Related papers: A duality and free boundary approach to adverse se…

Synthesizing realistic and diverse anomalous samples from limited data is vital for robust model generalization. However, existing methods struggle to reconcile fidelity and diversity, often hampered by distribution misalignment and…

We study the problem of online dynamic pricing with two types of fairness constraints: a "procedural fairness" which requires the proposed prices to be equal in expectation among different groups, and a "substantive fairness" which requires…

We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…

We study how market segmentation affects consumers when a monopolist can adjust both prices and product qualities across segments, engaging in second- and third-degree price discrimination simultaneously. We characterize the…

We study the fair allocation of indivisible resources among agents. Most prior work focuses on fairness and/or efficiency among agents. However, the allocator, as the resource owner, may also be involved in many scenarios (e.g., government…

We study the regulation of a monopolistic firm using a robust-design approach. We solve for the policy that minimizes the regulator's worst-case regret, where the regret is the difference between his complete-information payoff minus his…

The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for distortion risk measures, we give some necessary and sufficient conditions…

We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multi-dimensional preferences over several possible configurations of the good…

This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…

We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…

We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the…

Using duality theory techniques we derive simple, closed-form formulas for bounding the optimal revenue of a monopolist selling many heterogeneous goods, in the case where the buyer's valuations for the items come i.i.d. from a uniform…

Online platforms in the Internet Economy commonly incorporate recommender systems that recommend products (or "arms") to users (or "agents"). A key challenge in this domain arises from myopic agents who are naturally incentivized to exploit…

We develop a novel optimization model to maximize the profit of a Demand-Side Platform (DSP) while ensuring that the budget utilization preferences of the DSP's advertiser clients are adequately met. Our model is highly flexible and can be…

We study the envy free pricing problem faced by a seller who wishes to maximize revenue by setting prices for bundles of items. If there is an unlimited supply of items and agents are single minded then we show that finding the revenue…

We address the challenging problem of dynamically pricing complementary items that are sequentially displayed to customers. An illustrative example is the online sale of flight tickets, where customers navigate through multiple web pages.…

We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the…

Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…

In this paper, we study expected utility maximization under ratchet and drawdown constraints on consumption in a general incomplete semimartingale market using duality methods. The optimization is considered with respect to two parameters:…

We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller's problem consists of determining the optimal subset of products to offer to potential customers. To describe the…