Mingxi Zhu

Mingxi Zhu
PhD Student, Operations, Information & Technology
PhD Program Office Graduate School of Business Stanford University 655 Knight Way Stanford, CA 94305

Mingxi Zhu

I am a fifth-year PhD student in Operations, Information & Technology at the Stanford Graduate School of Business. My research interest lies in developing large scale optimization algorithms to facilitate online platforms operations and revenue management, with applications in machine learning, pricing/mechanism design and empirical marketing.

Faculty Advisors

Research Interests

  • Optimization
  • Online Platform Revenue Management

Publications

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The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. Unfortunately, the multi-block ADMM, with more than two blocks, is not guaranteed to be convergent. In this paper, we add more randomness into the ADMM by developing a randomly assembled cyclic ADMM (RAC-ADMM) where the decision variables in each block are randomly assembled. We discuss the theoretical properties of RAC-ADMM and show when random assembling helps and when it hurts, and develop a criterion to guarantee that it converges almost surely. Using the theoretical guidance on RAC-ADMM, we conduct multiple numerical tests on solving both randomly generated and large-scale benchmark quadratic optimization problems, which include continuous, and binary graph-partition and quadratic assignment, and selected machine learning problems. Our numerical tests show that the RAC-ADMM could significantly improve the computation efficiency on solving most quadratic optimization problems.

Work in Progress

Benefit of Data Exchange in Distributed Optimization and Learning (with Yinyu Ye)

Distributed optimization algorithms have been widely used in machine learning problems. In this paper, we focus on the benefit of data exchange in distributed optimization problems, with applications in linear and logistic regression. We present the theoretical evidence on showing that without data-exchange, distributed optimization algorithm achieves the worst case convergence rate under a specific class of data structures. We further propose a randomized data exchange algorithm via solving the dual problem, DRC-ADMM (Dual Randomly-assembled Cyclic ADMM) algorithm, that carefully balance the trade-off between data-exchange and computation efficiency. From numerical results, we are convinced that our algorithm provides good quality estimators within fewer iterations by only randomly exchanging 5% of pre-fixed data.

Dynamic Exploration and Exploitation: The Case of Online Lending (with Haim Mendelson)

We studied dynamic optimal credit line for the online lender under uncertainty of borrower’s type. We proved that the online lender’s optimal strategy is a mixture of exploration and exploitation. We also provided analytical solution to the optimal policy for the dynamic control problem under certain class of distributions.

Information Disclosure in Markets: An Empirical Analysis of a Search Advertising Market with Heterogeneous Advertisers (with Michelle Song)
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Bidding in search advertising is commonplace today. However, determining a bid can be challenging in light of the complexity of the auction process. By designing the mechanism and aggregating the information of many bidders, the advertiser platform can assist less sophisticated advertisers. We analyze data from a platform that initiated a bid recommendation system and find that some advertisers may simply adopt the platform's suggestion instead of constructing their own bids. We discover that these less sophisticated advertisers were lower-rated and uncertain about ad effectiveness before the platform began offering information through the recommended bids. We characterize an equilibrium model of bidding in the Generalized Second Price (GSP) auction and show that following the platform's bid suggestion is theoretically sub-optimal. We then identify sophisticated and less sophisticated advertisers' private values using observed bids and the disclosed information. Counterfactual results suggest that the ad platform can increase revenue and the total surplus when it shares more information. Furthermore, the hybrid of auto-bidding with manual bidding could be a more efficient mechanism as we substitute less sophisticated bidding behavior for algorithmic bidding. These results shed light on the importance of exploring interactions between sophisticated and less sophisticated players when designing a market.

Near-Optimal Dynamic Pricing in Large Networks (with Ozan Candogan and Yuwei Luo)

We consider networks generated by a branching process and assume that each agent/node has either low or high value for a product offered by a seller. We assume that the type of each agent coincides with that of her predecessor in the network with probability p>1/2. The seller sequentially offers prices to the agents in the network. Offering a low price to an agent guarantees a sale, but does not reveal the type of the agent, which in turn decreases the seller’s continuation payoff. The natural dynamic program for obtaining an optimal pricing policy appears to be intractable, and we propose approximation policies that partition the network into “active sets” and take optimal actions in each such set of nodes while ignoring the rest of the network. We establish that by choosing small active sets the seller can achieve tractable approaches that guarantee near-optimal revenues.