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We study online learning in \emph{constrained MDPs} (CMDPs), focusing on the goal of attaining sublinear strong regret and strong cumulative constraint violation. Differently from their standard (weak) counterparts, these metrics do not…
The k-regret query aims to return a size-k subset S of a database D such that, for any query user that selects a data object from this size-k subset S rather than from database D, her regret ratio is minimized. The regret ratio here is…
We consider the problem of stochastic $K$-armed dueling bandit in the contextual setting, where at each round the learner is presented with a context set of $K$ items, each represented by a $d$-dimensional feature vector, and the goal of…
We consider robust combinatorial optimization problems with cost uncertainty where the decision maker can prepare K solutions beforehand and chooses the best of them once the true cost is revealed. Also known as min-max-min robustness (a…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Tiering is an essential technique for building large-scale information retrieval systems. While the selection of documents for high priority tiers critically impacts the efficiency of tiering, past work focuses on optimizing it with respect…
We introduce an extension of Dual Dynamic Programming (DDP) to solve convex nonlinear dynamic programming equations. We call Inexact DDP (IDDP) this extension which applies to situations where some or all primal and dual subproblems to be…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably…
We address the online linear optimization problem with bandit feedback. Our contribution is twofold. First, we provide an algorithm (based on exponential weights) with a regret of order $\sqrt{d n \log N}$ for any finite action set with $N$…
We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…
Most bandit algorithm designs are purely theoretical. Therefore, they have strong regret guarantees, but also are often too conservative in practice. In this work, we pioneer the idea of algorithm design by minimizing the empirical Bayes…
We study the single machine scheduling problem with the objective to minimize the total weight of late jobs. It is assumed that the processing times of jobs are not exactly known at the time when a complete schedule must be dispatched.…
We consider online allocation problems with concave revenue functions and resource constraints, which are central problems in revenue management and online advertising. In these settings, requests arrive sequentially during a finite horizon…
This paper describes an efficient reduction of the learning problem of ranking to binary classification. The reduction guarantees an average pairwise misranking regret of at most that of the binary classifier regret, improving a recent…
In this paper a class of combinatorial optimization problems is discussed. It is assumed that a feasible solution can be constructed in two stages. In the first stage the objective function costs are known while in the second stage they are…
In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a global objective function, which is the sum of local convex…
Random projection has been widely used in data classification. It maps high-dimensional data into a low-dimensional subspace in order to reduce the computational cost in solving the related optimization problem. While previous studies are…