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Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…
Handling symmetries in optimization problems is essential for devising efficient solution methods. In this article, we present a general framework that captures many of the already existing symmetry handling methods. While these methods are…
Using AI approaches to automatically design mechanisms has been a central research mission at the interface of AI and economics [Conitzer and Sandholm, 2002]. Previous approaches that attempt to design revenue optimal auctions for the…
In this paper, we introduce a numeraire-free and original probability based framework for financial markets. We reformulate or characterize fair markets, the optional decomposition theorem, superhedging, attainable claims and complete…
We consider a general problem where an agent is in a multi-agent environment and must plan for herself without any prior information about her opponents. At each moment, this pivotal agent is faced with a trade-off between exploiting her…
Convergence (virtual) bidding is an important part of two-settlement electric power markets as it can effectively reduce discrepancies between the day-ahead and real-time markets. Consequently, there is extensive research into the bidding…
Conditional risk minimization arises in high-stakes decisions where risk must be assessed in light of side information, such as stressed economic conditions, specific customer profiles, or other contextual covariates. Constructing reliable…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
Posted price mechanisms are prevalent in allocating goods within online marketplaces due to their simplicity and practical efficiency. We explore a fundamental scenario where buyers' valuations are independent and identically distributed,…
In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the…
This paper studies optimal market making for large-tick assets in the presence of latency. We consider a random walk model for the asset price, and formulate the market maker's optimization problem using Markov Decision Processes (MDP). We…
We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii)…
Recent years have witnessed increasing concerns towards unfair decisions made by machine learning algorithms. To improve fairness in model decisions, various fairness notions have been proposed and many fairness-aware methods are developed.…
Various distributed optimization methods have been developed for solving problems which have simple local constraint sets and whose objective function is the sum of local cost functions of distributed agents in a network. Motivated by…
With some regularity conditions maximum likelihood estimators (MLEs) always produce asymptotically optimal (in the sense of consistency, efficiency, sufficiency, and unbiasedness) estimators. But in general, the MLEs lead to non-robust…
We design an expected polynomial-time, truthful-in-expectation, (1-1/e)-approximation mechanism for welfare maximization in a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are m matroid rank…
We consider data-driven inventory and pricing decisions in the feature-based newsvendor problem, where demand is influenced by both price and contextual features and is modeled without any structural assumptions. The unknown demand…
We develop a unified framework to characterize the power of higher-level algorithms for the constraint satisfaction problem (CSP), such as $k$-consistency, the Sherali-Adams LP hierarchy, and the affine IP hierarchy. As a result,…
Combinatorial optimization problems (COPs) with discrete variables and finite search space are critical across numerous fields, and solving them in metaheuristic algorithms is popular. However, addressing a specific COP typically requires…
Optimizing shared vehicle systems (bike/scooter/car/ride-sharing) is more challenging compared to traditional resource allocation settings due to the presence of \emph{complex network externalities} -- changes in the demand/supply at any…