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We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
We consider an assortment optimization problem under the multinomial logit choice model with general covering constraints. In this problem, the seller offers an assortment that should contain a minimum number of products from multiple…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
We address control synthesis of stochastic discrete-time linear multi-agent systems under jointly chance-constrained collaborative signal temporal logic specifications in a distribution-free manner using available disturbance samples, which…
This paper proves that a wide class of local search algorithms extend as is to the fully dynamic setting with an adaptive adversary, achieving an amortized $\tilde{O}(1)$ number of local-search steps per update. A breakthrough by Moser…
For input $x$, let $F(x)$ denote the set of outputs that are the "legal" answers for a computational problem $F$. Suppose $x$ and members of $F(x)$ are so large that there is not time to read them in their entirety. We propose a model of…
Consider the problem of finding a population or a probability distribution amongst many with the largest mean when these means are unknown but population samples can be simulated or otherwise generated. Typically, by selecting largest…
Given n elements with nonnegative integer weights w1,..., wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given…
Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…
The linear Support Vector Machine (SVM) is a classic classification technique in machine learning. Motivated by applications in modern high dimensional statistics, we consider penalized SVM problems involving the minimization of a…
We give efficient deterministic algorithms for converting randomized query algorithms into deterministic ones. We first give an algorithm that takes as input a randomized $q$-query algorithm $R$ with description length $N$ and a parameter…
Most classical scheduling formulations assume a fixed and known duration for each activity. In this paper, we weaken this assumption, requiring instead that each duration can be represented by an independent random variable with a known…
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible…
We present a novel algorithm that efficiently computes near-optimal deterministic policies for constrained reinforcement learning (CRL) problems. Our approach combines three key ideas: (1) value-demand augmentation, (2) action-space…
Constrained counting is important in domains ranging from artificial intelligence to software analysis. There are already a few approaches for counting models over various types of constraints. Recently, hashing-based approaches achieve…
In this study, we present a deep learning-optimization framework to tackle dynamic mixed-integer programs. Specifically, we develop a bidirectional Long Short Term Memory (LSTM) framework that can process information forward and backward in…
Interior point algorithms for solving linear programs have been studied extensively for a long time [e.g. Karmarkar 1984; Lee, Sidford FOCS'14; Cohen, Lee, Song STOC'19]. For linear programs of the form $\min_{Ax=b, x \ge 0} c^\top x$ with…
Declarative spatial reasoning denotes the ability to (declaratively) specify and solve real-world problems related to geometric and qualitative spatial representation and reasoning within standard knowledge representation and reasoning (KR)…
In contrast to the advances in characterizing the sample complexity for solving Markov decision processes (MDPs), the optimal statistical complexity for solving constrained MDPs (CMDPs) remains unknown. We resolve this question by providing…
We give a simple deterministic $O(\log K / \log\log K)$ approximation algorithm for the Min-Max Selecting Items problem, where $K$ is the number of scenarios. While our main goal is simplicity, this result also improves over the previous…