Related papers: An Improved Combinatorial Polynomial Algorithm for…
We consider the assortment optimization problem with disjoint-cardinality constraints under two-level nested logit model. To solve this problem, we first identify a candidate set with $O(mn^2)$ assortments and show that at least one optimal…
Kakade, Kearns, and Ortiz (KKO) introduce a graph-theoretic generalization of the classic Arrow--Debreu (AD) exchange economy. Despite its appeal as a networked version of AD, we argue that the KKO model is too local, in the sense that…
We develop a unified ascending-auction framework for computing Walrasian equilibria in combinatorial markets with strong substitutes valuations and piecewise-linear payment functions. Our auction extends the celebrated ascending auctions of…
Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are…
Causal effect estimation from observational data is a fundamental task in empirical sciences. It becomes particularly challenging when unobserved confounders are involved in a system. This paper focuses on front-door adjustment -- a classic…
We consider an algorithm to approximate complex-valued periodic functions $f(e^{i\theta})$ as a matrix element of a product of $SU(2)$-valued functions, which underlies so-called quantum signal processing. We prove that the algorithm runs…
This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances. By…
In this paper, we present an improved algorithm for the All Pairs Non-decreasing Paths (APNP) problem on weighted simple digraphs, which has running time $\tilde{O}(n^{\frac{3 + \omega}{2}}) = \tilde{O}(n^{2.686})$. Here $n$ is the number…
We present a midpoint policy iteration algorithm to solve linear quadratic optimal control problems in both model-based and model-free settings. The algorithm is a variation of Newton's method, and we show that in the model-based setting it…
The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…
Online learning algorithms are widely used in strategic multi-agent settings, including repeated auctions, contract design, and pricing competitions, where agents adapt their strategies over time. A key question in such environments is how…
We apply Reinforcement Learning algorithms to solve the classic quantitative finance Market Making problem, in which an agent provides liquidity to the market by placing buy and sell orders while maximizing a utility function. The optimal…
We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of $N$ items and a discrete time horizon of…
Consider sellers in a competitive market that use algorithms to adapt their prices from data that they collect. In such a context it is plausible that algorithms could arrive at prices that are higher than the competitive prices and this…
In this paper, we establish a connection between ranking theory and general equilibrium theory. First of all, we show that the ranking vector of PageRank or Invariant method is precisely the equilibrium of a special Cobb-Douglas market.…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
Complements between goods - where one good takes on added value in the presence of another - have been a thorn in the side of algorithmic mechanism designers. On the one hand, complements are common in the standard motivating applications…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
He and Yuan's prediction-correction framework [SIAM J. Numer. Anal. 50: 700-709, 2012] is able to provide convergent algorithms for solving separable convex optimization problems at a rate of $O(1/t)$ ($t$ represents iteration times) in…
The solution of linear systems of equations is a very frequent operation and thus important in many fields. The complexity using classical methods increases linearly with the size of equations. The HHL algorithm proposed by Harrow et al.…