight arising from Hotelling’s model. We further show that an equilibrium must...

Framework Agreements in Procurement: An Auction Model and Design Recommendations

Framework agreements (FAs) are procurement mechanisms commonly used by buying agencies around the world to satisfy demand that arises over a certain time horizon. This paper is one of the first in the literature that provides a formal understanding of FAs, with a particular focus on the cost uncertainty bidders face over the FA time horizon. We generalize standard auction models to include this salient feature of FAs and analyze this model theoretically and numerically. First, we show that FAs are subject to a sort of winner’s curse that in equilibrium induces higher expected buying prices relative to running first-price auctions as needs arise. Then, our results provide concrete design recommendations that alleviate this issue and decrease buying prices in FAs, highlighting the importance of (i) monitoring the price charged at the open market by the FA winner to bound the buying price; (ii) implementing price indexes for the random part of suppliers’ costs; and (iii) allowing suppliers the flexibility to...