No abstract

Rideshare platforms, when assigning requests to drivers, tend to maximize profit for the system and/or minimize waiting time for riders. Such platforms can exacerbate biases that drivers may have over certain types of requests. We consider the case of peak hours when the demand for rides is more than the supply of drivers. Drivers are well aware of their advantage during the peak hours and can choose to be selective about which rides to accept. Moreover, if in such a scenario, the assignment of requests to drivers (by the platform) is made only to maximize profit and/or minimize wait time for riders, requests of a certain type (e.g., from a nonpopular pickup location, or to a non-popular drop-off location) might never be assigned to a driver. Such a system can be highly unfair to riders. However, increasing fairness might come at a cost of the overall profit made by the rideshare platform. To balance these conflicting goals, we present a flexible, non-adaptive algorithm, NAdap, that allows the platform designer to control the profit and fairness of the system via parameters α and β respectively. We model the matching problem as an online bipartite matching where the set of drivers is offline and requests arrive online. Upon the arrival of a request, we use NAdap to assign it to a driver (the driver might then choose to accept or reject it) or reject the request. We formalize the measures of profit and fairness in our setting and show that by using NAdap, the competitive ratios for profit and fairness measures would be no worse than α/e and β/e respectively. Extensive experimental results on both real-world and synthetic datasets confirm the validity of our theoretical lower bounds. Additionally, they show that NAdap under some choice of (α, β) can beat two natural heuristics, Greedy and Uniform, on both fairness and profit. Code is available at: https://github.com/ nvedant07/rideshare-fairness-peak/.

We consider two fundamental problems in stochastic optimization: approximation algorithms for stochastic matching, and sampling bounds in the black-box model. For the former, we improve the current-best bound of 3.709 due to Adamczyk, Grandoni, and Mukherjee [1], to 3.224; we also present improvements on Bansal, Gupta, Li, Mestre, Nagarajan, and Rudra [2] for hypergraph matching and for relaxed versions of the problem. In the context of stochastic optimization, we improve upon the sampling bounds of Charikar, Chekuri, and Pál [3].

Online bipartite graph matching is attracting growing research attention due to the development of dynamic task assignment in sharing economy applications, where tasks need be assigned dynamically to workers. Past studies lack practicability in terms of both problem formulation and solution framework. On the one hand, some problem settings in prior online bipartite graph matching research are impractical for real-world applications. On the other hand, existing solutions to online bipartite graph matching are inefficient due to the unnecessary real-time decision making. In this paper, we propose the dynamic bipartite graph matching (DBGM) problem to be better aligned with real-world applications and devise a novel adaptive batch-based solution framework with a constant competitive ratio. As an effective and efficient implementation of the solution framework, we design a reinforcement learning based algorithm, called Restricted Q-learning (RQL), which makes near-optimal decisions on batch splitting. Extensive experimental results on both real and synthetic datasets show that our methods outperform the state-of-the-arts in terms of both effectiveness and efficiency.• We propose the dynamic bipartite graph matching (D-BGM) problem, which is a more practical formulation of dynamic task assignment in emerging intelligent transportation and spatial crowdsourcing applications. • We devise a novel adaptive batch-based framework to solve the DBGM problem and prove that its performance is guaranteed by a constant competitive ratio 1 C−1 under the adversarial model , where C is the maximum duration of a worker/task.• We propose an effective and efficient RL-based algorithm, Restricted Q-learning (RQL), to retrieve a near-optimal batch-based strategy. • We validate the effectiveness and efficiency of our methods on synthetic and real datasets. Experimental results show that our methods outperform state-of-the-arts in terms of the overall revenue and running time. In the rest of this paper, we review related work in Sec. II and formally define the DBGM problem in Sec. III. We introduce the adaptive batch-based framework and analyze its competitive ratio in Sec. IV and propose an RL-based solution to find the batch splitting strategy in Sec. V. We evaluate our solutions in Sec. VI and finally conclude in Sec. VII.

Online matching problems have garnered significant attention in recent years due to numerous applications in e-commerce, online advertisements, ride-sharing, etc. Many of them capture the uncertainty in the real world by including stochasticity in both the arrival and matching processes. The Online Stochastic Matching with Timeouts problem introduced by Bansal, et al., (Algorithmica, 2012) models matching markets (e.g., E-Bay, Amazon). Buyers arrive from an independent and identically distributed (i.i.d.) known distribution on buyer profiles and can be shown a list of items one at a time. Each buyer has some probability of purchasing each item and a limit (timeout) on the number of items they can be shown.Bansal et al., (Algorithmica, 2012) gave a 0.12-competitive algorithm which was improved by Adamczyk, et al., (ESA, 2015) to 0.24. We present several online attenuation frameworks that use an algorithm for offline stochastic matching as a black box. On the upper bound side, we show that one framework, combined with a black-box adapted from Bansal et al., (Algorithmica, 2012), yields an online algorithm which nearly doubles the ratio to 0.46. Additionally, our attenuation frameworks extend to the more general setting of fractional arrival rates for online vertices. On the lower bound side, we show that no algorithm can achieve a ratio better than 0.632 using the standard LP for this problem. This framework has a high potential for further improvements since new algorithms for offline stochastic matching can directly improve the ratio for the online problem.Our online frameworks also have the potential for a variety of extensions. For example, we introduce a natural generalization: Online Stochastic Matching with Two-sided Timeouts in which both online and offline vertices have timeouts. Our frameworks provide the first algorithm for this problem achieving a ratio of 0.30. We once again use the algorithm of Bansal et al., (Algorithmica, 2012) as a black-box and plug it into one of our frameworks. * This is the full version of the paper that appeared in AAMAS-2017 [10]. There was an error in one of the offline black-box. This version fixes all the ratios in the theorems.