We study how small amount of data sharing could benefit distributed optimization and learning for higher order optimization algorithms. Specifically, we consider how data sharing could benefit distributed multi-block alternating direction method of multipliers (ADMM) and preconditioned conjugate gradient method (PCG) with application in machine learning tasks of least square and logistic regression. Theoretically, we prove that a small amount of data share leads to improvements from near-worst to near-optimal convergence rate when applying ADMM and PCG methods to machine learning tasks. We further propose a meta randomized data-sharing scheme and provide its tailored applications in ADMM and PCG methods in order to enjoy both the benefit from data-sharing and from the efficiency of distributed computing.

We study exploration/exploitation trade-offs in the context of online lending. Unlike traditional exploration/exploitation contexts, where the cost of exploration is an opportunity cost of lost revenue or some other implicit cost, in the case of unsecured online lending, the lender effectively gives away money in order to learn about the borrower's ability to repay. In our model, the lender maximizes the expected net present value of the cash flow she receives by dynamically adjusting the loan amounts and the interest rate as she learns about the borrower's unknown income. The lender has to carefully balance the trade-offs between earning more interest when she lends more and the risk of default, and we provide the optimal dynamic policy for the online lender. Under certain regime, the optimal policy is characterized by a large number of small experiments; while under other regime, the optimal policy consists of a two-step explore-then-commit policy.

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.

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.