The use of product reviews in online platforms is ubiquitous and it is well established that reviews play a significant role on customer purchase decisions. The process in which reviews impact product purchases can be seen as a problem of social learning, which generically studies how agents update their beliefs for an unknown quantity of interest (e.g., product quality) based on observing actions of past agents (e.g., reading reviews by past customers). The typical assumption in the literature of social learning with reviews is that, when deciding whether to purchase a product, customers consider either all reviews provided by previous customers or a summary statistic such as their average rating. However, in practice, a common scenario may be somewhere "in between" the above two assumptions: customers read a small number of reviews in detail.

Thompson sampling has become a ubiquitous approach to online decision problems with bandit feedback. The key algorithmic task for Thompson sampling is drawing a sample from the posterior of the optimal action. We propose an alternative arm selection rule we dub TS-UCB, that requires negligible additional computational effort but provides significant performance improvements relative to Thompson sampling. At each step, TS-UCB computes a score for each arm using two ingredients: posterior sample(s) and upper confidence bounds. TS-UCB can be used in any setting where these two quantities are available, and it is flexible in the number of posterior samples it takes as input. TS-UCB achieves materially lower regret on a comprehensive suite of synthetic and real-world datasets, including a personalized article recommendation dataset from Yahoo! and a suite of benchmark datasets from a deep bandit suite proposed in Riquelme et al. (2018). Finally, from a theoretical perspective, we establish optimal regret guarantees for TS-UCB for both the K-armed and linear bandit models.

Motivated by the consideration of fairly sharing the cost of exploration between multiple groups in learning problems, we develop the Nash bargaining solution in the context of multi-armed bandits. Specifically, the 'grouped' bandit associated with any multi-armed bandit problem associates, with each time step, a single group from some finite set of groups. The utility gained by a given group under some learning policy is naturally viewed as the reduction in that group's regret relative to the regret that group would have incurred 'on its own'. We derive policies that yield the Nash bargaining solution relative to the set of incremental utilities possible under any policy. We show that on the one hand, the 'price of fairness' under such policies is limited, while on the other hand, regret optimal policies are arbitrarily unfair under generic conditions. Our theoretical development is complemented by a case study on contextual bandits for warfarin dosing where we are concerned with the cost of exploration across multiple races and age groups.

This paper provides the first sample complexity lower bounds for the estimation of simple diffusion models which seek to explain the diffusion of an epidemic in a network. The Susceptible-Infected-Recovered (SIR) model is a classic example, proposed nearly a century ago [2]. The SIR model remains a cornerstone for the forecasting of epidemics. The so-called Bass model [1] remains a basic building block in forecasting consumer adoption of new products and services. The durability of these models arises from the fact that they have shown an excellent fit to data, in numerous studies spanning both the epidemiology and marketing literatures. Somewhat paradoxically, using these same models as reliable forecasting tools presents a challenge.

As airport arrival capacities increasingly constrain the air transportation system, there is a need for mechanisms by which airlines can exchange landing slots amongst each other. We analyze two such mechanisms, scaled airline preferences and two-for-two trades, from a game-theoretic perspective. This paper investigates the extent to which strategic behavior on part of the airlines can impact the performance of each mechanism. In addition to increasing system efficiency, the reallocation mechanisms should exhibit desirable fairness and incentive properties, notions that we formally investigate in this paper. We show that neither mechanism has good incentive properties, and we develop simple, non-truthful strategies that airlines can use. Our empirical results show that for the scaled airline preferences mechanism, the best performing strategy depends greatly on the extent to which fairness is enforced. For the two-for-two trades mechanism, a simple threshold strategy can yield significant cost savings relative to the best-response strategy, and system efficiency increases when all airlines use the threshold strategy in equilibrium.